# Modelling Two Sugarcane Agro-Industrial Yields Using Sentinel/Landsat Time-Series Data and Their Spatial Validation at Different Scales in Costa Rica

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}, a clear improvement from 12.9 t·ha

^{−1}, which is the average obtained in previous works, whereas in SC, it displayed values below 4.0 kg·t

^{−1}. Finally, in SCY, the best validation result was obtained at the plot scale (RMSE of 7.7 t·ha

^{−1}), but this outcome was not verified in the case of SC validation because the RMSE was above 4.0 kg·t

^{−1}. In conclusion, our operational models try to represent a step forward in using RS techniques to improve sugarcane management at the farm and plot scales in Costa Rica.

## 1. Introduction

^{2}) and meteorological data in Brazil. In contrast, Mutanga et al. [19] used the same images to forecast yield at a regional scale in Zimbabwe. In Kenya, Mulianga et al. [20] showed the difficulty in forecasting the yield on an annual basis using low-resolution satellite images (MODIS) and precipitation data, whereas, in India, Dubey et al. [21] explored an RS-based approach for predicting yield using multiple linear regression, at the district scale, with the Vegetation Condition Index (VCI) and MODIS images, concluding that the relation between VCI and yield was poor in some districts. Another example of the combination of different satellite data, but with more spatial resolution, is Morel et al. [22] in Reunion Islands, where they used an NDVI time series derived from SPOT-4 and SPOT-5 in some farm fields to predict sugarcane yield, where a linear empirical model produced the best results. In Australia, Rahman and Robson [23] combined Landsat and Sentinel images using the same technique to estimate yield at the block level, and in Ethiopia, Abebe et al. [24] merged Landsat and Sentinel images (and different VIs) to estimate yield using a support vector regression, a multilayer perception neuronal network, and a multiple linear regression. Finally, dos Santos Luciano et al. [25] calibrated other predictors to forecast sugarcane yield but only using Landsat satellite images (and different VIs) and agronomic and meteorological data with Random Forest regression.

^{−1}[4]. Conversely, one issue or limitation is that most studies have been undertaken at a research level with less operational sugarcane yield-prediction models [4,13]. This situation may be worse in the case of Costa Rica because, in the literature review, an incipient development was observed in models for the estimation of sugarcane yields, including geospatial information [28,31].

^{−1}) and the sugar content prediction (kg·t

^{−1}), which are important for the sugarcane agro-industry. Indeed, from an economic point of view, the producers are paid based on these indicators. Nevertheless, two exceptions have been observed: Bégué et al. [35] obtained a better relationship between the sugarcane yield and the NDVI acquired before the maturation stage, whereas for sugar content and the NDVI the link was during the maturation stage. Moreover, Shendryk et al. [36] identified that the sugarcane yield and the sugar content can be estimated by integrating satellite variables and climatic data four months before harvest.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Sugarcane Crop Cycle in Costa Rica

#### 2.3. Available Data

#### 2.3.1. Yield and Climatic Data

^{−1}) is the sum of the tons of stalks harvested on a specific farm divided by its area in hectares, whereas sugar content (kg·t

^{−1}) is the mean of kilograms of sugar that can be obtained from one ton of stalks. The traditional harvesting process is used, which is manual, very labour-intensive, and time-consuming, while the yields are calculated following industrial processes. To validate the best-adjusted estimation models, an additional season was added, corresponding to 2021–2022, from the same source. In this last harvest season, the data were available at two scales: the farm scale and the plot scale (Figure 4). The data at the plot scale allowed validation with an improved spatial resolution, which is very uncommon in sugarcane research. According to production data, during the harvest cycles from 2017–2018 to 2020–2021, this cooperative had a mean sugarcane yield of 88.6 t·ha

^{−1}, while the mean sugar content was 119.3 kg·t

^{−1}during the same period. Based on empirical knowledge from the cooperative, the estimated RSME of sugarcane yield for the 2021–2022 harvest cycle was 12.9 t·ha

^{−1}.

#### 2.3.2. Satellite Images and Vegetation Indexes

#### 2.4. Multivariate Statistical Analysis and Spatio-Temporal Validation

^{2}) and the root mean square error (RMSE).

## 3. Results

#### 3.1. Harmonization of Vegetation Indexes and Temporal Phenological Signatures

^{2}parameter was almost greater than 0.9. In the four examples shown in Figure 5, the RMSE was also small for each VI, which validated the combined use of both sensors [63].

#### 3.2. Sugarcane Yield Models

#### 3.2.1. Modelling Sugarcane Yield at the Farm Scale

^{2}and RMSE results of the MLR models of sugarcane yield according to the first approach, following the additive temporal criterion for individual VIs (not combined), historical yield indicators, and growing cycle start. This table displays the results for every model per VI (each of them individually, as indicated in the rows) and per month (from May to January, presented in the columns), but without describing the specific significant independent variables. The best-selected model for sugarcane yield under this first approach is shown in Equation (1).

^{2}presented a growing trend from September until the maximum in December–January (0.68 with SR, Table 3). The SR and RI indices alternated as the most appropriate to estimate sugarcane yield between September to January, whereas no VI was significant in May, June, and July due to the high heterogeneity in the initial phenological stages of the plantation, as shown in Figure 6. On the other hand, RMSE appeared with a decreasing trend from September until the minimum in December–January (8.1 t·ha

^{−1}with SR). Therefore, after the additive temporal criterion was applied, the best results were obtained, including the SR indices from September, December, and January, as shown in Equation (1), and the rest of the months were not significant. This equation describes the regression model that presented the best results before using the other approaches for the estimation of sugarcane yield (ŷ

_{SCY}), obtaining a model that explained 68% of the variance (R

^{2}of 0.68), with an RMSE of 8.1 t·ha

^{−1}(Figure 7a).

_{SCY}is the historical average of sugarcane yield (t·ha

^{−1}) on each farm; G

_{CS}indicates the growing cycle start by year; M

_{SCY}indicates the maximum historical sugarcane yield obtained in the farm (from 2015 to 2021); and SR

_{Sep}, SR

_{Dec}, and SR

_{Jan}are the SR indices for September, December, and January, respectively.

