Modelagem da transferência radiativa em cultivo de cana-de-açúcar por meio da aproximação Two-Stream e do método das diferenças finitas

Abstract

The simulation processes of terrestrial ecosystems through biosphere-atmosphere models, which can be coupled to atmospheric numerical models, helps in the diagnosis and more accurate prognosis of weather and climate conditions. To make more realistic forecasts, calibrated models are needed for areas of interest that better reflect the interaction between biosphere and local atmosphere. Thus, the present study aims to implement, calibrate and evaluate a radiative transfer model based on the two-stream approximation from its resolution by finite differences applied in sugar cane cultivation. The radiative transfer model was implemented in an open modeling environment (Scilab) and solved by means of the Finite Differences Method: Euler method combined with Shooting Method and compared to data observed in the field. Its optimization (calibration) was performed using Reverse Modelling with the Luus-Jaakola method. For this, measurements of the components of the short-wave radiation balance above a sugarcane crop (cv RB 92579) were obtained in Rio Largo, state of Alagoas. The measurements were performed by a radiometer balance installed in a 6 m high micrometeorological tower from February 17 to 24, 2006. During this period, measurements were also made of the number of expanded leaves and the determinations of leaf length and width, used to estimate leaf area index (LAI). As the proposed model requires data of global solar irradiation incident on the top of the canopy, discriminated in its direct and diffuse components, two empirical models (polynomial of 3º and logistic) were previously tested, which relate the atmosphere transmittance and the fraction of diffuse to global radiation. In the adjustment of these empirical models, measured global and diffuse solar radiation between 1997 and 1999 were used. In the tests of the models, the accuracy and precision of the simulations expressed by the statistical coefficients were evaluated, respectively, coefficient of determination (r²), Willmott's concordance coefficient (d) and percentage root mean square error (RMSE). The polynomial of 3º model had higher precision (r² = 0.932) and accuracy (d = 0.965 and RMSE = 24%) in relation to logistic (r² = 0.895, d = 0.952 and RMSE = 28%) for the estimate of 𝑆􀬴 ↓. The parameters used for the proposed two-stream model were optimized in relation to reflected solar radiation (𝑆↑) at the top of the canopy and presented consistent results related to those reported in the literature (𝜒 = -0.3880, 𝛼􀯩􀯜􀯦 = 0.2468, 𝜏􀯩􀯜􀯦 = 0.0652, 𝜌􀯩􀯜􀯦 = 0.1759, 𝛼􀯜􀯩 = 0.4816, 𝜏􀯜􀯩 = 0.3436, 𝜌􀯜􀯩 = 0.6500). The simulations for 𝑆↑ at the top of the canopy showed high accuracy (d > 0.99 and RMSE < 3.6%) and precision (r² > 0.99). Despite this, the model underestimated 𝑆↑ at the beginning of the day, with the zenith angle less than 60°, around 7 o'clock in the morning. This observation corroborates the analysis made for albedo results. Although albedo precision and accuracy were observed within the accepted model standards (r² > 0.73, d > 0.89 and RMSE < 6.5%).