Improved Modeling of Gross Primary Production and Transpiration of Sugarcane Plantations with Time-Series Landsat and Sentinel-2 Images

: Sugarcane croplands account for ~70% of global sugar production and ~60% of global ethanol production. Monitoring and predicting gross primary production (GPP) and transpiration (T) in these fields is crucial to improve crop yield estimation and management. While moderate-spatial-resolution (MSR, hundreds of meters) satellite images have been employed in several models to estimate GPP and T, the potential of high-spatial-resolution (HSR, tens of meters) imagery has been considered in only a few publications, and it is underexplored in sugarcane fields. Our study evaluated the efficacy of MSR and HSR satellite images in predicting daily GPP and T for sugarcane plantations at two sites equipped with eddy flux towers: Louisiana, USA (subtropical climate) and Sao Paulo, Brazil (tropical climate). We employed the Vegetation Photosynthesis Model (VPM) and Vegetation Transpiration Model (VTM) with C4 photosynthesis pathway, integrating vegetation index data derived from satellite images and on-ground weather data, to calculate daily GPP and T. The seasonal dynamics of vegetation indices from both MSR images (MODIS sensor, 500 m) and HSR images (Landsat, 30 m; Sentinel-2, 10 m) tracked well with the GPP seasonality from the EC flux towers. The enhanced vegetation index (EVI) from the HSR images had a stronger correlation with the tower-based GPP. Our findings underscored the potential of HSR imagery for estimating GPP and T in smaller sugarcane plantations.


Introduction
Sugarcane (Saccharum spp.) croplands supply cane feedstock for biofuel (ethanol) and sugar production [1].Sugarcane represents nearly 70% of the sugar production worldwide and approximately 60% of the global bioethanol production [2][3][4].Brazil and the United States of America (USA) rank first and ninth among the global sugarcane-producing countries [5].Brazil produced an average of 538 million metric tons (mmt) of sugar from 1994 to 2019 [6], and through the Renovabio policy it aims to produce 50 billion liters of ethanol per year by 2030 by improving production and investment infrastructure [7].The USA produced an average of 29 mmt of sugar from 1994 to 2019 [6].
Sugarcane crop growth monitoring and assessment provide necessary information for crop management and sustainable production, as the changes in crop variety, field size and rotation, management, and climate may affect crop growth, water use efficiency, and yield prediction [8].Among the many metrics of crop growth, gross primary production (GPP), which is the amount of CO 2 fixed by vegetation photosynthesis, representing the largest carbon flux in the terrestrial ecosystem [9], is one useful metric, but it has received less attention in the crop production community.GPP has been used to calculate net primary production (NPP), aboveground biomass, and crop yield [10][11][12][13].GPP is used to monitor crop growing conditions and improve crop management practices and crop production estimates [13][14][15][16].GPP has previously been utilized to improve crop yield assessments, which are important for agricultural resiliency and food security [17][18][19].
There is no method for directly measuring GPP at the ecosystem and landscape scales [20,21].The eddy covariance (EC) method is widely applied to measure the net ecosystem exchange (NEE) between the atmosphere and the land surface [22], and the half-hourly NEE data are then partitioned into ecosystem respiration (ER) and GPP [23,24].Several algorithms have been used for the partitioning of the NEE into ER and GPP [25,26].The resultant GPP (hereafter GPP EC ) is utilized as the standard data to evaluate vegetation phenology, as well as GPP estimates derived from process-based models and data-driven models over multiple spatial and temporal resolutions [27][28][29] (p.200).However, because of the high cost and complexity associated with the operation of EC sites, to date, the carbon and water fluxes of sugarcane plantations have only been measured at a few sites worldwide [30][31][32][33][34][35].Time-series data of the carbon and water fluxes from these sites provide information on sugarcane crop phenology, GPP, and evapotranspiration.
Multiple global GPP data products from LUE models are now available to the public [52], driven by climate data and satellite images at a moderate spatial resolution (MSR)-for example, the Moderate Resolution Imaging Spectroradiometer (MODIS) at a 500 m spatial resolution.These GPP data products at an MSR are useful.Note that most cropland fields are small in size [53], so the monitoring and assessment of agriculture at the field scale (tens of meters) would need satellite images at a high spatial resolution (tens of meters).Furthermore, agricultural management practices [54][55][56] and land use changes have driven large spatial variation in the GPP in sugarcane plantations [32,57,58].The uncertainty of GPP estimates could increase when the GPP is calculated from MSR images [51,59,60].Therefore, there is a need to generate GPP data products at a high spatial resolution (HSR, tens of meters) as, to date, no global GPP data products derived from HSR images are available.
Transpiration (T) is a pivotal component of evapotranspiration (ET) in agricultural fields, playing a crucial role in assessing crop growth performance [61].Data products that partition ET into T and E (evaporation) offer valuable insights into water use efficiency.However, the practical application of T and ET data at the field level faces multiple challenges, including the course spatial resolution of current remote-sensing products [59,62], the high costs associated with field-scale ground T data, and the intricacies of ET partitioning methods [63].Multiple models have successfully integrated the Penman-Monteith (PM) method [64,65] with successful results [66], but the scalability limitations and structural uncertainties in the vegetation phenology complicate its application in commercial crops [67,68].
Satellite-derived ET products, like MOD16 [69], are popular for agricultural studies over large regions due the coarse spatial resolution but face challenges in water-rich crops (e.g., sugarcane and rice) and more extensively irrigated fields [70,71].Newer products (e.g., ECOSTRESS, [72]) offer finer resolutions but have strong limitations, including infre-quent data capture and validation issues [73].Several studies have pinpointed inaccuracies in ECOSTRESS data across various ecosystems [74,75].Such inconsistencies compromise the data's reliability for precise water management and crop yield forecasting.Given these challenges, there is a pressing need for a straightforward, accurate, and adaptable method to derive field-level T estimates in water-rich crops like sugarcane.
The performance of the VPM in estimating the GPP of sugarcane plantations has only been evaluated at a moderate spatial resolution (MSR) [35].Therefore, its performance at a high spatial resolution (HSR) for individual sugarcane plantations still needs to be assessed and better understood.On the other hand, the vegetation transpiration model (VTM) has not been tested on sugarcane croplands, and this study evaluated VTM's potential as a tool to estimate water use efficiency in this crop system.The study employed an integrated approach utilizing both MSR 8-day MODIS optical data and a combined time series of HSR data from Landsat and Sentinel-2.This methodology was specifically designed to derive vegetation indices at both the MSR and HSR levels.The vegetation indices used in our analysis included the enhanced vegetation index (EVI) and the land surface water index (LSWI), which served as critical inputs for our modeling efforts.The primary focus was on leveraging these indices to comprehensively analyze the seasonal dynamics of the sugarcane crop.By systematically collecting and processing these timeseries data, we were able to effectively utilize them as an input for predicting the temporal dynamics of GPP and T in sugarcane plantations over two different sites.This approach underscores the significance of time-series analysis in agricultural studies, where HSR data availability is limited and an MSR does not represent field patterns well [76], particularly for understanding and modeling the phenological and physiological changes in crop systems over time.
Moreover, given the 2030 objectives to increase sugarcane production, there is a need to assess and compare the VPM performance at distinct sugarcane plantations using MSR and HSR images before it can be applied to perform GPP estimations with HSR images at the regional, continental, and global scales.The core objectives of our investigation were: (1) to evaluate the consistency of satellite-derived vegetation indices (EVI and LSWI) from MSR (MODIS) and HSR (Landsat and Sentinel-2) images in tracking the vegetation phenology and sugarcane crop physiology at two distinct sites; (2) to assess the performance of the VPM in estimating the daily site-level vegetation carbon uptake of sugarcane croplands with different management practices when MSR and HSR images are used, which would shed new light on the advantages of estimating GPP with HSR images; and (3) to analyze the capabilities of the VTM in estimating the daily transpiration of sugarcane croplands.