_{SCY}), including the average sugarcane yield, the growing cycle start, and the maximum sugarcane yield as significant factors, replaced the SR

_{Sep}and SR

_{Jan}by RI

_{Sep}and DVI

_{Jan}, respectively. This approach reported an R

^{2}of 0.69 and an RMSE of 8.1 t·ha

^{−1}(Figure 7b) and, consequently, very similar to Model (1).

_{SCY}is the historical average of sugarcane yield (t·ha

^{−1}) on each farm (from 2015 to 2021); G

_{CS}indicates the growing cycle start by year; M

_{SCY}indicates the maximum historical sugarcane yield obtained on the farm (from 2015 to 2021); and RI

_{Sep}, SR

_{Dec}, and DVI

_{Jan}are the RI for September, the SR for December, and the DVI for January, respectively.

_{SCY}), considering the average sugarcane yield, the growing cycle start, and the maximum sugarcane yield as significant factors, included the RI, the SR, and the precipitation of December. This combination reported an R

^{2}of 0.70 and an RMSE of 8.0 t·ha

^{−1}(Figure 7c) and was consequently slightly better than models 1 and 2.

_{SCY}is the historical average of sugarcane yield (t·ha

^{−1}) on each farm (from 2015 to 2021); G

_{CS}indicates the growing cycle start by year; M

_{SCY}indicates the maximum historical sugarcane yield obtained on the farm (from 2015 to 2021); RI

_{Sep}, SR

_{Dec}, and SR

_{Jan}are the RI for September, December, and January, respectively; and P

_{Dec}is the precipitation in December.

_{SCY}) and its maximum historical yield (M

_{SCY}) were significant explanatory factors because the historical trend of the farms reflected the expected potential sugarcane yield (each farm has a maximum threshold that is related to its historical trend). At the same time, the growing cycle start (G

_{CS}) affected the development of the cultivation and the time that the plantation was maintained in the field before being harvested. According to Model (1), SR indexes presented an additive contribution when they were incorporated in September, December, and January. The second model introduces the RI

_{Sep}with a negative weight already being expected, given its formula (Red/NIR) and the DVI

_{Jan}. Finally, if the third model was considered, the influence of the December precipitation was significant.

#### 3.2.2. Spatial Validation of Sugarcane Yield at Farm and Plot Scales

^{2}values (0.66, 0.68, and 0.67, respectively) but with a better RMSE in the first model Equation (1). These figures, compared with Figure 7a–c, showed that the R

^{2}was slightly lower and the RMSE was higher, mainly in the second and third models (Figure 8b,c). Therefore, according to the validation process, Equation (1) was considered the best model for sugarcane yield at the farm scale because it had a similar R

^{2}but a better RSME than Equations (2) and (3). The main advantage of using this model compared to Equation (3), the best model before validating, is that Equation (1) is “simpler” because it just involves one VI (SR) and no climatic data are needed, which can sometimes be difficult to obtain at the local scale.

^{2}of 0.71 and an RMSE of 7.7 t·ha

^{−1}for Model (1), 0.73 and 7.9 t·ha

^{−1}for Model (2), and 0.71 and 8.6 t·ha

^{−1}for Model (3) (Figure 9a–c, respectively). Therefore, a slightly better validation was obtained at the plot scale compared to the farm scale due to the lower spatial variability that existed in the smallest units, the plots, unlike the farms, where the variability was greater. The same was true in the farm scale validation, where Equation (1) was the best model.

^{−1}), and the southwest, with lower values (about 50 t·ha

^{−1}).

#### 3.3. Sugar Content Models

#### 3.3.1. Modelling Sugar Content at Farm Scale

^{2}and RMSE results of the MLR models of sugar content according to the first approach, following the additive temporal criterion for individual VIs (not combined), historical yield indicators, and growing cycle start. This table shows the results for every model per VI (each of them individually, indicated in the rows) and per month (from May to January, shown in the columns) but without describing the specific significant independent variables. This information is shown in Equation (4), the best-selected model for sugar content under this first approach.

^{2}presented a growing trend from September until the maximum in January (0.49 with EVI, Table 4). The EVI and SR indices were the most appropriate to estimate sugar content between September to January, whereas in May, they were less explicative due to the high heterogeneity in the initial phenological stages of plantation (Figure 6); in June, July, and August, almost all the VIs were not significant. On the other hand, RMSE appeared with a slightly decreasing trend from September until the minimum in January (5.6 kg·t

^{−1}with SR). Therefore, after the additive temporal criterion was applied, the best results were obtained, including EVI indices from August, September, November, and January, as shown in Equation (4), where the rest of the months were not significant. This equation describes the best regression model before applying the other approaches, being a model that explained 49% of the variance (R

^{2}of 0.49) with an RMSE of 5.8 kg·t

^{−1}(Figure 11a).

_{SC}is the historical average of sugar content (kg·t

^{−1}) on each farm, and EVI

_{Aug}, EVI

_{Sep}, EVI

_{Nov}, and EVI

_{Jan}are the EVI for August, September, November, and January, respectively.

_{SC}), including the average sugar content and the combination of SR and GNDVI, reported an R

^{2}of 0.59 and an RMSE of 5.0 kg·t

^{−1}(Figure 11b) and was consequently a bit better than Model (4).

_{SC}is the historical average of sugar content (kg·t

^{−1}) on each farm (from 2015 to 2021) and SR

_{Aug}, GNDVI

_{Sep}, and GNDVI

_{Nov}are the SR for August, the GNDVI for September, and the SR for November, respectively.

_{SC}), including the average of sugar content with the joint of RVI and precipitation, reported an R

^{2}of 0.77 and an RMSE of 3.9 kg·t

^{−1}(Figure 11c) and was consequently the best model compared with Equations (4) and (5).

_{SC}is the historical average of sugar content (kg·t

^{−1}) on each farm (from 2015 to 2021), RVI

_{Nov}and RVI

_{Jan}are the RVI for November and January, and P

_{May}and P

_{Dec}are the precipitation of May and December.

