The Second Derivative of the NDVI Time Series as an Estimator of Fresh Biomass: A Case Study of Eight Forage Associations Monitored via UAS
A novel and simple method was proposed to estimate the fresh biomass of several forage associations based on the joint use of the FAO66 guidelines regarding water productivity together with a temporal series of UAS imagery. The validation of the approach was performed after a field campaign to determine the direct measurements of the biomass that were coincident with those of the flights. The novelty of our proposal lies in (1) the use of the second derivative to determine the period in which the biomass is produced and (2) the replacement of the crop transpiration coefficient with the NDVI summation as a synoptic value of the crop and its status. The calculation is totally independent of any AquaCrop software: only the second derivative and summation of the NDVI series are needed. The detailed scale of the UAS imagery, together with the comprehensive dataset of field measurements, could help to validate the approach in a robust manner. Ultimately, since the majority of the parameterizations used in biomass estimations are only available for single crops, this research enabled the study and comparison of the biomass estimation among eight intercropping forage mixtures, including cereals (rye, triticale, oats, and barley) and legumes (vetch and pea).
(180 kg/ha) was chosen based on the literature. However, this value could be adapted to the specific characteristics of the forage associations. As a given example, taking into account that the NDVI maximum is 1, the expected maximum daily productivity would be 180 kg/ha. Furthermore, considering that the number of days ranged between 34 and 50 (depending on the association and the scale), the possible maximum fresh biomass production ranged from 6300 to 9000 kg/ha, which are considered feasible values of forage yield in a semiarid rangeland ecosystem such as the dehesa [62,63]. The actual results for the forage associations ranged from 4200 to 7400 kg/ha (Table 5) and were in line with the observed values and the different behavior observed with respect to the vetch-based and pea-based associations. The accuracy of these estimations in terms of the RMSD (excluding the failed date at the end of May) ranged from 700 to 2000 kg/ha, and the MAB ranged from 600 to 1900 kg/ha (all the values were positive), which represented error percentages ranging from 10 to 30% (Table 6 and Table 7). Although rather high, these numbers are in accordance with other crop biomass/yield estimations that used remote sensing and more complex approaches or models. Ajith et al. (2017)  used an integrated NDVI for rice and found error percentages ranging from 11 to 21%. Benedetti and Rossini (1993)  found an error from 10 to 19% using cumulative NDVI profiles in a regression model for wheat, and in a similar approach, Doraiswamy and Cook (1995)  found much higher and variable errors at the county/regional levels in two regions of the USA. Using the simple algorithm for the yield estimates (SAFY) model for maize with high spatial and temporal resolution remote sensing data, Battude et al. (2016)  found a relative error for dry biomass of 14%. Using the same model, Claverie et al. (2012)  found a relative error of 25% for maize and of 39% for sunflower. Ji et al. (2022)  used three machine learning algorithms for faba beans, obtaining yield estimation errors from 18 to 31%. Many other examples may be cited , although most of them present the error in terms of absolute errors of biomass (kg or tons per ha) for a given crop; so, they are hardly comparable to the forage associations studied here, which, in addition, are not frequently studied in the literature. In any case, the estimation may supply a rough estimate of forage biomass for livestock feeding that could otherwise have been difficult to draw from traditional surveys, as also stated by Benedetti and Rossini (1993) .
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