Coupling Earth observation and eddy covariance data in light-use efficiency based model for estimation of forest productivity

Abstract The light use efficiency (LUE) approach is a well-established method for estimating gross primary productivity (GPP) over large areas using Earth observation data. The present study aims to determine maximum light use efficiency (LUEmax) values specific to the northwest Himalayan foothills of India. It also aims to estimate the spatio-temporal variability of GPP from 2001 to 2020 using remote sensing data in combination with eddy covariance data in the LUE-based model. The model was parameterized using different sets of default and calculated parameters. The study showed that the use of PFT-specific LUEmax and temperatures increased the accuracy of the model predictions. On validation, the LUE-based model predicted GPP showed R2 = 0.82 for moist deciduous and R2 = 0.83 for dry deciduous PFTs. The study revealed that with rigorous model parameterization, RS data can be used in an LUE-based model to achieve accurate spatio-temporal estimates of GPP.


Introduction
At the ecosystem level, the fixation of atmospheric carbon dioxide (CO 2 ) into organic carbon by the terrestrial vegetation via photosynthesis is termed as ecosystem gross primary productivity (GPP) (Chapin et al. 2002). GPP represents the carbon flux between the terrestrial biosphere and the atmosphere, which makes it the most vital component of the global carbon cycle (Zheng et al. 2018). GPP also provides information on the health of the ecosystem and the status of its functioning . It varies diurnally and seasonally as a response to the variability of the climatic factors and nutrient availability (Canadell et al. 2000;Anav et al. 2015;Srinet et al. 2020a). The accurate estimation of GPP is essential to get insights into the impact of climate change on terrestrial vegetation and ultimately on the global carbon cycle. Therefore, accurate, long-term modelling of GPP at regional scales has increasingly become a major focus of ecological and global change studies. Owing to its capability to provide large, synoptic, and temporal views at regional to global scales, remote sensing (RS) data are increasingly being utilized for mapping and monitoring the vegetation dynamics and productivity studies (Hilker et al. 2008;Kumar et al. 2014;Yan et al. 2018;Kushwaha et al. 2018;Ghosh et al. 2019;Srinet et al. 2020b).
To estimate GPP on a regional scale, satellite-based light use efficiency (LUE) models have emerged as important tools because of their specialized forward physics and practicality (Monteith 1972;Field et al. 1995;Running et al. 2000Running et al. , 2004Yuan et al. 2014;Gonsamo and Chen 2018). The RS-based empirical models, such as temperature-greenness (TG) model (Sims et al. 2008), greenness-radiation (GR) model (Wu et al. 2011), have been widely used to predict the GPP in various regions across the globe. However, these methods rely on the statistical relation between measured values of GPP and RS variables. The data-driven approaches like artificial neural network (ANN), generalized regression neural network (GRNN), support vector machine (SVM) (Dou et al. 2018a), adaptive neuro-fuzzy inference system (ANFIS), extreme learning machine (ELM) (Dou et al., 2018b), and random forest (RF) (Wang et al. 2021) need large datasets and are highly dependent on the climatic forcings. Among different productivity modelling techniques, LUE models have the potential to adequately address the spatial and temporal dynamics of GPP as they can leverage RS data and present a balance between simplicity and precision in the predictions (Hilker et al. 2008;Cai et al. 2014;Jin et al. 2020). The LUE models are based upon two fundamental assumptions (Running et al. 2004), first, the GPP is directly related to absorbed photosynthetically active radiation (APAR) through LUE, where LUE is defined as the amount of carbon produced per unit of APAR (Monteith 1972;Monteith and Moss 1977), and second, the realized LUE may be reduced below its theoretical potential value by environmental stresses such as low temperatures or water shortages (Landsberg 1986). Lately, various LUE models have been developed and applied to estimate GPP and net primary productivity (NPP) at various spatial and temporal scales (Potter et al. 1993;Landsberg and Waring 1997;Law et al. 2000a;Xiao et al. 2004a;Turner et al. 2006;Mahadevan et al. 2008;Coops et al. 2009;Chen et al. 2014).