_{SC}), including the historical average sugar content with the combination of SR and GNDVI and precipitation, reported an R

^{2}of 0.77 and an RMSE of 3.8 kg·t

^{−1}(Figure 11d) and was consequently a better model compared with models (4) and (5), but very similar to Model (6).

_{SC}is the historical average of sugar content (kg·t

^{−1}) on each farm (from 2015 to 2021); GNDVI

_{Sep}and SR

_{Jan}are the GNDVI VI for September, SR is the VI for January, and P

_{May}and P

_{Dec}are the precipitation of May and December.

_{SCY}) was an essential explanatory factor in estimating sugar content because it reflected the expected potential content, as it happened with the models to estimate sugarcane yield. According to Model (4), EVI indices presented an additive contribution when they were incorporated in different months, i.e., August, September, November, and January, whereas the fifth model introduced the combination of SR

_{Aug}, GNDVI

_{Sep,}and GNDVI

_{Nov}. The sixth model considered RVI

_{Nov}and RVI

_{Jan}and the precipitation of May and December, while the last model involved the influence of GNDVI

_{Sep}and SR

_{Jan}and the precipitation of May and December as significant factors.

#### 3.3.2. Spatial Validation of Sugar Content at Farm and Plot Scales

^{2}(0.59, 0.58, 0.56, and 0.57, respectively) but a better RMSE in the sixth model Equation (6). These figures, compared with Figure 11a–d, showed that the R

^{2}was better in Model (4), similar to Model (5), and lower in Models (6) and (7). The RMSE was lower in the fourth and sixth models but higher in the fifth and seventh. Therefore, Equation (6) was considered the best model for sugar content because, although it had a similar R

^{2}, the RMSE was clearly better. The main advantage of using this model compared with the others is that it uses only one VI (RVI) combined with precipitation.

^{2}of 0.45 and an RMSE of 6.8 kg·t

^{−1}from Equation (4), 0.43 and 11.3 kg·t

^{−1}from Equation (5), 0.46 and 4.7 kg·t

^{−1}from Equation (6), and 0.49 and 4.9 kg·t

^{−1}from Equation (7) (Figure 13a–d). A clearly worse sugar content validation was obtained at the plot scale compared with the farm scale, mainly in Models (4) and (5). Like the validation obtained at the farm scale, Equation (6) followed being the best model.

## 4. Discussion

^{2}and RMSE results, whereas the spatial validation presented a few smaller R

^{2}values in all the models, demonstrating that the best RMSE value is in Model (1). The spatial validation at the plot scale showed similar R

^{2}results for all the models but higher than those obtained at the farm scale, whereas the best RMSE followed being in Model (1).

^{2}values around 0.7 and RMSEs about 8.0 t·ha

^{−1}. However, the first model was shown to be the most constant during the modelling and validating steps, and consequently, including only the SR in different months (September, December, and January) makes it possible to obtain a robust estimation.

^{2}of 0.64 and an RMSE of 10.4 t·ha

^{−1}. Also, according to the review by Som-Ard et al. [4], it is the most common yield-estimation method, achieving an RMSE of 12.9 t·ha

^{−1}on average. In our work, and as one of the main objectives, the RMSE values of the models were improved, with values around 8.0 t·ha

^{−1}. Two possible reasons for this improvement could be the consideration of the local peculiarities of sugarcane’s temporal phenological signature in Costa Rica through VIs and the inclusion of explicative factors that comprise historic crop management extracted from the Cooperative data.

^{2}and RMSE results than in sugarcane yield, and the models including precipitation Equations (6) and (7) were better, whereas the spatial validation presented similar R

^{2}values in all the models, although the best RMSE was obtained in Model 6. The spatial validation at the plot scale showed a few lower R

^{2}and RMSE indicators compared with the validation at the farm scale. The best R

^{2}values were obtained in Models 6 and 7, and the best RMSE values were obtained in Model 6. Therefore, our results showed that the model estimation of sugar content was good enough at the farm scale, combining VIs and precipitation data, with an RMSE below 5.0 kg·t

^{−1}in the sixth and seventh models but worse R

^{2}and the RMSE values at the plot scale. This outcome rules out this work’s hypothesis that the validation at the plot scale would give better results than at the farm scale because, at the former scale, the spatial generalisation is lower as a result of calculating an average from fewer pixels. One possible explanation for this issue could be the harvest calendar. Those plots harvested at the beginning of the season have less sugar content concentration than those harvested at the end of the season. This fact could be an important source of error at this detailed scale, which is a concern to analyse in future work.

^{2}above 0.6. According to some authors, an alternative technique to MLR for predicting sugarcane yields can be machine learning (ML) approaches. Concretely, they asserted that Random Forest (RF), which is a non-parametric method, is more accurate to estimate yields when sample plots and variation are relatively large. For instance, Canata et al. [34] used filtered and interpolated yield data generated by harvesters at the field level for two years to conclude that RF performed better than MLR in predicting sugarcane yield. Additionally, in opposition to our outputs, they found better results when using the spectral bands directly rather than involving VIs. Dos Santos Luciano et al. [25] also applied an RF algorithm to forecast sugarcane yield and obtained an RMSE a little worse than ours (9.4 t·ha

^{−1}versus 8.0 t·ha

^{−1}).

^{−1}. Therefore, in spite of the benefits and advances of ML reported by other authors, more research is required because the differences in accuracy between ML and linear regression were not always of practical significance, which stresses the importance of proper model calibration and selection [64].

## 5. Conclusions

^{−1}, a clear improvement from 12.9 t·ha

^{−1}on average obtained in previous works, where sugar content displayed values below 4.0 kg·t

^{−1}.

