Daily Estimates of Global Radiation in the Brazilian Amazon from Simplified Models

Solar radiation is an element and a meteorological factor that is present in several processes, such as evapotranspiration, photosynthesis, and energy generation, among others. However, in some regions, there is a limitation in surface data measurements. In this study, 87 empirical models were evaluated to estimate global radiation (Hg) in the Brazilian Amazon biome; these models were divided into five groups according to the input variables, such as insolation (group I), air temperature (group II), relative humidity (group III), astronomical variables (group IV), and hybrid models (group V). The estimates were evaluated by their significance (<i>t</i>-test) and then according to the statistical metrics of the models’ performance (R², MBE, RMSE, and d). The group V model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced open="[" close="]" separators="|"><mrow><mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">g</mi></mrow><mo>/</mo><mrow><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mi mathvariant="normal">a</mi><mo>+</mo><mi mathvariant="normal">b</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mo>∆</mo><mi mathvariant="normal">T</mi><mo>+</mo><mi mathvariant="normal">c</mi></mrow></mrow><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi mathvariant="normal">S</mi></mrow><mo>/</mo><mrow><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mi mathvariant="normal">d</mi></mrow></msup></mrow></mfenced></mrow></semantics></math></inline-formula> presented the best statistical performance in all the evaluated indicators, followed by the group I model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced open="[" close="]" separators="|"><mrow><mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">g</mi></mrow><mo>/</mo><mrow><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mi mathvariant="normal">a</mi><mo>+</mo><mi mathvariant="normal">b</mi></mrow></mrow><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi mathvariant="normal">S</mi></mrow><mo>/</mo><mrow><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msup></mrow></mfenced></mrow></semantics></math></inline-formula>, and then the group II model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced open="[" close="]" separators="|"><mrow><mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">g</mi></mrow><mo>/</mo><mrow><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mi mathvariant="normal">a</mi><mo>+</mo><mi mathvariant="normal">b</mi><mo>∆</mo><mi mathvariant="normal">T</mi><mo>+</mo><mi mathvariant="normal">c</mi><msup><mrow><mo>∆</mo><mi mathvariant="normal">T</mi></mrow><mrow><mn>0.25</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">d</mi></mrow></mrow><msup><mrow><mo>∆</mo><mi mathvariant="normal">T</mi></mrow><mrow><mn>0.5</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">e</mi><mfenced separators="|"><mrow><mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi></mrow><mo>/</mo><mrow><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>. The group III models presented a low statistical performance, and the group IV models were not significant (NS) in all the evaluated meteorological stations. In general, it was found that the simplified or hybrid models based on insolation and air temperature were efficient in estimating Hg in the Brazilian Amazon biome.