The eddy covariance (EC) towers provide robust measures of carbon fluxes with concurrent measurements of meteorological variables such as temperature, precipitation, humidity, and incoming solar radiation. With the increase in the number of EC towers, the EC flux data is playing an important role in the parameterization and evaluation of various productivity models for different ecosystem types (Law et al. 2000b;Wang et al. 2010;Joiner et al. 2018;Pillai et al. 2019;Zhou and Xin 2019). The development of most of the LUE models has been based on EC measurements, which have been calibrated and evaluated for various ecosystem types (Heinsch et al. 2006;Li et al. 2013;Jin et al. 2020).
The realized LUE (e) value is a key parameter used in the LUE models for the estimation of GPP. For calculation of realized LUE, maximum LUE (LUE max , e max ) value is required. LUE max is defined as the maximum conversion efficiency of APAR to GPP by the vegetation. Some studies used a universal mean LUE max value (Sannigrahi 2017;Sun et al. 2019), which can be taken from the literature sources as model inputs for various ecosystems. However, the research suggests that LUE max is not a universal constant (Russell et al. 1989) and its values need to be calibrated rigorously because they significantly impact the accuracy of the model (Jin et al. 2020). It is difficult to estimate LUE max directly as it depends on physiological processes of photosynthesis, which are linked to the plant foliar biochemical composition, age, and environmental factors like temperature, precipitation, and incoming solar radiation (Goetz and Prince 1999;Chen et al. 2009;Jin et al. 2020). Thus, it may differ spatially with the type of vegetation, and climatic conditions (Ahl et al. 2004;Bradford et al. 2005). The photosynthetic potential of a forest, which is the foundation for ecosystem production and carbon storage, is temperaturedependent (Tan et al. 2017). Hence, it is essential to characterize the temperature appropriately to get accurate estimates of GPP.
The LUE-based model, which expresses GPP as the product of APAR and realized LUE, uses the inputs from remotely sensed data and can be parameterized using the local parameters. For the calculation of realized LUE in such models, a prior specification of a constant LUE max for the region is required, which is downscaled by the environmental stress coefficients including temperature, water, and phenology (Xiao et al. 2004a(Xiao et al. , 2004b. The APAR is calculated as a product of photosynthetically active radiation (PAR) and fraction of absorbed photosynthetically active radiation (fAPAR). Various studies have used different methods to calculate fAPAR (Xiao et al. 2004a;Sims et al. 2006;Zhang et al. 2017).
The forests of the northwest Himalayan (NWH) foothills of India are diverse and they provide huge carbon sinking capabilities Nandy et al. 2019). The phenological behavior of the forests in combination with the variations in topography and climate gives rise to the different plant functional types (PFTs) in this area (Srinet et al. 2020b). For these PFTs, accurate information about LUE max is still deficient. For GPP modelling using LUE-based model, the application of a constant value of LUE max for these PFTs is not suitable. Thus, the present study focuses on evaluating the influence of default and PFT-specific parameters like LUE max , optimum temperatures on the GPP estimates from LUE-based model and using RS data in combination with EC data in LUEbased model to estimate the productivity in these PFTs.

Study area
The study area is located in the NWH foothills of India, which is spread across Uttarakhand, Uttar Pradesh, Himachal Pradesh, Punjab, and Jammu and Kashmir ( Figure 1). The area has a tropical to subtropical humid climate. The mean annual temperature ranges from 20 to 25 C. The area experiences most of its rainfall from the southwest monsoon from June-end to September (Srinet et al. 2020b). The NWH foothills comprise flat to undulating terrain with hills and valleys. The elevation in the study area ranges from 187 to 1300 m above mean sea level. The forest in the study area (Table S1) can be classified into moist and dry deciduous PFTs (Srinet et al. 2020b) which provide valuable ecosystem services by playing a vital role in carbon storage, biodiversity, water, and soil conservation . Two EC flux towers are located in the foothills of NWH, in Uttarakhand state, India. One is, Barkot Flux Site (BFS) located at Dehradun Forest Division in the moist deciduous PFT and the other is Haldwani Flux Site (HFS), located at Tarai Central Forest Division in the dry deciduous PFT (Table S2) (Watham et al. 2020).