^{−1}), as hypothesized, given the lower spatial generalisation, because the average was calculated from fewer pixels. Nevertheless, this outcome was not verified in the case of sugar content validation because the RMSE was around 5.0 kg·t

^{−1}.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Angulo, Á.; Rodríguez, M.; Chaves, M. Guía Técnica Cultivo Caña De Azúcar Región: Guanacaste. Available online: https://servicios.laica.co.cr/laica-cv-biblioteca/index.php/Library/download/jieyzwRDmVvUeWJGLRfYLzXbibjfLZNW (accessed on 18 April 2023).
- INEC (Instituto Nacional de Estadística y Censos). Encuesta Nacional Agropecuaria 2021 Resultados Generales de La Actividad Agrícola y Forestal. Available online: https://inec.cr/estadisticas-fuentes/encuestas/encuesta-nacional-agropecuaria?page=3 (accessed on 18 April 2023).
- Chaves, M.; Bermúdez, L. Agroindustria Azucarera Costarricense: Un Modelo Organizacional y Productivo Efectivo Con 75 Años de Vigencia. Available online: https://servicios.laica.co.cr/laica-cv-biblioteca/index.php/Library/download/DSCmSdyqoIJhQAUmeqVMAwOPjrySXJdh (accessed on 1 September 2021).
- Som-Ard, J.; Atzberger, C.; Izquierdo-Verdiguier, E.; Vuolo, F.; Immitzer, M. Remote Sensing Applications in Sugarcane Cultivation: A Review. Remote Sens.
**2021**, 13, 4040. [Google Scholar] [CrossRef] - Allison, J.C.S.; Pammenter, N.W.; Haslam, R.J. Why Does Sugarcane (Saccharum Sp. Hybrid) Grow Slowly? S. Afr. J. Bot.
**2007**, 73, 546–551. [Google Scholar] [CrossRef] - Cock, J.H. Sugarcane Growth and Development. Int. Sugar J.
**2003**, 105, 540–552. [Google Scholar] - Inman-Bamber, N.G. Temperature and Seasonal Effects on Canopy Development and Light Interception of Sugarcane. Field Crop. Res.
**1994**, 36, 41–51. [Google Scholar] [CrossRef] - Saez, J.V. Dinámica de Acumulación de Sacarosa en Tallos de Caña de Azúcar (Saccharum spp.) Modulada por Cambios en la Relación Fuente-Destino. Ph.D. Thesis, Facultad de Ciencias Agropecuarias, Universidad Nacional de Cordoba, 2017. Available online: http://hdl.handle.net/11086/6836 (accessed on 3 December 2020).
- Molijn, R.A.; Iannini, L.; Rocha, J.V.; Hanssen, R.F. Sugarcane Productivity Mapping through C-Band and L-Band SAR and Optical Satellite Imagery. Remote Sens.
**2019**, 11, 1109. [Google Scholar] [CrossRef] - Pinter, P.J.; Hatfield, J.L.; Schepers, J.S.; Barnes, E.M.; Moran, M.S.; Daughtry, C.S.; Upchurch, D.R. Remote Sensing for Site-Specific Crop Management. Photogramm. Eng. Remote Sens.
**2003**, 69, 647–664. [Google Scholar] [CrossRef] - Liaghat, S.; Balasundram, S.K. A Review: The Role of Remote Sensing in Precision Agriculture. Am. J. Agric. Biol. Sci.
**2010**, 5, 50–55. [Google Scholar] [CrossRef] - Segarra, J.; Buchaillot, M.L.; Araus, J.L.; Kefauver, S.C. Remote Sensing for Precision Agriculture: Sentinel-2 Improved Features and Applications. Agronomy
**2020**, 10, 641. [Google Scholar] [CrossRef] - Abdel-Rahman, E.M.; Ahmed, F.B. The Application of Remote Sensing Techniques to Sugarcane (Saccharum spp. Hybrid) Production: A Review of the Literature. Int. J. Remote Sens.
**2008**, 29, 3753–3767. [Google Scholar] [CrossRef] - Rudorff, B.F.T.; Batista, G.T. Yield Estimation of Sugarcane Based on Agrometeorological-Spectral Models. Remote Sens. Environ.
**1990**, 33, 183–192. [Google Scholar] [CrossRef] - Bannari, A.; Morin, D.; Bonn, F.; Huete, A.R. A Review of Vegetation Indices. Remote Sens. Rev.
**1995**, 13, 95–120. [Google Scholar] [CrossRef] - Rao, P.V.K.; Rao, V.V.; Venkataratnam, L. Remote Sensing: A Technology for Assessment of Sugarcane Crop Acreage and Yield. Sugar Technol.
**2002**, 4, 97–101. [Google Scholar] [CrossRef] - Almeida, T.I.R.; De Souza Filho, C.R.; Rossetto, R. ASTER and Landsat ETM+ Images Applied to Sugarcane Yield Forecast. Int. J. Remote Sens.
**2006**, 27, 4057–4069. [Google Scholar] [CrossRef] - Fernandes, J.L.; Rocha, J.V.; Lamparelli, R.A.C. Sugarcane Yield Estimates Using Time Series Analysis of Spot Vegetation Images. Sci. Agric.
**2011**, 68, 139–146. [Google Scholar] [CrossRef] - Mutanga, S.; van Schoor, C.; Olorunju, P.L.; Gonah, T.; Ramoelo, A. Determining the Best Optimum Time for Predicting Sugarcane Yield Using Hyper-Temporal Satellite Imagery. Adv. Remote Sens.
**2013**, 2, 269–275. [Google Scholar] [CrossRef] - Mulianga, B.; Bégué, A.; Simoes, M.; Todoroff, P. Forecasting Regional Sugarcane Yield Based on Time Integral and Spatial Aggregation of MODIS NDVI. Remote Sens.
**2013**, 5, 2184–2199. [Google Scholar] [CrossRef] - Dubey, S.K.; Gavli, A.S.; Yadav, S.K.; Sehgal, S.; Ray, S.S. Remote Sensing-Based Yield Forecasting for Sugarcane (Saccharum officinarum L.) Crop in India. J. Indian Soc. Remote Sens.
**2018**, 46, 1823–1833. [Google Scholar] [CrossRef] - Morel, J.; Todoroff, P.; Bégué, A.; Bury, A.; Martiné, J.F.; Petit, M. Toward a Satellite-Based System of Sugarcane Yield Estimation and Forecasting in Smallholder Farming Conditions: A Case Study on Reunion Island. Remote Sens.
