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The improved performance of the mangrove LUE model considering coastal environments in this study was mainly attributed to the determination of environmental scalars. Parameters determining environmental stressors (e.g., Topt, Tmin, Tmax, VPDmin, and VPDmax) were set based on the general characteristics of mangroves worldwide. It may not be as accurate for the mangroves in our study sites, but it generally reflects the response of mangroves to environmental changes. Furthermore, as can be seen in Fig. S1, it is applicable to our study sites. Despite the specific characteristics of each mangrove ecosystem at different sites being preferred, this study first offers the possibility to estimate mangrove productivity at a larger scale to track GPP, thus emphasizing the role of mangrove ecosystems nationally or worldwide.The validation results showed that the LUE values of the mangrove model agreed well with those estimated by EC method (Fig. 3) and indicated improved performance (slope = 0.8218–1.0108, intercept = -0.0006–0.0052, R2 = 0.54–0.64, RMSE = 0.0051–0.0068, Pearson’s r = 0.73–1), compared to the MOD17 model (slope = 0.4993–0.5566, intercept = 0.0311–0.0313, R2 = 0.24–0.45, RMSE = 0.0217–0.0220, Pearson’s r = 0.45–0.49). Firstly, the RS-based LUE model for terrestrial ecosystems (MOD17) considers only the environmental stressors of Tair and VPD. The photosynthesis in mangrove forests is influenced by other unique environmental factors caused by tidal inundation. According to Fig. S3, PAR caused the most significant effect on LUE, which is consistent with previous studies14,30,32. The impact of SST has not been quantitatively assessed, however, SST is a critical control that determines the upper latitudinal range of mangrove ecosystems12,33. In our study, the effects of SST and salinity on the mangrove LUE were quantified and helped improve LUE modeling.Secondly, LUEmax was typically defined for different land covers, however, there were no specific values for mangrove forests. In this study, the LUEmax of mangroves was first determined. It is worth noting that daytime NEE responses to PAR vary depending on the Tair23,30,34 so that LUEmax was determined separately at high, optimal, and low temperatures. The results showed that LUEmax reached a maximum when Tair was within the optimal range for mangroves, which represents the high productivity of mangrove ecosystems. Furthermore, the estimated LUEmax of mangrove forests (0.057) was larger than most terrestrial forests35,36,37, which could contribute to the high production and carbon sequestration in mangrove forests.Lastly, the relatively low stomatal conductance of mangroves leads to low LSP compared with terrestrial forests, which could result in the high-irradiance stress for photosynthesis38,39. Mangrove LSP ranges from about 0.2–1.2 mmol/m2/s, depending on the species and environments40,41,42. LUE was relatively low in April and May when seasonal PAR was high, as photosynthesis is more likely to reach saturation. Therefore, we assumed the LUE of mangroves decreased with increasing PAR. In addition, we found that the downscaling effect of PAR on LUE was not constant, but varied with increasing PAR. As follows, different PAR scalars were set for mangroves according to different PAR values. This is a first attempt at refining PARscalar considering different solar radiation, which represents a significant departure from the assumption of a constant downscaling effect of PAR in RS-driven models14,43. The accuracy of the LUE model was improved by refining the PARscalar with different downscaling slopes, especially in periods of high PAR values.Compared with the results obtained from flux-tower measurements, the modeled GPP was basically within the confidence interval of the measured results. The annual averages of GPP in Zhangjiang were 1729 g C/m2/year and 1924 g C/m2/year, in 2012 and 2016, and the annual mean value of GPP in Zhanjiang was 1434 g C/m2/year in 2015. The previous study showed that the GPP in Zhangjiang ranged from 1763 to 1919 g C/m2/year with a mean value of 1871 g C/m2/year32,44,45, which is in good agreement with the estimated values obtained in this study. Liu and Lai46 reported that the GPP of the Mai Po mangrove reserve was 2827 g C/m2/year. Rodda, et al.20 found a GPP value of 1271 g C/m2/year for Sunderbans mangroves in India. Gnanamoorthy, et al.47 estimated a GPP of 2305 g C/m2/year for Pichavaram mangroves. Variations in these estimates across sites were possibly caused by different climate-hydrological conditions, mangrove species, and ages. Differences in the same location