Remote sensing and climate reanalysis data
The 8-day Terra MODIS Surface Reflectance product (MOD09A1), with a spatial resolution of 500 m for 2001 to 2020 was used in this study. The data was used to calculate the normalized difference vegetation index (NDVI) (Rouse et al. 1974) and land surface wetness index (LSWI) (Xiao et al. 2004b) which was used as an input to calculate the fAPAR, water scalar (W scalar ) and phenology scalar (P scalar ) used to estimate PFT-wise GPP at monthly intervals following the LUE model algorithms. The data processing, including the calculation of indices and scalars, was carried out in Google Earth Engine (GEE).
For temperature, ERA5-Land monthly averaged 2 m temperature data, which provides the temperature of air at 2 m above the surface of land, was used. The PAR was calculated from ERA5-Land monthly averaged surface solar radiation downwards data, which provides the amount of solar radiation (shortwave radiation, SWRad) reaching the surface of the Earth. PAR was determined as a fraction of SWRad as (Ruimy et al. 1995):

Eddy covariance tower data
EC-based measurements of C-fluxes and meteorological data from BFS and HFS sites for five years (2016-2020) were used in this study. An integrated CO 2 /H 2 O open-path infrared gas analyser and 3 D sonic anemometer (IRGASON, Campbell Scientific) was used to measure the CO 2 and H 2 O fluxes. To calculate the carbon flux, the collected data was processed using EddyPro 6.2.0 software (Li-COR Biosciences, USA), which involved splitting the data into 30 min files; despiking; coordinate rotation; Webb, Pearman and Leuning (WPL) and other corrections; and quality control (Burba 2013). The processed data was filtered and gap-filled using the REddyProc package (Wutzler et al. 2018) in the R environment. The partitioning of obtained net ecosystem exchange (NEE) values was carried out to calculate the ecosystem respiration (Re) (Falge et al. 2002) and the GPP was calculated as the sum of NEE and Re. The details about the data and its processing can be found in Watham et al. (2020) and Srinet et al. (2020a). The GPP estimates obtained after the flux data processing were used to parameterize and validate the LUE model. The GPP estimates from 2016-2018 (Watham et al. 2020) were used to calculate the maximum LUE for both the PFTs, which was provided as an input to the LUE model for calculation of GPP in both the PFTs. Whereas the GPP estimates of 2019 and 2020 were used as an independent set to validate the predicted GPP estimates. The minimum (T min ), maximum (T max ), and optimum (T opt ) temperatures for photosynthesis for the PFTs under study were calculated from the temperature data obtained from EC tower sites. The PAR data was also obtained from the EC tower sites.

LUE-based model
An LUE-based model, similar to the Vegetation Photosynthesis Model (Xiao et al. 2004a(Xiao et al. , 2004b was used for the study. It uses the LUE concept, which here was considered to be constrained by temperature, land surface moisture condition, and leaf phenology. The GPP was estimated as: where e is the LUE; fAPAR is the fraction of absorbed photosynthetically active radiation and PAR is the photosynthetically active radiation (lmol, photosynthetic photon flux density (PPFD)). The LUE depends on temperature, water or moisture availability, and leaf phenology and is calculated as: where e max is LUE max , (lmol CO 2 /lmol PPFD), and T scalar , W scalar and P scalar are the scalars for the effects of temperature, water, and leaf phenology on LUE of vegetation, respectively.