Study Sites
Two sugarcane sites were selected for this study, based on EC flux data availability and quality: one sugarcane site at Pirassununga, State of Sao Paulo, Southeastern Brazil [31] and the other in Schriever, Louisiana, USA at the Ardoyne farm [77] (Figure 1).The Louisiana site is under the management of the USDA-ARS Sugarcane Research Unit, and the Sao Paulo site is under the management of Embrapa Meio Ambiente.
The Louisiana EC flux tower site (Chacahoula) (29.6341 • N, 90.8349 • W) had an annual mean temperature of 23.6 • C and an annual precipitation of 1200 mm.The site had Cancienne silty clay loam (Fluvaquentic Epiaquepts) type soil.The fields were graded with a 0.2% slope towards the south, and the elevation of the fields ranged between 2.40 m and 0.61 m over 700-900 m.Sugarcane cultivation in Louisiana dates back to 1850 [78], and the study site had experienced more than 50 years of continuous sugarcane production.The field was cultivated with sugarcane variety HoCP 04-838 ′ , reg.no.CV-181, PI 687221, and the sugarcane plants were spaced at 1.83 m intervals for single-planted rows and 2.44 m for double-planted rows (<1% total field area).Sugarcane crop green up typically occurs in April, while it is harvested between October and December.The EC tower on the site was in a 60 m 2 unplanted area surrounded by commercial sugarcane crops.The sugarcane annually received 89 kg ha −1 of nitrogen fertilizer in April.The Louisiana EC flux tower site (Chacahoula) (29.6341°N, 90.8349°W) had an annual mean temperature of 23.6 °C and an annual precipitation of 1200 mm.The site had Cancienne silty clay loam (Fluvaquentic Epiaquepts) type soil.The fields were graded with a 0.2% slope towards the south, and the elevation of the fields ranged between 2.40 m and 0.61 m over 700-900 m.Sugarcane cultivation in Louisiana dates back to 1850 [78], and the study site had experienced more than 50 years of continuous sugarcane production.The field was cultivated with sugarcane variety HoCP 04-838', reg.no.CV-181, PI 687221, and the sugarcane plants were spaced at 1.83 m intervals for single-planted rows and 2.44 m for double-planted rows (<1% total field area).Sugarcane crop green up typically occurs in April, while it is harvested between October and December.The EC tower on the site was in a 60 m 2 unplanted area surrounded by commercial sugarcane crops.The sugarcane annually received 89 kg ha-1 of nitrogen fertilizer in April.
The Sao Paulo EC flux tower site (FAYS) (21.9506°S, 47.3394°W) had an annual mean temperature of 21.4 °C, annual precipitation of 1410 mm, and gentle slope of < 2%.Sugarcane new stem cutting (IAC-5000 variety) was completed on 10/2015 (DOY 275), and the distance between the plotting rows was 1.5 m, with a canopy height of ~5 m during the growing season.The soil type was clay (65% clay, 21% sand, silt 14%), and the site was managed under regular tillage, receiving superphosphate (28% P2O5) and 100 Mg ha −1 dry matter of filter cake (sugar production residue) [31].The flux tower at this site was installed 24 days after planting.Sugarcane is a multi-year ratoon crop; typically, in Brazil, the crop cycle includes one plant crop and four ratoon crops [30].The first harvest took place in late October 2016, and the ground trash was left on the soil; nitrogen fertilizer (80 kg N ha −1 ) and potassium (180 Kg K2O ha −1 ) were applied two days later [31].

Weather and CO2 Flux Data for the Sugarcane Plantations
The 10 m tower had an integrated open-path infrared gas analyzer, and climate and CO2 flux data outputs were produced at a 30 min temporal resolution (Irgason, Campbell Scientific, Logan, UT, USA).The ecosystem carbon uptake was estimated using the The Sao Paulo EC flux tower site (FAYS) (21.9506 • S, 47.3394 • W) had an annual mean temperature of 21.4 • C, annual precipitation of 1410 mm, and gentle slope of <2%.Sugarcane new stem cutting (IAC-5000 variety) was completed on 10/2015 (DOY 275), and the distance between the plotting rows was 1.5 m, with a canopy height of ~5 m during the growing season.The soil type was clay (65% clay, 21% sand, silt 14%), and the site was managed under regular tillage, receiving superphosphate (28% P 2 O 5 ) and 100 Mg ha −1 dry matter of filter cake (sugar production residue) [31].The flux tower at this site was installed 24 days after planting.Sugarcane is a multi-year ratoon crop; typically, in Brazil, the crop cycle includes one plant crop and four ratoon crops [30].The first harvest took place in late October 2016, and the ground trash was left on the soil; nitrogen fertilizer (80 kg N ha −1 ) and potassium (180 Kg K 2 O ha −1 ) were applied two days later [31].

Weather and CO 2 Flux Data for the Sugarcane Plantations 2.2.1. Louisiana, USA Site
The 10 m tower had an integrated open-path infrared gas analyzer, and climate and CO 2 flux data outputs were produced at a 30 min temporal resolution (Irgason, Campbell Scientific, Logan, UT, USA).The ecosystem carbon uptake was estimated using the difference between the measured net ecosystem exchange (NEE) and daytime ecosystem respiration (R); daytime and night-time R were calculated based on fitted exponential equations [25,79].The data covered three growing seasons at the sugarcane plantation (01/2018-12/2020).Multiple sensors at the Chacahoula site were recalibrated in the month of April in 2018 and 2019, resulting in major flags in the CO 2 flux data during the subsequent months; for this reason, some of the data were removed from the study.

Sao Paulo, Brazil Site
The tower had an incorporated open-path infrared gas analyzer.Weather and CO 2 flux data were obtained at a 30 min temporal resolution, and the height of the tower was 9 m.Gross primary production (GPP) and R a were calculated at the EC tower based on the NEE observations using the flux-partitioning REddyProc package [80].The data covered two growing seasons for the Sao Paulo site (October 2015-August 2017).2.2.3.Pre-Processing of CO 2 Flux and Climate Data GPP at both the sites was estimated from the partitioning of the half-hourly NEE data using the algorithms in [25,26].The estimated half-hour GPP (GPP EC ) and photosynthetically active radiation (PAR) data were recalculated into 1-day and 8-day data using the method presented in [35].PAR data were estimated as 0.48 of the total incoming shortwave radiation and converted into photosynthetic photon flux density (PPFD) using the approximation 1 W m −2 ≈ 4.57 µmol m −2 s −1 [81].
Air temperature was averaged into daily daytime mean air temperature (T DT ) and daily mean air temperature (T DA ).We calculated T DT as the average temperature over the half-hour periods that had more than 10 µmol m −2 s −1 PAR within a day.We calculated the 8-day averages of T DT and T DA .There are notable differences between T DA and T DT , and we used T DT for the photosynthesis-temperature relationship in our previous studies [35,49].