**2014**, 6, 6620–6635. [Google Scholar] [CrossRef] - Rahman, M.M.; Robson, A. Integrating Landsat-8 and Sentinel-2 Time Series Data for Yield Prediction of Sugarcane Crops at the Block Level. Remote Sens.
**2020**, 12, 1313. [Google Scholar] [CrossRef] - Abebe, G.; Tadesse, T.; Gessesse, B. Combined Use of Landsat 8 and Sentinel 2A Imagery for Improved Sugarcane Yield Estimation in Wonji-Shoa, Ethiopia. J. Indian Soc. Remote Sens.
**2022**, 50, 143–157. [Google Scholar] [CrossRef] - dos Santos Luciano, A.C.; Picoli, M.C.A.; Duft, D.G.; Rocha, J.V.; Leal, M.R.L.V.; le Maire, G. Empirical Model for Forecasting Sugarcane Yield on a Local Scale in Brazil Using Landsat Imagery and Random Forest Algorithm. Comput. Electron. Agric.
**2021**, 184, 106063. [Google Scholar] [CrossRef] - Som-ard, J.; Hossain, M.D.; Ninsawat, S.; Veerachitt, V. Pre-Harvest Sugarcane Yield Estimation Using UAV-Based RGB Images and Ground Observation. Sugar Technol.
**2018**, 20, 645–657. [Google Scholar] [CrossRef] - Sumesh, K.C.; Ninsawat, S.; Som-ard, J. Integration of RGB-Based Vegetation Index, Crop Surface Model and Object-Based Image Analysis Approach for Sugarcane Yield Estimation Using Unmanned Aerial Vehicle. Comput. Electron. Agric.
**2021**, 180, 105903. [Google Scholar] [CrossRef] - Alemán-Montes, B.; Henríquez-Henríquez, C.; Ramírez-Rodríguez, T.; Largaespada-Zelaya, K. Estimación de Rendimiento En El Cultivo de Caña de Azúcar (Saccharum officinarum) a Partir de Fotogrametría Con Vehículos Aéreos No Tripulados (VANT). Agron. Costarric.
**2021**, 45, 67–80. [Google Scholar] [CrossRef] - Akbarian, S.; Xu, C.; Wang, W.; Ginns, S.; Lim, S. Sugarcane Yields Prediction at the Row Level Using a Novel Cross-Validation Approach to Multi-Year Multispectral Images. Comput. Electron. Agric.
**2022**, 198, 107024. [Google Scholar] [CrossRef] - Barbosa Júnior, M.R.; Moreira, B.R.d.A.; de Brito Filho, A.L.; Tedesco, D.; Shiratsuchi, L.S.; da Silva, R.P. UAVs to Monitor and Manage Sugarcane: Integrative Review. Agronomy
**2022**, 12, 661. [Google Scholar] [CrossRef] - Hidalgo, N. Análisis del Rendimiento del Cultivo de Caña de Azúcar Mediante Índices de Vegetación y Monitores de Rendimiento Durante el Periodo de Zafra 2021–2022 en la Empresa Central Azucarera Tempisque S.A. (CATSA) Guanacaste, Costa Rica. Licenciature’s Thesis, Escuela de Ingeniería Agrícola, Instituto Tecnológico de Costa Rica, 2022. Available online: https://repositoriotec.tec.ac.cr/handle/2238/13994 (accessed on 25 April 2023).
- Jeffries, G.R.; Griffin, T.S.; Fleisher, D.H.; Naumova, E.N.; Koch, M.; Wardlow, B.D. Mapping Sub-Field Maize Yields in Nebraska, USA by Combining Remote Sensing Imagery, Crop Simulation Models, and Machine Learning. Precis. Agric.
**2020**, 21, 678–694. [Google Scholar] [CrossRef] - Dimov, D.; Uhl, J.H.; Löw, F.; Seboka, G.N. Sugarcane Yield Estimation through Remote Sensing Time Series and Phenology Metrics. Smart Agric. Technol.
**2022**, 2, 100046. [Google Scholar] [CrossRef] - Canata, T.F.; Wei, M.C.F.; Maldaner, L.F.; Molin, J.P. Sugarcane Yield Mapping Using High-Resolution Imagery Data and Machine Learning Technique. Remote Sens.
**2021**, 13, 232. [Google Scholar] [CrossRef] - Bégué, A.; Lebourgeois, V.; Bappel, E.; Todoroff, P.; Pellegrino, A.; Baillarin, F.; Siegmund, B. Spatio-Temporal Variability of Sugarcane Fields and Recommendations for Yield Forecast Using NDVI. Int. J. Remote Sens.
**2010**, 31, 5391–5407. [Google Scholar] [CrossRef] - Shendryk, Y.; Davy, R.; Thorburn, P. Integrating Satellite Imagery and Environmental Data to Predict Field-Level Cane and Sugar Yields in Australia Using Machine Learning. Field Crop. Res.
**2021**, 260, 107984. [Google Scholar] [CrossRef] - LAICA Ley Orgánica de La Agricultura e Industria de La Caña de Azúcar N° 7818 Del 22 de Setiembre de 1998. Available online: http://www.pgrweb.go.cr/scij/Busqueda/Normativa/Normas/nrm_texto_completo.aspx?param2=NRTC&nValor1=1&nValor2=44897&strTipM=TC (accessed on 8 May 2023).
- Montenegro Ballestero, J.; Chaves Solera, M. Análisis de Ciclo de Vida Para La Producción Primaria de Caña de Azúcar En Seis Regiones de Costa Rica. Rev. Ciencias Ambient.
**2022**, 56, 96–119. [Google Scholar] [CrossRef] - Chaves, M.; Chavarría, E. Estimación Del Área Sembrada Con Caña de Azúcar En Costa Rica Según Región Productora. Periodo 1985–2020 (36 Zafras). Available online: https://laica.cr/wp-content/uploads/2022/05/revista-entre-caneros-no22.pdf (accessed on 8 May 2023).
- Mata, R.; Rosales, A.; Sandoval, D.; Vindas, E.; Alemán, B. Subórdenes de Suelos de Costa Rica [Mapa Digital]. Escala 1:200000. Available online: http://www.cia.ucr.ac.cr/es/mapa-de-suelos-de-costa-rica (accessed on 30 September 2022).
- Alfaro, E.J. Caracterización del “Veranillo” en dos Cuencas de la Vertiente Del Pacífico de Costa Rica, América Central. Rev. Biol. Trop.