Monthly T scalar was calculated as (Xiao et al. 2004a): where T is the air temperature, T min , T max , and T opt are the minimum, maximum, and optimum temperatures for photosynthesis.
To account for the effects of water stress, the monthly value of W scalar was calculated as (Xiao et al. 2004a): where LSWI is the land surface water index, calculated as shown in Eq. (6), and LSWI max is the maximum LSWI within the plant growing season for individual pixels.
where q 858 and q 1640 represent the spectral reflectance in the near-infrared and shortwave infrared range, respectively. The present study was carried out from 2001 to 2020. It utilizes multi-year data, hence, mean monthly LSWI for every individual pixel was calculated over multiple years and then the maximum value of LSWI within the photosynthetically active period was selected to get the value of LSWI max (Xiao et al. 2004a).
To capture the effect of leaf phenology on photosynthesis at the canopy level, P scalar was used. It was calculated as (Xiao et al. 2004a): fAPAR was calculated as a linear function of NDVI (Sims et al. 2006;Yuan et al. 2007): fAPAR ¼ 1:24 Â NDVI À 0:168 (9)

Parameter estimation and parameterization of LUE-based model
The PFT-specific LUE values were calculated as the ratio of EC tower obtained GPP and APAR for mid-day fluxes (1000 hrs to 1400 hrs) from 2016 to 2018 (Jenkins et al. 2007;Watham et al. 2017a;Noumonvi and Ferlan 2020): where GPP is the gross primary production calculated from EC tower data for different PFTs, PAR is the photosynthetically active radiation observed at EC tower sites, and fAPAR is the fraction of photosynthetically active radiation. The maximum LUE values obtained for both the PFTs were used as LUE max (gC MJ À1 ) for respective PFTs. T min , T opt, and T max were calculated from EC tower data. To obtain the GPP estimates using LUE model, the model was run with multiple sets of parameters including combinations of default and calculated values of T min , T opt , T max , and LUE max .

Spatio-temporal variability of GPP
Using the best set of parameters in the LUE-based model, GPP was estimated from January 2001 to December 2020. The spatio-temporal variability of GPP was mapped. The obtained GPP was validated using a separate set of EC observed GPP for 2019-2020.

Parameter estimation and parameterization of LUE-based model
The carbon conversion rate of APAR is assumed to have maximum value under optimal environmental conditions, like, temperature, water availability, and incoming solar radiation. The linear relationship between mid-day GPP and APAR gave the highest value during September-October months for both the PFTs. LUE max value was observed to be 2.42 gC MJ À1 for moist deciduous PFT and 1.69 gC MJ À1 for dry deciduous PFT. Based on the EC tower observations, T min and T max were found to be 1.8 C and 42 C, respectively whereas T opt for photosynthesis was 26.45 C for moist deciduous PFT and 29.17 C for dry deciduous PFT. The default value of LUE max was considered as 2.54 gC MJ À1 and T min , T opt , and T max were considered to be 0 C, 28 C, and 48 C, respectively (Xiao et al. 2005). To study the importance of specifying PFT-specific parameters for GPP estimation, LUE model was implemented using default and calculated values of these parameters (Table 1). To ensure the comparability of LUE model outputs, identical datasets were used while modelling. LUE model GPP obtained using default LUE max and temperature values showed the least R 2 (0.47 for moist and 0.41 for dry deciduous PFTs). The use of PFT-specific temperature values resulted in a slight increase in R 2 for both the PFTs (0.49 for moist and 0.51 for dry deciduous PFTs). The introduction of the PFT-specific LUE max resulted in more accurate predictions (R 2 ¼ 0.64 for moist and R 2 ¼ 0.69 for dry deciduous PFTs). However, the use of PFT-specific LUE max and temperatures increased the accuracy of the model predictions significantly (R 2 ¼ 0.89 for moist deciduous PFT and R 2 ¼ 0.90 for dry deciduous PFT) (Figure 2). The GPP scatter plots with PFT-specific parameters showed a close clustering around the 1:1 line (Figure 2d and 2h).