Land Surface Reflectance and Vegetation Index Data
We used the surface reflectance data from MODIS (MOD09A1), Landsat (7 ETM+ and 8 OLI/TIRS), and Sentinel-2/A-2/B, which are accessible on the Google Earth Engine (GEE) platform [82].For each flux tower site, we selected one MODIS pixel, one Landsat pixel, and one Sentinel-2 pixel centered on the tower coordinates.
The MOD09A1 Collection 6 product [83] provides surface reflectance at a 500 m spatial resolution and 8-day temporal resolution.We employed the Google Earth Engine (GEE) platform [82] to calculate the enhanced vegetation index (EVI) [84] and land surface water index (LSWI) [85] using the surface reflectance data (see Equations ( 1) and ( 2 For Landsat 7 ETM+ and Landsat 8 OLI sensors, atmospherically corrected surface reflectance data at a 30 m spatial resolution were used to calculate the EVI and LSWI.We assessed the individual observations' data quality using cloud, shadow, water, and snow masks [86].The blue band was used for an additional quality check by detecting the observations with cloudy and water pixels [87]. Sentinel-2 provides optical data at high spatial resolutions (10 m, 20 m, 60 m) and a 10-day temporal resolution [88].S2-A (launched June 2015) and S2-B (launched March 2017) have 13 spectral bands, including visible and NIR bands at a 10 m spatial resolution and red-edge and SWIR bands at a 20 m spatial resolution [89].We used the 10 m S2 orthorectified atmospherically corrected surface reflectance available on GEE.We assessed the quality of individual observations using the cloud bit mask, cirrus bit mask, and blue band [87].
For each eddy flux tower site, the time-series Landsat and Sentinel-2 observations were combined to form one time series of collated data.Both systems provide a 12-bit radiometric resolution with similar reflective wavelengths [88,90,91] and information sensed over the same areas.The similarities between the Landsat and Sentinel-2 spectral resolutions facilitates the combined use of their datasets in several different ways, including data fusion, as reported in previous studies [92].Landsat and Sentinel-2 were combined without resampling the Landsat 30 m data into 10 m data, since the pixel chosen was within the tower's footprint and there were no changes in the crop management landcover type within the 30 m Landsat pixel.In our analysis, we integrated various vegetation indices derived from different optical datasets and, in cases where there were observations with overlapping dates, we selected a single observation for each date.This selection was based on the data quality (maximum NDVI), as in past studies [90,92,93].Ultimately, the gaps in the combined Landsat/Sentinel time-series data were filled in, but the data were not subjected to smoothing.This decision was possible as there was at least one good-quality observation per week, and we ran the model at weekly intervals.
We analyzed the time-series data of the EVI, LSWI, and GPP at the sugarcane sites to identify the start, end, and length of the sugarcane growing season (SOS, EOS, GSL).This information was determined using the VI data with the thresholds of EVI > 0.1 and LSWI > 0 for the SOS and EVI < 0.1 and LSWI < 0 for the EOS.The VI-based GSL was compared with a GPP-based GSL that used SOS > 1 g C m −2 day −1 and EOS < 1 g C m −2 day −1 over three consecutive 8-day periods as thresholds.

Vegetation Photosynthesis Model (VPM)
The vegetation photosynthesis model (VPM) produces daily estimates of GPP [29].The VPM calculates the amount of solar energy absorbed by chlorophyll in the canopy (APAR chl ) and the light use efficiency (LUE g ).The EVI is used as a proxy for FPAR chl (5).
LUE 0 is the apparent quantum yield or maximum light use efficiency (µmol CO 2 /µmol PPFD), and it has different values for C3 and C4 plants in the VPM.The LUE 0 value for C4 plants (e.g., sugarcane) is 0.075 mol of CO 2 mol −1 PPFD (0.9 g C mol −1 PPFD) according to earlier works on the vegetation carbon uptake and quantum yield of photosynthesis for sugarcane [35,94].The LUE 0 for C3 plants ranges between 0.42 and 0.65 g CO 2 mol −1 PPFD (5.0-7.8 g C mol −1 PPFD) [47,95,96].The VPM accounts for the presence of C3 and C4 plants in areas that have both by including the fractions of C3 plants (C3F) and C4 plants (C4F).
The effects of temperature and water on GPP [49,97] are introduced by T scalar and W scalar , respectively.The LSWI is used to calculate W scalar .T scalar is based on the Terrestrial Ecosystem Model (TEM) [98].
• T is the air temperature, and T min , T opt , and T max are the minimum, optimum, and maximum temperatures for photosynthetic activity, respectively.We defined T min as −1 • C and T max as 48 • C using the same cropland biome parameter values as in [47].T opt was set as 28 • C, following [35], which estimated T opt from the relationship between the daily average daytime temperature (T DT ) and either the GPP EC or vegetation index (EVI).
For comparison, we carried out two sets of VPM simulations to estimate daily GPP using site climate data alongside (1) time-series EVI and LSWI data from Landsat and Sentinel images (GPP VPM-LS ) and ( 2) time-series EVI and LSWI data from MODIS images (GPP VPM-MOD ).

Vegetation Transpiration Model (VTM)
In a crop field, evapotranspiration comprises evaporation (E) from the soil and intercepted canopy water and transpiration (T) from plants [66,99].During the crop growing season, transpiration usually exceeds evaporation [100][101][102].At the foliar level, there is a strong linkage between photosynthesis (gross primary production, GPP) and transpiration.This often results in the calculation of the leaf-level water use efficiency as the ratio between these two (i.e., WUE Leaf = GPP/T, expressed in mol CO 2/ mol H 2 O).The Vegetation Transpiration Model (VTM) predicts daily transpiration as an outcome of GPP and WUE Leaf , and it was first tested in grassland ecosystems [103].Literature data indicate that the WUE Leaf_C3 for C3 plants is 500 µmol CO 2 /µmol H 2 O, while for C4 plants, the WUE Leaf_C4 is 250 µmol

Statistical Analysis
We assessed the biophysical performance of the EVI in terms of GPP changes and seasonal behavior at the sugarcane plantations.We analyzed data from two growing seasons for the Brazil site and three growing seasons for the USA site.
GPP VPM data were assessed with GPP EC data at daily and 8-day scales.In a similar way, the T VTM estimates were compared against the ET EC .In addition, 8-day ET estimates from the MOD16 product were included in the comparison with the ET EC to provide a reference for the performance of one of the most common data products for this variable.The metrics for assessment included the coefficient of determination (R-squared, R 2 ), the Pearson correlation coefficient (p), the mean absolute error (MAE), and the normalized root mean squared error (NRMSE).Finally, we compared the ET EC :P and T VTM :ET EC ratios for the periods with data available to better explore the interannual changes and performance of the model capturing this variability.

Seasonal Dynamics of Climate
The Brazil site (Figure 2a) had a tropical climate, characterized by a dry and a wet season, which is typical in tropical regions, with January being the wettest month (247 mm) and July the driest month (27 mm) [30,31].The annual rainfall was higher during the first crop cycle (1651 mm) than during the second crop cycle (1446 mm).The seasonal dynamics of the daily mean air temperature (T DA ) ranged between 14 • C and 26 • C. The mean daily PAR in a year was 39.9 mol m −2 day −1 , varying from the lowest in June (19.18mol m −2 day −1 ) to the highest in February (55.7 mol m −2 day −1 ) (Figure 2a).
The USA site had a sub-tropical climate, characterized by four seasons and a moderately cold winter.On average, March was the driest month (48 mm) and August the wettest month (188 mm) at this site.The second crop cycle was the wettest (1720 mm), and the third cycle was the driest (1477 mm).The air temperature ranged between 5 • C T DA in the winter and 30 • C T DA in the summer.The daily daytime mean air temperature (T DT ) was 2-3 degrees higher than the daily mean air temperature (T DA ).The average daily PAR in a year was 18.19 (mol m −2 day −1 ) for the three crop cycles, varying from the lowest in the winter (1.8 mol m −2 day −1 in January) to the highest in the summer (34 mol m −2 day −1 in June) (Figure 2b). the third cycle was the driest (1477 mm).The air temperature ranged between 5 °C TDA i the winter and 30 °C TDA in the summer.The daily daytime mean air temperature (TD was 2-3 degrees higher than the daily mean air temperature (TDA).The average daily PA in a year was 18.19 (mol m −2 day −1 ) for the three crop cycles, varying from the lowest in th winter (1.8 mol m −2 day −1 in January) to the highest in the summer (34 mol m −2 day −1 i June) (Figure 2b).