may be due to different time scales and different methods of data gap filling and flux partitioning.In a similar way to the GPP model for terrestrial ecosystems48, the effect of the mangrove GPP model on the accuracy of GPP estimates can vary considerably under different environmental conditions. However, in comparison with the accuracy of models built for other vegetation types, the GPP model in this study performed substantially in two sites with RMSE of 2.54–3.41 g C/m2/day. Wang et al.49 adopted different models to estimate GPP for global vegetation and validation results showed the RMSE ranged from 1.79 to 2.33 g C/m2/day. Xiao, et al.50 demonstrated that the deviation between observed and predicted GPP was about 35–282 g C/m2 in an evergreen needleleaf forest. Also, the absolute GPP errors were 7.94–20.92% and 9.97–13.70% for maize cropland and degraded grassland36. Despite the discrepancy, our results were generally consistent with previous studies and were verified by field observations near the flux towers.The comparison of MODIS GPP and EC-estimated GPP showed that the MODIS GPP had a large fluctuation and weakly reflected productivity, being overestimated in 2012 and underestimated in 2015. Different meteorological inputs, different environmental scalars and fraction of absorbed photosynthetic active radiation (fAPAR) products in MODIS GPP and our mangrove GPP model can explain their different results. However, the improvements in our GPP model may help to obtain more accurate GPP estimates. The response of mangrove productivity to Tair has not been well-calibrated in the MODIS GPP product, which may partly account for the poor correlation between the MODIS GPP and EC estimates. Besides, MODIS GPP product was developed based on the International Geosphere-Biosphere Programme (IGBP) land cover map, which doesn’t include mangroves as a specific land cover37. Therefore, LUEmax and environmental parameters were not defined for mangroves, which varied with different environments. This may lead to uncertainty in MODIS GPP product for mangrove forests14. However, the GPP model generated in our study showed similar trends to the field measurements, capturing seasonal variations. The increase in the difference between MODIS GPP and EC estimates may be due to the assumption that the increase in GPP is linear with respect to PAR. In our model, the response of GPP to PAR was suppressed, resulting in seasonal changes in GPP that better match the observations. In addition, the GPP derived from this study was in higher agreement with measured values compared with GPP estimated from the vegetation photosynthesis model (VPM), as shown in Fig. S4. The improvement of this model was more obvious in winter (December to February), which may be due to the environmental stress of SST and PAR. The VPM without considering SSTscalar and PARscalar overestimated GPP in winter. It is indicated that the performance of the mangrove GPP model in this study varied with season. It is recommended to improve the estimation of GPP in the future by considering the seasonal variation of mangrove forests when determining environmental variables.Most studies provide EC-based estimates of GPP that are measurements from a limited footprint. It is possible to extrapolate results across similar vegetation types and geographic settings, but not to areas of heterogeneous vegetation. The RS-based GPP model offers spatial-scale estimates that can be directly incorporated into ecosystem-type models. PAR, SST, and salinity are the key environmental parameters of this RS-based mangrove GPP model. SST and salinity data were derived from the satellite images, while PAR was generated from the reconstructed PAR data, since it is more accurate than the existing RS data and has historical year data. However, PAR products from Hamawari-8, MERIS, and SeaWiFS are available now, which provide an opportunity to obtain large-scale PAR data using RS in the future. In addition to this, GPP of two mangrove forests was assessed and validated with three-year measurements. Validation at different sites and years showed similar results, which indicated the model has similar performance across mangrove forests. Nonetheless, these estimates need to be corroborated with EC databases, which are relatively accurate and provide many additional variables that are currently beyond the scope of higher spatial-resolution RS estimates. The proposed GPP model considering coastal environments was well suited to extend the study area by incorporating RS information and meteorological data. Currently, there are still few mangrove carbon flux towers worldwide. The LUE and GPP models