Spatio-temporal variations of GPP
Based on the PFT-specific LUE max values, GPP modelling was carried out for the NWH foothills of India from 2001 to 2020. The annual GPP was plotted from 2001 to 2020, which ranged from 336.75 gC m À2 year À1 to 4012.56 gC m À2 year À1 (Figure 3, Table S3). From 2001 to 2020, the spatially averaged annual GPP ranged from 2640.83 to 3129.69 gC m À2 year À1 with a mean of 2865.30 gC m À2 year À1 in moist deciduous PFT, and from 1621.16 to 1985.32 gC m À2 year À1 with a mean of 1781.97 gC m À2 year À1 in dry deciduous PFT (Table S3). The mean monthly GPP was calculated from 2001 to 2020 and intraannual variability of GPP was mapped (Figure 4, Table S4). For moist deciduous PFT, GPP ranged from 0.50 gC m À2 day À1 to 17.25 gC m À2 day À1 with a mean of 7.85 gC m À2 day À1 whereas for dry deciduous PFT, it ranged between 0.14 gC m À2 day À1 and 14.23 gC m À2 day À1 with a mean of 4.89 gC m À2 day À1 (Table S4). To study the interannual variability of GPP, the mean monthly GPP from January 2001 to December 2020 was plotted ( Figure 5). The GPP in both the PFTs of NWH foothills showed similar trends. The minimum GPP was observed during January-February, which started increasing from March and peaked during August-September and started reducing from October. Over a period of 20 years, an increasing trend was observed in the mean GPP.
In comparison of LUE model obtained GPP and MODIS GPP (MOD17A2) with the GPP observed at the flux tower sites (Figure 6), MODIS GPP was found to underestimate the GPP in both the PFTs whereas LUE model obtained GPP was found to be closer to the flux tower obtained GPP. On validation with an independent set of EC tower calculated GPP, LUE model GPP showed R 2 ¼ 0.82 with %RMSE of 11.50% for moist deciduous and R 2 ¼ 0.83 with %RMSE of 10.53% for dry deciduous PFTs.

Discussion
Due to their ability to utilize the spatial and temporal vegetation information obtained from RS data, the LUE-based models have been used for GPP modelling at various scales ranging from site to global scales (Xiao et al. 2004a;Madani et al. 2017;Watham et al. 2017a;Noumonvi and Ferlan 2020;Jin et al. 2020). In the LUE-based model, the LUE max value plays a very important role, as it is the basis of all the LUE-based models. The LUE   remains maximum when the plants experience the best environmental conditions, hence, for the calculation of LUE max only mid day GPP and PAR were considered (Jenkins et al. 2007). The value of LUE max varies with the ecosystem PFT and as this value provides the foundation for the realized LUE, any misrepresentation of LUE max will inherently affect the accuracies of the GPP estimates (Zhu et al. 2016;Jin et al. 2020).