Seasonal Dynamics of Vegetation Indices
At the Brazil site (Figure 3c), the EVI and LSWI rose rapidly in December, reachin the maximum value in May 2015.The EVI and LSWI gradually decreased, and by Octobe the EVI reached below 0.1 and the LSWI below 0. The field was harvested in October 201 The VI-based start of the sugarcane growing season (SOS) at this site was November 201 for the first cycle and early December 2016 for the second cycle.The end of the growin season (EOS) was in late October 2016, according to the thresholds used in our previou study [35], which were EVI < 0.1 and LSWI < 0. The results indicated a ~12 month suga cane growing season length (GSL).
At the USA site (Figure 3d), the EVI and LSWI started to rise in late April and earl May and reached their highest values between July and August.The EVI and LSWI grad ually dropped, reaching LSWI < 0 and EVI < 0.1 by early November.The VI-based sta and end of the sugarcane growing season (SOS and EOS) at this site were May and No vember, respectively, with a growing season length of 7 months.

Seasonal Dynamics of Carbon Fluxes (NEE and GPP)
At the Brazil site (Figure 3a), the GPPEC rose steadily in November 2015 to higher tha 1 g C m −2 day −1 , reached the top levels in March, and dropped to 1 g C m −2 day −1 in Octobe 2016.The GPPEC rose again in November 2016, which indicated the start of a new suga cane growing cycle (Figure 3a).Following the GPP > 1 g C m −2 day −1 criterion, the GPP based start and end of the growing season (SOS and EOS) at the Brazil site were in No vember 2015 and October 2016, respectively, which adequately matched the SOS metric outlined by the vegetation indices (Figure 3a).

Seasonal Dynamics of Vegetation Indices
At the Brazil site (Figure 3c), the EVI and LSWI rose rapidly in December, reaching the maximum value in May 2015.The EVI and LSWI gradually decreased, and by October the EVI reached below 0.1 and the LSWI below 0. The field was harvested in October 2016.The VI-based start of the sugarcane growing season (SOS) at this site was November 2015 for the first cycle and early December 2016 for the second cycle.The end of the growing season (EOS) was in late October 2016, according to the thresholds used in our previous study [35], which were EVI < 0.1 and LSWI < 0. The results indicated a ~12 month sugarcane growing season length (GSL).At the USA site (Figure 3b), the GPPEC began to increase in late April, was high in th summer, and decreased below 1 g C m −2 day −1 by September in 2018 and November i 2019 and 2020, due to sugarcane harvesting.Following the GPP >= 1 g C m −2 day −1 condi tion, the GPP-based GSL of sugarcane oscillated between April and November (Figur 3b), which fit sufficiently with the growing season metrics based on the vegetation indice (Figure 3d).

The Relationships between GPPEC and Vegetation Indices from MODIS, Landsat, and Sentinel-2 Images
For both sugarcane plantations, we assessed in terms of GPP dynamics the biophys ical response of the vegetation indices.Figures 4 and 5 show the agreement during th cane growing seasons between the GPPEC and EVI at both plantations.
At the Brazil site, the GPPEC had a sturdier linear relationship with EVILS-S2 from th Landsat and Sentinel-2 images (R 2 = 0.74) than with EVIMODIS from the MODIS image (R 2 0.67).The difference between Landsat/Sentinel-2 and MODIS can be attributed to th MODIS pixel containing information from neighboring fields with different planting and harvesting dates.Figure 4 illustrates the differences in the crop management of sugarcan At the USA site (Figure 3d), the EVI and LSWI started to rise in late April and early May and reached their highest values between July and August.The EVI and LSWI gradually dropped, reaching LSWI < 0 and EVI < 0.1 by early November.The VI-based start and end of the sugarcane growing season (SOS and EOS) at this site were May and November, respectively, with a growing season length of 7 months.

Seasonal Dynamics of Carbon Fluxes (NEE and GPP)
At the Brazil site (Figure 3a), the GPP EC rose steadily in November 2015 to higher than 1 g C m −2 day −1 , reached the top levels in March, and dropped to 1 g C m −2 day −1 in October 2016.The GPP EC rose again in November 2016, which indicated the start of a new sugarcane growing cycle (Figure 3a).Following the GPP > 1 g C m −2 day −1 criterion, the GPP-based start and end of the growing season (SOS and EOS) at the Brazil site were in November 2015 and October 2016, respectively, which adequately matched the SOS metrics outlined by the vegetation indices (Figure 3a).
At the USA site (Figure 3b), the GPP EC began to increase in late April, was high in the summer, and decreased below 1 g C m −2 day −1 by September in 2018 and November in 2019 and 2020, due to sugarcane harvesting.Following the GPP >= 1 g C m −2 day −1 condition, the GPP-based GSL of sugarcane oscillated between April and November (Figure 3b), which fit sufficiently with the growing season metrics based on the vegetation indices (Figure 3d).

The Relationships between GPP EC and Vegetation Indices from MODIS, Landsat, and Sentinel-2 Images
For both sugarcane plantations, we assessed in terms of GPP dynamics the biophysical response of the vegetation indices.Figures 4 and 5 show the agreement during the cane growing seasons between the GPP EC and EVI at both plantations.At the USA site, GPPEC also had a stronger correlation with EVILS-S2 (R 2 = 0.76) than EVIMODIS (R 2 = 0.71) (Figure 5).The sugarcane fields around the EC study field had differen planting and harvest dates (Figure 5a-d), which affected the data analysis of the relation ship between GPPEC and EVIMOD.Wind conditions influenced the tower's fetch footprin and varied depending on the season and the landcover type [105,106].May and June 201 had high EVI values (0.628) (Figure 3d), and the field was green in June (Figure 5a), bu there was no vegetation cover on some of the fallowed sugarcane fields nearby, resultin in a low GPPEC of 3.7 g C/m 2 .Similar situations were observed on 22 September 2018 (Fig ure 5b), the date with the highest EVI of 2018 (0.72); October 2019 (Figure 5c); and Sep tember 2020 (Figure 5d), for which there were high EVI values (>0.5), relatively low GPPE values (<5.45 g C/m 2 ), and a harvested field contiguous with the green sugarcane planta tion EC site.The sugarcane fields adjacent to the EC site were managed differently and could introduce uncertainty in the MSR data products (i.e., EVIMOD) as some of the field At the Brazil site, the GPP EC had a sturdier linear relationship with EVI LS-S2 from the Landsat and Sentinel-2 images (R 2 = 0.74) than with EVI MODIS from the MODIS image (R 2 = 0.67).The difference between Landsat/Sentinel-2 and MODIS can be attributed to the MODIS pixel containing information from neighboring fields with different planting and harvesting dates.Figure 4 illustrates the differences in the crop management of sugarcane fields around the EC site.In February 2016 and August 2016 (Figure 4a,b), within the 500 m MODIS pixel, the south field (February) and the plantation west of the EC tower (August) had bare soil landcover, while the study field had green vegetation.In addition, the effects of radiation changes and cloud cover on the relationship between the GPP EC and the vegetation index are supported by Figure 4d, where green vegetation is visible, but the estimated GPP EC was below 5 g C/m 2 .