**2014**, 62, 1–15. [Google Scholar] [CrossRef] - Vignola, R.; Poveda, K.; Watler, W.; Vargas, A.; Berrocal, Á. Cultivo de Caña de Azúcar En Costa Rica. Available online: https://www.mag.go.cr/bibliotecavirtual/F01-8327.pdf (accessed on 8 May 2023).
- Chaves, M. Suelos, Nutrición y Fertilización de la Caña de Azúcar en Costa Rica. Available online: https://servicios.laica.co.cr/laica-cv-biblioteca/index.php/Library/download/xznuAsbXHGPzjuDRWFDDwEOtAUrWraua (accessed on 8 May 2023).
- Ramburan, S.; Wettergreen, T.; Berry, S.D.; Shongwe, B. Effects of Variety, Environment and Management on Sugarcane Ratoon Yield Decline. Int. Sugar J.
**2012**, 85, 180–192. [Google Scholar] - Dlamini, N.E.; Zhou, M. Soils and Seasons Effect on Sugarcane Ratoon Yield. Field Crop. Res.
**2022**, 284, 108588. [Google Scholar] [CrossRef] - Panigrahy, S.; Sharma, S.A. Mapping of Crop Rotation Using Multidate Indian Remote Sensing Satellite Digital Data. ISPRS J. Photogramm. Remote Sens.
**1997**, 52, 85–91. [Google Scholar] [CrossRef] - Zhao, Y.; Della Justina, D.; Kazama, Y.; Rocha, J.V.; Graziano, P.S.; Lamparelli, R.A.C. Dynamics Modeling for Sugar Cane Sucrose Estimation Using Time Series Satellite Imagery. In Remote Sensing for Agriculture, Ecosystems, and Hydrology XVIII; Neale, C.M.U., Maltese, A., Eds.; SPIE: Bellingham, WA, USA, 2016; Volume 9998, p. 99980J. [Google Scholar]
- Chaves, M.; Picoli, M.; Sanches, I. Recent Applications of Landsat 8/OLI and Sentinel-2/MSI for Land Use and Land Cover Mapping: A Systematic Review. Remote Sens.
**2020**, 12, 3062. [Google Scholar] [CrossRef] - USGS (United States Geological Survey). Landsat 8-9 Collection 2 (C2) Level 2 Science Product (L2SP) Guide. Available online: https://www.usgs.gov/media/files/landsat-8-9-collection-2-level-2-science-product-guide (accessed on 28 September 2022).
- Mueller-Wilm, U.; Devignot, O.; Pessiot, L. Sen2Cor Configuration and User Manual. Available online: http://step.esa.int/thirdparties/sen2cor/2.3.0/[L2A-SUM] S2-PDGS-MPC-L2A-SUM [2.3.0].pdf (accessed on 30 June 2023).
- Jiménez-Jiménez, S.I.; Marcial-Pablo, M.d.J.; Ojeda-Bustamante, W.; Sifuentes-Ibarra, E.; Inzunza-Ibarra, M.A.; Sánchez-Cohen, I. VICAL: Global Calculator to Estimate Vegetation Indices for Agricultural Areas with Landsat and Sentinel-2 Data. Agronomy
**2022**, 12, 1518. [Google Scholar] [CrossRef] - Richardson, A.J.; Wiegand, C.L. Distinguishing Vegetation from Soil Background Information. Photogramm. Eng. Remote Sens.
**1977**, 43, 1541–1552. [Google Scholar] - Huete, A.; Didan, K.; Miura, T.; Rodriguez, E.P.; Gao, X.; Ferreira, L.G. Overview of the Radiometric and Biophysical Performance of the MODIS Vegetation Indices. Remote Sens. Environ.
**2002**, 83, 195–213. [Google Scholar] [CrossRef] - Gitelson, A.A.; Kaufman, Y.J.; Merzlyak, M.N. Use of a Green Channel in Remote Sensing of Global Vegetation from EOS- MODIS. Remote Sens. Environ.
**1996**, 58, 289–298. [Google Scholar] [CrossRef] - Rouse, J.W.; Hass, R.H.; Schell, J.A.; Deering, D.W. Monitoring Vegetation Systems in the Great Plains with ERTS. In Proceedings of the Third Earth Resources Technology Satellite (ERTS) Symposium, Washington, DC, USA, 10–14 December 1973; Volume 351, pp. 309–317. [Google Scholar]
- Escadafal, R.; Huete, A. Étude Des Propriétés Spectrales Des Sols Arides Appliquée à Lamélioration Des Indices de Vegetation Obtenus Par Télédection. CR Académie Sci. Paris
**1991**, 312, 1385–1391. [Google Scholar] - Pearson, R.L.; Miller, L.D. Remote Mapping of Standing Crop Biomass for Estimation of the Productivity of Shortgrass Prairie, Pawnee National Grasslands, Colorado. In Proceedings of the 8th International Symposium on Remote Sensing of the Environment, Ann Arbor, MI, USA, 2–6 October 1972. [Google Scholar]
- Huete, A. A Soil-Adjusted Vegetation Index (SAVI). Remote Sens. Environ.
**1988**, 25, 295–309. [Google Scholar] [CrossRef] - Jordan, C.F. Derivation of Leaf-Area Index from Quality of Light on the Forest Floor. Ecology
**1969**, 50, 663–666. [Google Scholar] [CrossRef] - Simões, M.d.S.; Rocha, J.V.; Lamparelli, R.A.C. Variáveis Espectrais e Indicadores de Desenvolvimento e Produtividade da Cana-de-Açúcar. Sci. Agric.
**2005**, 62, 199–207. [Google Scholar] [CrossRef] - Li, J.; Lu, X.; Cheng, K.; Liu, W. Package ‘StepReg’. Available online: https://cran.r-project.org/web/packages/StepReg/index.html (accessed on 15 October 2020).
- Max, A.; Wing, J.; Weston, S.; Williams, A.; Keefer, C.; Engelhardt, A.; Cooper, T.; Mayer, Z.; Ziem, A.; Scrucca, L.; et al. Package ‘Caret’ R. Available online: https://cran.r-project.org/web/packages/caret/index.html (accessed on 17 October 2020).
- Alemán-Montes, B.; Serra, P.; Zabala, A. Modelos Para La Estimación Del Rendimiento de La Caña de Azúcar En Costa Rica Con Datos de Campo e Índices de Vegetación. Rev. Teledetección
**2023**, 2023, 1–13. [Google Scholar] [CrossRef] - Meroni, M.; Waldner, F.; Seguini, L.; Kerdiles, H.; Rembold, F. Yield Forecasting with Machine Learning and Small Data: What Gains for Grains? Agric. For. Meteorol.
**2021**, 308–309, 108555. [Google Scholar] [CrossRef]