Various studies have reported LUE max values specific to the ecosystems (Zhu et al. 2006;Wang et al. 2010;Yebra et al. 2015;Zhu et al. 2016;Madani et al. 2017;Zheng et al. 2018;Noumonvi and Ferlan 2020;Jin et al. 2020). Zhu et al. (2006) calculated LUE max for some typical vegetation types in China. They reported LUE max ¼ 2.19 gC MJ À1 for evergreen broadleaf forests and LUE max ¼ 2.52 gC MJ À1 for deciduous broadleaved forest. Wang et al. (2010) used data from EC flux sites representing the dominant vegetation/land cover types in China. They found the LUE max values of 3.34 gC MJ À1 for deciduous broadleaved forest site whereas 3.01 gC MJ À1 for mixed forest site. In China, Zhu et al. (2016) reported LUE max ¼ 1.68 gC MJ À1 for mixed forest ecosystem, LUE max ¼ 1.07 gC MJ À1 and 1.59 gC MJ À1 for two different evergreen broadleaf forests. Madani et al. (2017) calculated LUE max values based on the data obtained from various sites under FLUXNET, they found LUE max ¼ 1.4 ± 0.2 gC MJ À1 for evergreen broadleaf forest and LUE max ¼ 1.68 ± 0.35 gC MJ À1 for the deciduous broadleaf forest. Zheng et al. (2018) found LUE max values ranging from 2.59 to 5.39 gC MJ À1 for deciduous broadleaf forest in northern China using different parameters. Depending upon the approaches used for LUE estimation, the reported LUE max values showed large differences. However, in the present study, the estimated LUE max value for moist deciduous PFT was found to be 2.42 gC MJ À1 and for dry deciduous PFT, it was found to be 1.69 gC MJ À1 . The LUE max values have been assumed to vary according to the vegetation type and climate (Bartlett et al. 1989;Madani et al. 2017), hence, there are differences in the reported values. The Figure 6. Comparison of the mean monthly GPP obtained from LUE model, MODIS GPP product (MOD17A2) and EC tower in moist and dry deciduous plant functional types from January 2016 to December 2020. differences in the LUE max values observed in the two PFTs of NWH foothills under study can be attributed to their vegetation composition.
According to the MODIS PFT (Sulla-Menashe and Friedl 2018), the forests of NWH foothills have been classified as evergreen broadleaf and deciduous broadleaf. The LUE max values reported for evergreen broadleaf forest and deciduous broadleaf forest in the biome properties look-up table for MODIS GPP product are 1.268 gC MJ À1 and 1.165 gC MJ À1 , respectively. The LUE max reported in the present study for moist and dry deciduous PFTs differs from that used in the biome properties look-up table for MOD17. There occurs huge diversity in the biomes across the earth surface due to the environmental and climatic conditions, hence, assigning a constant value in of LUE max despite these differences may not conform to the regional conditions Zhu et al. 2016).
In LUE model, for the calculation of the temperature scalar, it is vital to choose T min , T opt and T max carefully to avoid the over or under corrections of the temperature scalar values (Xiao et al. 2004a;Noumonvi and Ferlan 2020). Therefore, these values were calculated for each PFT from the observed GPP and temperature relationships from the EC tower sites. It is evident that PFT-specific T opt can affect model predictions. The photosynthetic capacity increases with temperature, till an optimum temperature and above this, it declines sharply as electron-transport and Rubisco enzymatic capacities become impaired (Medlyn et al. 2002). The global average T opt over the vegetated areas has been estimated to be 23 ± 6 C and T opt in the tropical evergreen broadleaved forest was found to be 29 ± 3 C (Huang et al. 2019). The changes in the growth conditions may result in the shift of this optimum temperature (Berry and Bjorkman 1980). Alternatively, the temperatures exceeding T opt may result in a sharp decline in photosynthetic carbon sequestration (Doughty and Goulden 2008;Vårhammar et al. 2015) which in turn may increase atmospheric CO 2 and would further accelerate warming through positive feedback (Tan et al. 2017).
The LUE model obtained GPP in moist deciduous PFT was higher than that of the dry deciduous PFT of NWH foothills. As per the assumption of the LUE concept, the intraannual variability in the predicted GPP was strongly influenced by the environmental stress factors, including climatic conditions and the phenological cycle in both the PFTs. The lowest GPP was observed in the leaf-fall period, which starts from December-end to January in the dry deciduous PFT and February-March in the moist deciduous PFT, followed by the leaf expansion and slight increase in the GPP during April-May which signify the dry season in the study area. The study area experiences rainfall from the southwest monsoon during the July-September months. Hence, the higher GPP observed during that period can be credited to the optimal environmental conditions including the temperature, moisture availability, and leaf area index (Ahongshangbam et al. 2016;Watham et al. 2017b;Srinet et al. 2020a). As the temperature starts to reduce and the winter approaches, the GPP also starts reducing.