Relationships between Air Temperature and GPP and Enhanced Vegetation Index (EVI)
Given the importance of the optimal temperature in multiple biophysical processes and the limited availability of these data, we assessed the relationships between the GPPEC and air temperature (TDT, TDA) during the growing seasons (Figure 6), as this is one of the most reliable methods to estimate Topt.For the site in Brazil, tGPPEC increased as the TDT and TDA rose and reached its plateau at ~25 °C and 23 °C, respectively (Figure 6a,c).In the USA plantation, the GPPEC increased when the TDT and TDA rose and found its plateau at 28 °C and 26 °C, respectively (Figure 6b,d).At the USA site, GPP EC also had a stronger correlation with EVI LS-S2 (R 2 = 0.76) than EVI MODIS (R 2 = 0.71) (Figure 5).The sugarcane fields around the EC study field had different planting and harvest dates (Figure 5a-d), which affected the data analysis of the relationship between GPP EC and EVI MOD .Wind conditions influenced the tower's fetch footprint and varied depending on the season and the landcover type [105,106].May and June 2018 had high EVI values (0.628) (Figure 3d), and the field was green in June (Figure 5a), but there was no vegetation cover on some of the fallowed sugarcane fields nearby, resulting in a low GPP EC of 3.7 g C/m 2 .Similar situations were observed on 22 September 2018 (Figure 5b), the date with the highest EVI of 2018 (0.72); October 2019 (Figure 5c); and September 2020 (Figure 5d), for which there were high EVI values (>0.5), relatively low GPP EC values (<5.45 g C/m 2 ), and a harvested field contiguous with the green sugarcane plantation EC site.The sugarcane fields adjacent to the EC site were managed differently and could introduce uncertainty in the MSR data products (i.e., EVI MOD ) as some of the fields were within the 500 m MODIS pixel centered on the EC tower.
The slightly lower R 2 values at the Brazil site when compared to the USA site were partly attributed to the effect of cloud coverage, increase in shadow during the rainy season, fetch footprint changes throughout the seasons, and influence of the crop management (rotation and harvest) of neighboring sugarcane fields, as evinced by the moderate differences in the vegetation indices (Figure 3a,c).

Relationships between Air Temperature and GPP and Enhanced Vegetation Index (EVI)
Given the importance of the optimal temperature in multiple biophysical processes and the limited availability of these data, we assessed the relationships between the GPP EC and air temperature (T DT, T DA ) during the growing seasons (Figure 6), as this is one of the most reliable methods to estimate T opt .For the site in Brazil, tGPP EC increased as the T DT and T DA rose and reached its plateau at ~25 • C and 23 • C, respectively (Figure 6a,c).In the USA plantation, the GPP EC increased when the T DT and T DA rose and found its plateau at 28 • C and 26 • C, respectively (Figure 6b,d).We also studied the relationships between the vegetation index (EVILS-S2, EVIMODIS) and air temperature (TDT and TDA) (Figure 7) as a potential method to calculate Topt.At the Brazil site, both EVILS-S2 and EVIMOD had weak but similar relationships with air temperature (TDT and TDA) (Figure 7a  We also studied the relationships between the vegetation index (EVI LS-S2 , EVI MODIS ) and air temperature (T DT and T DA ) (Figure 7) as a potential method to calculate T opt .At the Brazil site, both EVI LS-S2 and EVI MOD had weak but similar relationships with air temperature (T DT and T DA ) (Figure 7a,b).For the T DT , the EVI rose and peaked at 20

Comparison between GPP from VPM Simulations (GPPVPM) and GPP Estimates from the Eddy Flux Sites (GPPEC)
At the Brazil site, the seasonal dynamics of the GPPEC and GPPVPM agreed reasonably well (Figure 8a).The Pearson correlation coefficients and R 2 values indicated that there was a stronger relationship between the GPPEC and GPPVPM_LS-S2 (r = 0.86, R 2 = 0.74) than

Comparison between GPP from VPM Simulations (GPP VPM ) and GPP Estimates from the Eddy Flux Sites (GPP EC )
At the Brazil site, the seasonal dynamics of the GPP EC and GPP VPM agreed reasonably well (Figure 8a).The Pearson correlation coefficients and R 2 values indicated that there was a stronger relationship between the GPP EC and GPP VPM_LS-S2 (r = 0.86, R 2 = 0.74) than between the GPP EC and GPP VPM-MOD (r = 0.78, R 2 = 0.62) (Figure 8c, Table 1).The seasonal sums of the GPP EC and GPP VPM within the sugarcane growing season differed noticeably (Table 2).At the USA site, the seasonal dynamics of the GPP EC and GPP VPM agreed reasonably well (Figure 8b).The GPP VPM_LS-S2 values had a stronger relationship with the GPP EC (CC = 0.90, R 2 = 0.82) than the GPP VPM-MOD values did with the GPP EC (CC = 0.79, R 2 = 0.63) (Figure 8d, Table 1).The seasonal sums of the GPP EC and GPP VPM throughout the growing season also differed noticeably (Table 2).