proposed in this study are difficult to validate with measurements from flux towers in other countries. However, local measurements are available in many countries with large mangrove forests, such as Thailand, Vietnam, India, and Bangladesh. Therefore, it is expected that comparisons with measurements from previous studies can be conducted to show the consistency and applicability.The LUE model considering the effects of SST, salinity, and PAR performed well, however, the GPP estimated from the LUE, fAPAR, and PAR showed discrepancies and were generally lower than the measured values. Although the results are better than MODIS GPP products, limitations exist still.Firstly, the effects of salinity and SST on mangrove productivity were directly related to tidal activities. The soil pore water and surface water salinity could affect the osmotic pressure of mangroves especially for the submerged parts which would control the stomatal conductance. In the same way, SST could influence the temperature of mangrove root systems and soil sediments which has impacts on mangrove roots’ respiration and transpiration. Although, theoretically, salinity and SST should be considered as environmental variables affecting mangrove LUE, our results (Fig. S3) indicated that salinity and SST have little influence on mangrove productivity51. To date, the quantitative impact of SST has not been comprehensively unfolded, but it is a global control that determines the upper limit of the latitudinal range of mangroves12,33. The weak relationships between salinity, SST, and mangrove GPP could be due to the uncertainty caused by tidal inundation. Tide duration, tide height, and tide cycle would determine the effect of salinity and SST on the mangrove LUE and GPP. However, quantifying the influence from the tidal cycle remains a challenging task, which could result in the relatively poor performance of Salinityscalar and SSTscalar as shown in Fig. S3. Quantifying the soil temperature and surface water salinity considering the tidal cycle will contribute to model the LUE and GPP of mangrove forests.Secondly, mangroves of different species and ages exhibit diverse structural and physical conditions, resulting in different LUEmax, and optimal growing conditions such as Topt and VPDmin. The environmental settings would also vary from region to region. Liu and Lai46 found that LUE increased slightly with the increasing salinity below 15 ppt (R2 = 0.16). However, it was noted that photosynthetic activity of mangroves would be inhibited when the surface water salinity was high30,51,52,53. Probably, the mutual relationship between LUE and salinity depends on the salinity level and mangrove species. However, we have not specified the variables for different mangrove species, ages and locations which could be improved in the future. Besides, there are multicollinearities between different environmental variables. For example, Tair may have effects on SST and VPD, but as shown in Fig. S5, they are all important for mangrove photosynthesis. However, the correlations between them are not clear and need to be quantified in the future.Thirdly, the relatively low spatial and temporal resolution of the environmental data from RS would influence the accuracy of the model. The datasets have a relatively coarse resolution (usually 500 m–1 km and daily) and are thereby less suitable for smaller nature reserves, especially in the narrow patches of mangrove areas that are rapidly being exploited in coastal China. Moreover, the variability in LUE decreases with increasing temporal scale54. In our study, we determined the PARscalar based on the response of LUE to hourly-scale PAR and found the different down-regulation effects with increasing PAR. However, this phenomenon is not obvious in previous studies. Most RS-based LUE models were developed at a daily or 8-day temporal scale6,50,55,56,57. In terrestrial forests, the light saturated effect caused by increasing PAR was neglectable with coarse temporal scale because the average PAR was usually lower than the LSP. However, as the time scale increases, the effect of light saturation on LUE becomes more pronounced32,58,59. More importantly, this effect is more obvious in mangroves due to their lower LSP18,38, which makes it important in mangrove LUE modeling. The results in Fig. 3 show similar performances of LUE model on hourly and daily scale. Thus, we suggested that our model can be adopted in hourly and daily temporal resolution. However, the PARscalar developed in this study was based on the mangrove forests in one study site which may be influenced by the mangrove species with different LSP and light