**Figure 1.**Localization of the study area. Costa Rica, a country in Central America (

**a**). The six sugarcane regions defined by LAICA (

**b**). Spatial distribution of sugarcane farms of CoopeVictoria R.L., located in Valle Central region (

**c**).

**Figure 2.**Accumulated precipitation and mean temperature by month on the five sugarcane harvest cycles used in this work. Precipitation, extracted from two meteorological stations (Argentina and DIECA), is represented by two continuous lines, and temperature is represented by two dash lines.

**Figure 3.**Theoretical calendar of sugarcane cycle for new planting by region in Costa Rica according to [42].

**Figure 5.**Vectorial points scatter plot of harmonization between Sentinel-2 (S2) and Landsat-8 (L8) for NDVI, SR, SAVI, and RI vegetation indexes.

**Figure 6.**Mean and standard deviation of sugarcane phenological evolution (using NDVI extracted from Sentinel-2 and Landsat-8 imagery) for the 2017–2018 to 2021–2022 harvest cycles on the farms of CoopeVictoria R.L.

**Figure 7.**Best multivariate linear regressions for sugarcane yield estimation at the farm scale, obtained with Equation (1) (

**a**), Equation (2) (

**b**), and Equation (3) (

**c**).

**Figure 8.**Validation of best multivariate linear regressions for sugarcane yield estimation at farm scale, obtained with Equation (1) (

**a**), Equation (2) (

**b**), and Equation (3) (

**c**).

**Figure 9.**Validation of the best multivariate linear regressions for sugarcane yield estimation at the plot scale, obtained with Equation (1) (

**a**), Equation (2) (

**b**), and Equation (3) (

**c**).

**Figure 10.**Spatial distribution of sugarcane yield estimated with Equation (1), with a pixel size of 10 m × 10 m; the plot boundaries are overlaid. All plots (

**a**). Celina Farm (

**b**). Grupo Agualote Farm (

**c**). The blue arrows show the selected farms.

**Figure 11.**Best multivariate linear regressions for sugar content estimation at the farm scale, obtained with Equation (4) (

**a**), Equation (5) (

**b**), Equation (6) (

**c**), and Equation (7) (

**d**).

**Figure 12.**Validation of the best multivariate linear regression for sugar content estimation at the farm scale, obtained with Equation (4) (

**a**), Equation (5) (

**b**), Equation (6) (

**c**), and Equation (7) (

**d**).

**Figure 13.**Validation of best multivariate linear regressions for sugar content estimation at the plot scale, obtained with Equation (4) (

**a**), Equation (5) (

**b**), Equation (6) (

**c**), and Equation (7) (

**d**).

**Figure 14.**Spatial distribution of sugar content estimated with Equation (6), with a pixel size of 10 m × 10 m; the plot boundaries are overlaid. All plots (

**a**). Celina Farm (

**b**). Grupo Agualote farm (

**c**). The blue arrows show the selected farms.

**Table 1.**Availability of Landsat-8 (L8) and Sentinel-2 (S2) images in the study area for the five harvest cycles, 2017–2018 to 2021–2022.

Month | Harvest Cycles | ||||
---|---|---|---|---|---|

2017–2018 | 2018–2019 | 2019–2020 | 2020–2021 | 2021–2022 | |

May | L8-2017-05-18 | S2-2018-05-11 | S2-2019-05-16 | L8-2020-05-26 | S2-2021-05-15 |

June | L8-017-06-19 | L8-2018-06-22 | S2-2019-06-30 | ND | S2-2021-06-19 |

July | S2-2017-07-15 | L8-2018-07-24 | L8-2019-07-27 | ND | L8-2021-07-16 |

August | L8-2017-08-22 | L8-2018-08-25 | S2-2019-08-24 | S2-2020-08-28 | L8-2021-08-17 |

September | L8-2017-09-07 | S2-2018-09-13 | S2-2019-09-08 | L8-2020-09-15 | S2-2021-10-02 * |

October | L8-2017-11-10 * | S2-2018-11-07 * | L8-2019-10-31 | S2-2020-10-22 | ND |

November | S2-2017-11-17 | L8-2018-11-13 | S2-2019-11-22 | S2-2020-11-26 | S2-2021-11-26 |

December | S2-2017-12-22 | S2-2018-12-27 | S2-2019-12-27 | S2-2020-12-21 | S2-2021-12-31 |

January | S2-2018-01-26 | S2-2019-01-31 | S2-2020-01-31 | S2-2021-01-30 | S2-2022-01-20 |

Vegetation Index | Equation | Source |
---|---|---|

DVI | $NIR-Red$ | [52] |

EVI | $2.5\times \frac{NIR-Red}{(NIR+{C}_{1}Red-{C}_{2}Blue+L)}$ ${C}_{1}=6,{C}_{2}=7.5,L=1$ | [53] |