Seasonal Dynamics of ET as Measured at the Tower Site (ET EC ) and Transpiration as Estimated by VTM Simulations (T VTM )
At the Brazil site, the seasonal dynamics of the ET EC and T VTM_EC agreed reasonably well (Figure 9a).The peak ET EC values ranged between 4 and 5 mm/day during December to February, while the peak T VTM_EC values varied between 2 and 3 mm/day for the same peak periods.The Pearson correlation coefficients and R 2 values indicated that there was a moderate relationship between the ET EC and T VTM_EC (p = 0.68, R 2 = 0.47) at the Brazil site (Table 3).The Brazil site had the worst performance of the two sites, as the VTM estimates had weak to moderate relationships with the ET EC and T VTM , whereas these relationships at the site in the USA were moderate to strong.The T VTM-LS2 in Brazil (p = 0.45, R 2 = 0.21) had a stronger linear relationship than the T VTM-MOD , which had the weakest correlation across the study (p = 0.09, R 2 = 0.009).The ET EC /P ratio was consistently ~72.5% in Brazil during the study period, while the T VTM :ET EC ratio for 2016 (complete calendar year) ranged between 64% and 75%, compared to the range of 78% to 95% for 2017 (only including data until August) (Tables 4 and 5).At the Brazil site, the seasonal dynamics of the ETEC and TVTM_EC agreed reasonably well (Figure 9a).The peak ETEC values ranged between 4 and 5 mm/day during December to February, while the peak TVTM_EC values varied between 2 and 3 mm/day for the same peak periods.The Pearson correlation coefficients and R 2 values indicated that there was a moderate relationship between the ETEC and TVTM_EC (p = 0.68, R 2 = 0.47) at the Brazil site (Table 3).The Brazil site had the worst performance of the two sites, as the VTM estimates had weak to moderate relationships with the ETEC and TVTM, whereas these relationships at the site in the USA were moderate to strong.The TVTM-LS2 in Brazil (p = 0.45, R 2 = 0.21) had a stronger linear relationship than the TVTM-MOD, which had the weakest correlation across the study (p = 0.09, R 2 = 0.009).The ETEC/P ratio was consistently ~72.5% in Brazil during the study period, while the TVTM:ETEC ratio for 2016 (complete calendar year) ranged between 64% and 75%, compared to the range of 78% to 95% for 2017 (only including data until August) (Tables 4 and 5).
The USA site displayed stronger and clearer seasonal dynamics.It had peaks during the summer months, showing ETEC values ranging between 3 and 5 mm/day and TVTM_EC values between 2 and 3 mm/day (2018 and 2019), with higher rates in 2020 ranging between 3 mm/day and 4 mm/day.The year 2020 was the driest year, with an annual total P of 1438 mm, and 2019 was the wettest with a value of 1721 mm.This site displayed the strongest Pearson correlation coefficients and R 2 values of either site.For this site, the strongest relationship was between ETEC and TVTM_LS-S2 (p = 0.78, R 2 = 0.61), while the relationship between ETEC and TVTM_MOD remained moderate (p = 0.72, R 2 = 0.52) (Table 3).Tables 4 and 5 display the results of the TVTM estimates derived using the GPPEC (TVTM-EC), GPPVPM-LS2 (TVTM-LS2), and GPPVPM-MOD09 (TVTM-MOD09).The ETEC:P ratios had a similar magnitude over the years (45% to 51%), the TVTM:ETEC ratios varied widely, with a 41% average for 2018, 79% average for 2019, and abnormally high average of 91% for 2020.The USA site displayed stronger and clearer seasonal dynamics.It had peaks during the summer months, showing ET EC values ranging between 3 and 5 mm/day and T VTM_EC values between 2 and 3 mm/day (2018 and 2019), with higher rates in 2020 ranging between 3 mm/day and 4 mm/day.The year 2020 was the driest year, with an annual total P of 1438 mm, and 2019 was the wettest with a value of 1721 mm.This site displayed the strongest Pearson correlation coefficients and R 2 values of either site.For this site, the strongest relationship was between ET EC and T VTM_LS-S2 (p = 0.78, R 2 = 0.61), while the relationship between ET EC and T VTM_MOD remained moderate (p = 0.72, R 2 = 0.52) (Table 3).Tables 4 and 5 display the results of the T VTM estimates derived using the GPP EC (T VTM-EC ), GPP VPM-LS2 (T VTM-LS2 ), and GPP VPM-MOD09 (T VTM-MOD09 ) .The ET EC :P ratios had a similar magnitude over the years (45% to 51%), the T VTM :ET EC ratios varied widely, with a 41% average for 2018, 79% average for 2019, and abnormally high average of 91% for 2020.The one advantage of MODIS sensors (MSR images) is that they acquire images daily and could provide enough good-quality observations to track temporal changes in the vegetation canopy.Many studies have demonstrated that time-series VI data derived from MODIS images at daily and 8-day temporal resolutions can effectively track the seasonal variation and interannual dynamics of vegetation canopies [29, [107][108][109][110].In comparison, as Landsat and Sentinel-2 (HSR images) acquire images at multi-day intervals (for example, Landsat has a 16-day revisit cycle and Sentinel-2 has a 10-day revisit cycle), one sensor often cannot provide enough good-quality observations to track temporal changes in the vegetation canopy.A few studies have combined Landsat images and Sentinel-2 images to construct VI time series and then used them to track the seasonal dynamics of the vegetation canopy [76,[111][112][113].In comparison to the MODIS time-series data, our results also showed that a combination of Landsat and Sentinel-2A/B images increased the number of good-quality observations, providing sufficient data to track the seasonal dynamics and interannual variation of the sugarcane canopy at the Brazil (tropical climate) and USA (subtropical climate) sites.Furthermore, our results indicated that despite the limitations of HSR data in tropical climates, the combined time series of the Landsat and Sentinel-2A/B images provided a better representation of the vegetation carbon uptake, with a linear relationship (R 2 = 0.74) stronger than the linear relationship between EVI MODIS and the EC site vegetation carbon uptake data (R 2 = 0.67).
One MODIS pixel (MSR, 500 m) often contains multiple crop fields, which could be cultivated with different types of crops or the same type of crop with different management practices, and thus reflects the spectral properties of mixed-crop fields and/or crops under various management practices [114][115][116].For example, within the MODIS pixel for the USA sugarcane site, there were seven sugarcane fields at different stages in the crop cycle (e.g., fallow, recently planted cane, and ratooning cane) with different management practices, which may have affected the relationship between the MODIS-based VI values and the GPP EC .The results from this study showed that the relationships between the GPP EC and EVI at the sugarcane plantations were stronger when the EVI was calculated from the Landsat/Sentinel-2 (HSR) images than when the EVI was calculated from the MODIS (MSR) images.Other studies have found similar results, highlighting the benefits of high-spatial-resolution images and their contribution to stronger correlations between carbon flux data and vegetation indices on grasslands and croplands [117][118][119].This is important for estimating crop performance and vegetation health insurance indices over farms with multiple types of crops, rotations, and management techniques [119][120][121].
Sugarcane yields are affected by genotype, environmental conditions, and the time of harvest [122].Our results showed that the EVI and LSWI tracked the phenological dynamics of sugarcane plantations well, providing a detailed cultivation history for the sugarcane at both plantations [31,77,123].The LSWI was able to delineate the phenological metrics (SOS, EOS) and identify the harvest dates, consistent with previous studies on sugarcane and other crop types [35,124,125].As the sugarcane plants at these two sites were harvested while they were still green, the unique phenomenon of the LSWI dropping to <0 reflected the physical system change from green sugarcane fields to brown crop residue and bare soils after harvest at both sites.The harvest date, or EOS, corresponded with the time of the initial negative LSWI value.Our results showed that the harvest dates at the Brazil and USA plantations were accurately recognized by the VI-based algorithms.However, these algorithms had limitations in identifying the SOS at the USA site, which was detected 2 to 4 weeks later across the three growing seasons.These differences could potentially impact the annual total vegetation carbon uptake in the fields.Note that the seasonal changes in GPP EC and NEE EC could also be used to track and delineate the surface phenology of croplands in terms of physiology.The GPP EC accurately tracked the vegetation carbon fixation period using the GPP EC ≥ 1 g C/m 2 /day criterion.Our results showed that the temporal agreement of the land surface phenology metrics derived from the VI-based and GPP EC -based approaches was stronger for the USA site when the VI values from Landsat/Sentinel-2 (HSR) images were used, in part because the MODIS pixel at the USA site covered several crop fields.Finally, the results agreed well with other studies, like that of Zhang (2022) [76], which highlighted the potential of Landsat/Sentinel-2 images in representing planting patterns over agroecosystems.Finally, this study demon-strated the capabilities and limitations of the VI-based method in determining the growing season length.