conditions. What’s more, VPD was on a monthly scale, which cannot reflect environmental dynamics. However, the hourly and daily VPD data are currently not available for coastal areas in China. Therefore, we used monthly averages to represent daily VPD, which may lead to uncertainty in the derived GPP estimates (Figs. 6 and 7). Besides, porewater salinity is controlled by sea surface salinity, precipitation, and river discharge. However, currently, pore water salinity was expressed in terms of sea surface salinity, which may lead to an underestimation of Salinityscalar. More systematic study is necessary to make it more applicable and accurate on a large scale, of which modeling the LUE for different mangrove species and locations is inevitable. However, serving as a fundamental and preliminary step, our study aims to provide a framework for RS-based mangrove GPP modeling. Recently, with the advancement of satellite imagery, hourly-scale RS data for PAR, temperature and SST are available. It can be expected that our current work could be further improved by investigating the light saturation effects in different mangrove forests and adopt higher temporal resolution RS products such as Himawari-8 and GCOM-C in the future.Lastly, the overall underestimation of GPP was mainly caused by the underestimation of fAPAR. Even though the fAPAR computed from Sentinel-2 had higher resolution and accuracy than MODIS fAPAR products, future improvements are still needed. Sentinel-2 fAPAR products (fAPAR-S2) was calculated as the instantaneous fAPAR obtained at 10:00 local solar time which only roughly represented the daily average but was not accurate. Besides, RS-derived fAPAR only considers the absorptions by living green vegetation elements, whereas the ground measured fAPAR refers to the contributions from all absorbing components60. The lower fAPAR-S2 values in mangrove forests may be due to the exposed-to-air root systems which absorb the radiation. Moreover, the spatial distribution of PAR was determined by Co-Kriging interpolation. The elevation was taken as the covariate to estimate spatial PAR. There are many other variables affecting the incoming PAR (e.g., slope and clearness)61. A more comprehensive set of variables needs to be included in the Co-kriging interpolation to improve the PAR estimation.The spatial and seasonal variations of the mangrove GPP were related to environmental changes along the shoreline. The low summer GPP was explained by the lower fAPAR in summer compared with other seasons, which was principally due to the underestimation of fAPAR in summer. Furthermore, PARscalar took a mean value of LSP as 1 mmol/m2/s, however, LSP varied with different species and environmental conditions. In summer, mangroves are more likely to obtain light saturation, and thus PARscalar may lead to an underestimation of LUE and thus GPP. On the contrary, PAR values in winter were relatively low but increased slightly with decreasing latitude. Thus, the inhibitory effect of PAR on LUE was not significant, and GPP increased with decreasing latitude. Salinity and VPD were more stable across years and locations and had no noticeable effect on the mangrove LUE and GPP. The seasonal latitudinal patterns and effects on mangrove productivity were similar for Tair and SST. Tair and SST were lower in winter, especially at high latitudes where mangroves were more sensitive to cold weather. Therefore, the GPP of mangroves at high latitudes in winter was the lowest throughout the year. However, hot weather in summer also limited the photosynthesis in mangroves, especially at low latitudes, where Tair and SST were higher. Nevertheless, there were some correlations among these environmental constants. For example, the Tair affects the vapor pressure and SST. There was a positive correlation between PAR and Tair. The multicollinearity among these variables and the various conditions of mangroves may affect the performance of the model and show variations along the coastline, which would be improved in future studies.Additionally, the GPP of mangroves increased from 2007 to 2018, which was mainly due to the expansion of mangrove forests in the coastal areas. As mangroves grow, canopy size and tree density increase, which may lead to higher LUE and less underestimation of fAPAR, thus contributing to high productivity. However, Zhejiang province (27° 02′ N–31° 11′ N) experienced extremely cold weather in January 2016 caused by the East Asia cold wave62,63, and large areas of mangrove forests died or became sick, leading to a decline in the mangrove GPP at high latitudes in 2018. More

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