GNDVI | $\frac{Green-Red}{Green+Red}$ | [54] |

NDVI | $\frac{NIR-Red}{NIR+Red}$ | [55] |

RI | $\frac{Red-Green}{Red+Green}$ | [56] |

RVI | $\frac{Red}{NIR}$ | [57] |

SAVI | $\frac{NIR-Red}{\left(NIR+Red+0.5\right)\times (1+0.5)}$ | [58] |

SR * | $\frac{NIR}{Red}$ | [59] |

**Table 3.**Results of multivariate linear regressions to estimate sugarcane yield (2017–2021, in t·ha

^{−1}) per VI (each of them individually, shown in the rows) and per month (from May to January, shown in the columns) after applying the additive temporal criterion and excluding those months and VIs without statistical significance, including historical yield indicators and growing cycle start.

Month | May | June | July | August | September | October | November | December | January | |
---|---|---|---|---|---|---|---|---|---|---|

DVI | R^{2} | * | * | * | * | 0.48 | 0.50 | * | * | 0.61 |

RMSE | 10.2 | 10.1 | 9.1 | |||||||

EVI | R^{2} | * | * | * | 0.48 | 0.49 | * | * | * | * |

RMSE | 10.7 | 10.1 | ||||||||

GNDVI | R^{2} | * | * | * | * | * | * | * | 0.56 | 0.56 |

RMSE | 9.2 | 9.2 | ||||||||

NDVI | R^{2} | * | * | * | * | * | 0.53 | 0.56 | 0.60 | 0.63 |

RMSE | 10.2 | 9.5 | 9.0 | 8.9 | ||||||

RI | R^{2} | * | * | * | 0.48 | 0.55 | 0.61 | 0.64 | 0.64 | 0.66 |

RMSE | 10.8 | 9.4 | 9.1 | 8.7 | 8.7 | 8.5 | ||||

RVI | R^{2} | * | * | * | * | 0.47 | 0.53 | 0.55 | 0.60 | 0.60 |

RMSE | 10.2 | 10.3 | 9.6 | 9.0 | 9.0 | |||||

SAVI | R^{2} | * | * | * | * | * | * | * | * | * |

RMSE | ||||||||||

SR | R^{2} | * | * | * | 0.47 | 0.53 | 0.56 | 0.57 | 0.65 | 0.68 |

RMSE | 10.8 | 9.9 | 9.6 | 9.2 | 8.4 | 8.1 |

^{2}and RMSE; darker colours indicate a better fit, while lighter colours suggest a less optimal fit.

**Table 4.**Results of multivariate linear regressions to estimate sugar content (2017–2021, in kg·t

^{−1}) per VI (each of them individually, shown in the rows) and per month (from May to January, shown in the columns) after the application of the additive temporal criterion and excluding those months and VIs without statistical significance, including historical yield indicators and growing cycle start.

Month | May | June | July | August | September | October | November | December | January | |
---|---|---|---|---|---|---|---|---|---|---|

DVI | R^{2} | 0.29 | * | * | * | 0.28 | 0.37 | 0.37 | * | * |

RMSE | 6.7 | 6.3 | 5.8 | 6.0 | ||||||

EVI | R^{2} | 0.29 | * | * | * | 0.39 | 0.39 | 0.38 | 0.48 | 0.49 |

RMSE | 6.7 | 5.9 | 5.8 | 6.0 | 5.7 | 5.8 | ||||

GNDVI | R^{2} | 0.26 | * | * | * | 0.33 | * | * | * | * |

RMSE | 6.9 | 6.1 | ||||||||

NDVI | R^{2} | 0.28 | * | * | * | 0.34 | 0.39 | * | * | * |

RMSE | 6.8 | 6.1 | 5.7 | |||||||

RI | R^{2} | 0.29 | * | * | * | 0.30 | 0.35 | 0.34 | 0.40 | 0.40 |

RMSE | 6.7 | 6.2 | 5.9 | 6.1 | 6.0 | 6.0 | ||||

RVI | R^{2} | 0.29 | * | * | 0.27 | 0.34 | 0.39 | 0.46 | 0.46 | 0.46 |

RMSE | 6.8 | 6.7 | 6.1 | 5.8 | 5.6 | 5.6 | 5.6 | |||

SAVI | R^{2} | 0.29 | * | * | * | 0.28 | 0.38 | * | * | * |

RMSE | 6.7 | 6.3 | 5.8 | |||||||

SR | R^{2} | 0.28 | * | * | * | 0.31 | 0.40 | 0.48 | 0.48 | 0.48 |

RMSE | 6.8 | 6.2 | 5.8 | 5.6 | 5.6 | 5.6 |

^{2}and RMSE; darker colours indicate a better fit, while lighter colours suggest a less optimal fit.

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**MDPI and ACS Style**

Alemán-Montes, B.; Zabala, A.; Henríquez, C.; Serra, P.
Modelling Two Sugarcane Agro-Industrial Yields Using Sentinel/Landsat Time-Series Data and Their Spatial Validation at Different Scales in Costa Rica. *Remote Sens.* **2023**, *15*, 5476.
https://doi.org/10.3390/rs15235476

**AMA Style**

Alemán-Montes B, Zabala A, Henríquez C, Serra P.
Modelling Two Sugarcane Agro-Industrial Yields Using Sentinel/Landsat Time-Series Data and Their Spatial Validation at Different Scales in Costa Rica. *Remote Sensing*. 2023; 15(23):5476.
https://doi.org/10.3390/rs15235476

**Chicago/Turabian Style**

Alemán-Montes, Bryan, Alaitz Zabala, Carlos Henríquez, and Pere Serra.
2023. "Modelling Two Sugarcane Agro-Industrial Yields Using Sentinel/Landsat Time-Series Data and Their Spatial Validation at Different Scales in Costa Rica" *Remote Sensing* 15, no. 23: 5476.
https://doi.org/10.3390/rs15235476