Comparison of GPP Estimates Using Landsat/Sentinel-2 Data and MODIS Data
In comparison to major grain crops (e.g., maize, soybean, winter wheat, and rice), only a few studies have assessed GPP estimates of sugarcane plantations from light use efficiency models with MODIS data [35,47,126].GPP EC estimates are widely used to assess GPP calculations from light use efficiency models [47,127,128].In our study analyzing data from 2015-2017 in Brazil and 2018-2020 in the USA, the GPP estimates from the VPM simulations with MODIS images and local climate data agreed reasonably well with the GPP EC data, being consistent with the results reported in Xin et al. 2020 [35], where GPP estimates were evaluated using 2005-2007 data from an eddy flux tower site in Brazil and 2017 data from an eddy flux tower site in USA.
The results of our study showed that the temporal agreement between GPP EC and GPP VPM-LS-S2 (R 2 0.82 and 0.74) was stronger than the temporal agreement between GPP EC and GPP VPM-MOD (R 2 0.63 and 0.62), which could largely be attributed to two factors: (1) individual MODIS pixels often included multiple crop fields that have different management practices and cultivation calendars (green-up dates and harvest dates), and (2) the footprints of the eddy flux tower sites were much smaller than the MODIS pixels (500 m), corresponding well with the MODIS limitations reported in other studies [129][130][131] investigating the vegetation carbon uptake in crops.In comparison, vegetation indices from Landsat and Sentinel-2 images, which are used to calculate fPAR chl and W scalar , often reflect the vegetation canopy dynamics from one crop field within the footprint of the eddy flux tower site [132,133].
The stronger correlations between EVI LS-S2 and GPP EC highlighted in Section 4.1 underscore the influence of vegetation indices on the VPM performance.On the other hand, the EVI values at both an MSR and HSR displayed similar results in estimating the site-specific optimal temperature, which is a crucial parameter to enhance the accuracy of GPP estimates.These results were consistent with other studies, where authors such as Velez (2022) [134] have highlighted the potential of HSR (10 m) vegetation index time series in assessing relevant agronomic parameters.In our study, the EVI was used as opposed to the NDVI given its limitations in canopies, which can become oversaturated, as with sugarcane.The results of our investigation evidenced the potential of the VPM fed with Landsat and Sentinel-2 images for estimating the GPP of sugarcane plantations under different climate zones, sugarcane varieties, and crop practices.Finally, the results underscored the potential of the VPM as a tool for crop growth monitoring in precision agriculture that addresses some of the complexity and scalability issues of typical crop models [135,136].

Sources of Uncertainties and Errors in VPM Simulations for Sugarcane Plantations
The sources of errors and uncertainties in the GPP estimates from light use efficiency models comprise the model structure; model parameters; and input datasets, including satellite images and climate data.Xin et al. (2020) discussed VPM simulations at two sugarcane sites with a focus on the LUE parameter.The maximum LUE affects the vegetation carbon uptake at the ecosystem level [48,[137][138][139] and can be estimated through a linear regression between the aboveground dry biomass and total amount of radiation captured by the vegetation [140,141] or based on the relationship between the PAR and GPP [142].The LUE values have a large range of variability over sugarcane depending on the climate conditions, altitude, and crop management [142][143][144][145][146]. Our results suggested a maximum LUE ranging between 0.7 and 0.9 g C mol −1 PPFD for Brazil, similar to the ranges reported in other studies in the Brazilian region [147].Xin et al. (2020) [35] reported that the maximum LUE for VPM simulations was set to 0.9 g C mol −1 PPFD for both sugarcane sites.Further studies are needed to evaluate the maximum LUE parameter over sugarcane plantation sites worldwide, as it could introduce a source of uncertainty for the regional and global GPP estimations.
The comparison of VPM simulations based on MSR images and HSR images illustrates the error sources and uncertainty associated with landcover types within one image pixel and the spatial mismatch (inconsistency) between image pixels and the footprints of an eddy flux tower site [148,149].One MSR pixel often contains multiple landcover types, often called a mixed pixel, while one HSR pixel most likely contains one landcover type, often called a pure pixel [117,150,151].The presence of different landcover types within a single pixel affects the model's representation of the fraction of PAR absorbed by chlorophyll and the vegetation water response, both strong drivers of vegetation carbon uptake.Moreover, the number of good-quality observations from satellite optical sensors would decrease if frequent clouds occurred.In addition, EC flux tower estimates are influenced by the surrounding fields as the footprint changes with the season, weather conditions, vegetation height, and vegetation cover [66,106,148].The sources of uncertainty from the EC tower increase the challenges of validating GPP estimates, and the sources of error in the system increase based on the condition of the instruments and sensors.In this study, we also used the NEE and latent heat flux data from the tower sties to identify additional poor-quality data in the time series that were not removed by the site's quality assurance filters.

Capabilities and limitations of VTM-Forecasted Transpiration for Sugarcane Plantations
The correlation between ET EC and T VTM for the Brazil site was moderate for the T VTM_EC model (R 2 = 0.47) but exhibited lower values for T VTM_MOD (R 2 = 0.009) and T VTM_LS-S2 (R 2 = 0.21), indicating that further improvement and additional variables should be considered in sites located in tropical environments like the Brazil site, where elements such as the residual straw and Bowen ratio variability can affect the transpiration and evapotranspiration rates [152], whereas the more wider spaced rows in Louisiana (1.5 m single row compared to 1.83 m single row and 2.4 m double row) could have affected these water rates [153].Conversely, the USA site showed a robust correlation across all VTM estimates, especially for the high-spatial-resolution T VTM_LS-S2 (R 2 = 0.61), which outperformed the estimates calculated using the GPP EC data as an input for the VTM.The observed differences could be attributed to various factors, including the climatic conditions, soil properties, row spacing, data quality, and sugarcane varieties.
The annual total data in Table 4 underscore the inherent variability in precipitation, ET EC , and T VTM across the sites.Ref. [154] highlighted the changes in actual evaporation and transpiration linked to climate change as one of the leading factors in the interannual yield variability of sugarcane in Brazil.The USA site exhibited the largest interannual variation in precipitation, ET EC , and transpiration VTM rates.Ref. [155] emphasized the impact of soil water conditions as the main driver of the interannual variability in ET and T, partially explaining some the differences observed in the T VTM :ET EC ratios over time.Moreover, ref. [156] addressed the significance of row spacing, as it increases soil water content and provides more space for the sugarcane to grow, significantly increasing transpiration in periods of low rainfall, which could partially explain some of the abnormally high T VTM rates at the USA site in 2020 (driest year).In addition, some of the differences between the MSR and HSR transpiration estimates can be linked to the fact that the MSR pixel included multiple fields containing different varieties and, in some cases, different management practices.
The VTM showed a strong capacity to capture the seasonal dynamics and some of the interannual variability in the transpiration rates.Despite the simplicity of the approach, overall, the T VTM results captured the seasonal dynamics of the water flux, underscoring the potential of this tool and its applications.However, the variability across different scales in the results suggests that for field-level and commercial applications the time-scale dependency should be further studied, and additional parameters such as initial water content and row spacing should be included to provide a better field representation of the transpiration water flux.

Conclusions
This study successfully explored the use of Landsat and Sentinel-2 imagery to monitor phenology and as an input for gross primary production (GPP) estimation in sugarcane plantations in São Paulo, Brazil, and Louisiana, USA.Our findings contribute significantly to the field of remote sensing in agriculture, offering new perspectives and methodologies.
The key conclusions and contributions include:

•
Potential of Landsat and Sentinel-2 over cloudy environments: We demonstrated the effective combination of Landsat and Sentinel-2 time-series images for monitoring phenology and as an input for GPP estimation in sugarcane plantations.This approach proved particularly effective in diverse environmental conditions, including cloudy scenarios where HSR images have the greatest limitations, thereby underscoring the robustness of these satellite images in capturing agricultural dynamics.Furthermore, HSR data better represented field vegetation uptake at both sites compared to MSR data.

•
EVI as a proxy for estimating optimal air temperature: The study revealed a novel application of the enhanced vegetation index (EVI) in estimating site-specific optimal air temperature (T opt ) for photosynthesis.This correlation between the GPP EC , EVI, and air temperature variables opens up new avenues for understanding the biophysical performance of vegetation indices across different pixels and fields.• VPM efficacy: Our research highlighted the VPM's capabilities for accurately estimat- ing the seasonal dynamics of GPP in sugarcane plantations at a high spatial resolution.The model's adaptability to varying environmental conditions was a key finding, showcasing its potential for broader application.Nonetheless, the field variability of the ECT footprint introduced some uncertainty into the ground data.• Transpiration modeling insights: The Vegetation Transpiration Model (VTM) effec- tively captured the seasonal dynamics of transpiration.However, its dependency on high-quality GPP data and the need for further research into time-scale dependency and initial water content impact were noted.The model showed promise in environments like Louisiana, but additional research is needed in settings like Brazil to refine its accuracy and address uncertainties.
Future work will include assessments of the models at additional sugarcane plantations with EC flux systems, spatial yield data, and detailed field information including variety type and row spacing, as this could increase our knowledge regarding likely sources of uncertainty and the prospects of deploying the models as tools for precision agriculture.