The annual GPP variability showed an increasing trend over the study period. This trend was consistent with the EC tower observed GPP from 2016 to 2020 in both the PFTs. In a study carried out in the midwestern and northeastern United States, Keenan et al. (2013) had reported a strong increase in annual net C uptake from 1992 to 2009. Their analysis indicated that only a small fraction of trends in carbon uptake can be explained by changes in climate forcings (temperature, precipitation, humidity, solar radiation) at any site. Finzi et al. (2020) also recapitulate the fact with their analysis in the mixed hardwood forest present at the Harvard Forest Environmental Measurements Site for a 24-year period spanning from 1992-2015. They reported about 168 gC m À2 yr À1 more carbon uptake in 2015 compared to 1992. Hollinger et al. (2021) also reported a small but significant trend of increasing carbon uptake through time using the eddy flux data of an unmanaged evergreen forest in central Maine, USA, for over 25 years. They noted a lack of influence of climate variability on annual carbon storage in the mature forest under study despite witnessing some of the most climate-extreme years in the last 125 years.
On the site-scale comparison, the LUE model obtained GPP was found to be closer to the EC tower GPP than the MODIS GPP in both moist and dry deciduous PFTs. The reason for this underestimation could be the differences in the EC-based calculated LUE max values and the values used in the MODIS GPP product. The underestimations of MODIS GPP due to the under-representation of LUE max have also been reported by various studies (Niu et al. 2016;Madani et al. 2017;Zheng et al. 2018). For any specific region or ecosystem type, using a fixed value for LUE max may result in systematic uncertainties or errors in GPP (Wagle et al. 2016;Zheng et al. 2018). Hence, rigorous model parameterization and calibration are critical for accurate carbon flux simulation using LUE-based models. GPP predictions in NWH foothills of India, using temperature greenness (TG) model-an RS-based empirical model, showed R 2 ¼ 0.79 for moist deciduous and R 2 ¼ 0.77 for dry deciduous PFTs (Srinet et al. 2020a), which were lower than the accuracy of the GPP predicted using LUE model (R 2 ¼ 0.88 for moist deciduous; R 2 ¼ 0.91 for dry deciduous) for the same area. Some over and underestimations of GPP in the TG model were also reported during the peak season in the moist and dry deciduous PFTs, respectively. Over the years, there was no significant trend observed in TG-predicted GPP, whereas the LUE model obtained GPP showed an increasing trend, which was also observed in the EC GPP. Hence, it can be concluded that in comparison with the simple empirical approach, the LUE-based approach was able to capture the trend in GPP more accurately.

Conclusions
In the present study, the LUE-based model was used to model the GPP of two major PFTs present in the NWH foothills of India. The PFT-specific parameters, viz., LUE max and temperature were calculated using the GPP and meteorological data from EC tower sites (2016)(2017)(2018). The comparison of LUE model outputs with and without PFT-specific parameters reflected that the PFT-specific LUE max and temperatures strongly influenced the modelling accuracy of GPP. Using these PFT-specific LUE max and temperature values, the spatio-temporal variability of GPP from 2001 to 2020 was quantified using LUE model obtained. The moist deciduous PFT was found to be more productive than the dry deciduous PFT. An increasing trend was observed in the forest GPP of NWH foothills during the study period. The study emphasized the importance of site-specific LUE max , which is a critical parameter used in many broad-scale carbon cycle models and T opt , which regulates the rate of photosynthetic activity. Due to the lack of reported values of these important parameters in the Indian Himalayan region, the accurate estimates of GPP of this unique ecosystem are unavailable. The present study is an attempt to report these parameters for two major PFTs of NWH foothills of India. An accurate representation of the spatial variability of LUE max can address its spatial heterogeneity and could help in a meticulous representation of the regional GPP. The present study also highlights that a relatively simple LUE model, with rigorous model parameterization and calibration, can be used for the accurate estimation of spatio-temporal variability of GPP using RS and climate data.