26 Figure 1 .
Figure 1.The two sugarcane locations with EC flux tower sites (red doted polygons; (a) USA and (b) Brazil) displaying the pixel size of the optical data utilized in the study: 10 m (red polygon, Sentinel-2), 30 m (blue polygon, Landsat), and 500 m (green polygon, MODIS).

Figure 1 .
Figure 1.The two sugarcane locations with EC flux tower sites (red doted polygons; (a) USA and (b) Brazil) displaying the pixel size of the optical data utilized in the study: 10 m (red polygon, Sentinel-2), 30 m (blue polygon, Landsat), and 500 m (green polygon, MODIS).

Figure 4 .
Figure 4. (Left panel): The relationships between gross primary production (GPPEC) and the en hanced vegetation index (EVI) derived from moderate-spatial-resolution images (MSR, MODIS) an high-spatial-resolution images (HSR, Landsat and Sentinel-2) within the growing season.(Righ panel): 3 m 4-band planet Scope and 5 m RapidEye Ortho tile surface reflectance true-color image of vegetation cover in the FAYS Brazil study area.The red circle represents the area used to obtai the time-series of HSR data.

Figure 4 .
Figure 4. (Left panel): The relationships between gross primary production (GPP EC ) and the enhanced vegetation index (EVI) derived from moderate-spatial-resolution images (MSR, MODIS) and high-spatial-resolution images (HSR, Landsat and Sentinel-2) within the growing season.(Right panel): 3 m 4-band planet Scope and 5 m RapidEye Ortho tile surface reflectance true-color images of vegetation cover in the FAYS Brazil study area.The red circle represents the area used to obtain the time-series of HSR data.

26 Figure 5 .
Figure 5. (Left panel): The relationship between the estimated gross primary production (GPPEC) and enhanced vegetation index derived from moderate-spatial-resolution images (MSR, MODIS) and high-spatial-resolution images (HSR, Landsat and Sentinel-2) within the growing season.(Right panel): 3 m 4-band planet Scope and 5 m RapidEye Ortho tile surface reflectance true-color images of vegetation cover in the Chacahoula, USA study area.The red circle represents the area used to obtain the time-series of HSR data.

Figure 5 .
Figure 5. (Left panel): The relationship between the estimated gross primary production (GPP EC ) and enhanced vegetation index derived from moderate-spatial-resolution images (MSR, MODIS) and high-spatial-resolution images (HSR, Landsat and Sentinel-2) within the growing season.(Right panel): 3 m 4-band planet Scope and 5 m RapidEye Ortho tile surface reflectance true-color images of vegetation cover in the Chacahoula, USA study area.The red circle represents the area used to obtain the time-series of HSR data.
,b).For the TDT, the EVI rose and peaked at 20 °C with a greater density of high values at 26 °C; the EVI reached its plateau at a TDA of 23 °C.The results at the USA location (Figure 7c,d) displayed high EVI values at 28 °C TDT and 25 °C TDA.The results were consistent for both sites and similar for HSR EVILS-S2 and MSR EVIMOD.EVILS-S2 reached a plateau at slightly warmer temperatures at both sites, but remained overall close to the EVIMOD (~0.15 °C).Following these results, the optimum air temperature (Topt) for modeling purposes was established as 25 °C (GPP-based) or 26 °C (EVI-based) for Brazil and 28 °C (GPP-based and EVI-based) for the USA.
• C with a greater density of high values at 26 • C; the EVI reached its plateau at a T DA of 23 • C. The results at the USA location (Figure 7c,d) displayed high EVI values at 28 • C T DT and 25 • C T DA .The results were consistent for both sites and similar for HSR EVI LS-S2 and MSR EVI MOD .EVI LS-S2 reached a plateau at slightly warmer temperatures at both sites, but remained overall close to the EVI MOD (~0.15 • C).Following these results, the optimum air temperature (Topt) for modeling purposes was established as 25 • C (GPP-based) or 26 • C (EVI-based) for Brazil and 28 • C (GPP-based and EVI-based) for the USA.Remote Sens. 2024, 16, x FOR PEER REVIEW 13 of 26

Figure 8 .
Figure 8. GPP estimate time series from the EC flux sites (black line) and the VPM (HSR GPP in blu and MSR GPP in red).(a) FAYS Brazil site GPP time series estimates (2015-2017).(b) Chacahou USA site GPP time series estimates (2018-2020).Relationship between GPPEC and the VPM (HS GPP in blue and MSR GPP in red) (c) FAYS Brazil.(d) Chacahoula, USA site.

Figure 8 .
Figure 8. GPP estimate time series from the EC flux sites (black line) and the VPM (HSR GPP in blue and MSR GPP in red).(a) FAYS Brazil site GPP time series estimates (2015-2017).(b) Chacahoula, USA site GPP time series estimates (2018-2020).Relationship between GPP EC and the VPM (HSR GPP in blue and MSR GPP in red) (c) FAYS Brazil.(d) Chacahoula, USA site.

26 3. 5 .
Remote Sens. 2024, 16, x FOR PEER REVIEW 15 of Seasonal Dynamics of ET as Measured at the Tower Site (ETEC) and Transpiration as Estimated by VTM Simulations (TVTM)

Figure 9 .
Figure 9. ETEC estimate time series from the EC flux sites (black line) and the TVTM_EC (red line) for (a) the FAYS Brazil site and (b) Chacahoula, USA.

Figure 9 .
Figure 9. ET EC estimate time series from the EC flux sites (black line) and the T VTM_EC (red line) for (a) the FAYS Brazil site and (b) Chacahoula, USA.

Table 1 .
A comparison of statistical metrics from the correlation analyses between GPPEC (g C m day −1 ) and GPPVPM (g C m −2 day −1 ) for the Brazil and USA sites.

Table 2 .
Seasonal sums of GPPEC and GPPVPM during the growing the season defined by the GP based method and VI-based method at the Brazil and USA sites.

Table 1 .
A comparison of statistical metrics from the correlation analyses between GPP EC (g C m −2 day −1 ) and GPP VPM (g C m −2 day −1 ) for the Brazil and USA sites.

Table 2 .
Seasonal sums of GPP EC and GPP VPM during the growing the season defined by the GPP-based method and VI-based method at the Brazil and USA sites.

Table 3 .
A comparison of statistical metrics from the correlation analyses between ET EC (mm day −1 ) and T VTM (mm day −1 ) for the Brazil and USA sites.

Table 4 .
A comparison of the seasonal sums of precipitation, evapotranspiration (ET EC ) from the tower observations, and transpiration (T VTM ) from the Vegetation Transpiration Model (VTM) simulations.Daily ET EC (mm day −1 ) and T VTM (mm day −1 ) from the study sites were aggregated over days with ET observations.

Table 5 .
A comparison of the ratio of transpiration (T VTM ) to evapotranspiration (ET EC ) according to the growing season at the Brazil and USA sites.Daily ET EC (mm day −1 ) and T VTM (mm day −1 ) from the study sites were aggregated over days with ET observations for the study period within each year.