Four products are introduced in this section, and a triplet of them is used for training of each of the LE, H, and GPP (Sect. 3.2). For LE and H, training is performed based on GLEAM, FLUXNET-MTE, and ECMWF ERA HTESSEL (Hydrology Tiled ECMWF Scheme for Surface Exchanges over Land). For GPP, training is performed on FLUXNET-MTE, ECMWF ERA HTESSEL, and MODIS-GPP. Table 1 summarizes the characteristics of the training datasets used here.

Six sets of observations are used as input to the WECANN retrieval algorithm. These are selected in a way that provides necessary physical constraints on the estimates from the ANN. Table 2 lists the characteristics of each of the datasets, and they are briefly introduced in the following.

We developed an ANN retrieval algorithm to estimate the surface fluxes (LE and H) and GPP based on our six sets of input observations: SIF, net radiation, air temperature, soil moisture, precipitation, and SWE (as described in Sect. 2.2). The ANN used here is a feedforward network consisting of three layers: (1) an input layer that directly connects to the input data, (2) one hidden layer, and (3) an output layer that produces the three output estimates. The number of neurons in the input and output layer is determined by the number of input and output variables, whereas for the hidden layer it has to be chosen according to the complexity of the problem (see below). The neuron output from each layer is fed to neurons in the subsequent layer through weighted connections. Each neuron output is the weighted sum of its inputs plus a bias, which is then subjected to a transfer function. In this study, we chose a tangent sigmoid transfer function for neurons in the hidden layer and a linear transfer function in the output layer. The change of the transfer function for the hidden layer (log sigmoid or tangent sigmoid) did not produce any significant changes in the retrievals (not shown); thus, we used the more common method. A schematic of the ANN architecture is provided in Fig. 1.

The training step of the ANN aims at estimating the weights for each of the neuron connections, such that the mismatch between the ANN outputs and target estimates is minimized. For this, we used the mean squared error (MSE) as the cost function and a backpropagation algorithm to adjust the ANN weights. During the training, the network implicitly learns the coupling of the LE, H, and GPP by using one set of neurons (with their respective weights and biases) to estimate the three variables. This is an advantage of using a machine learning technique that eliminates the need to define physical relationships between different variables.

For the purpose of training, the target data are divided into three subsets: training, validation, and testing constituting 60, 20, and 20 % of the target data, respectively. In each iteration, the training subset is used to estimates the weights in the network, and the convergence of the training towards the target data is checked using the validation subset. When overfitting of the network weights to the training data occurs, the validation estimates start diverging from the target data and the training is stopped (early stopping). The weights from the last iteration before the occurrence of the divergence represent the final solution. The testing subset is used to assess the ANN performance after the training phase.

As an additional measure to avoid overfitting, we repeated the training for several ANNs with an increasing number of neurons in the hidden layer (1 to 15). For one to five neurons, the R2 value between the target data and the ANN estimates increased with an increasing number of neurons. For more than five neurons, little change in the skill was observed when increasing the number of hidden layer neurons (Fig. S3). Thus, an ANN with five hidden layer neurons represents the simplest ANN that can converge to a solution and model the nonlinear relationship between the satellite inputs and the surface flux estimates.

To train the ANN, we used LE, H, and GPP estimates from the years 2008–2010. The target dataset was generated through a TC-based merging of triplets of the flux estimates introduced in Sect. 2.1 (details are discussed in Sect. 3.2). After completion of the training, the performance of the ANN and its ability to generalize was evaluated using the LE, H, and GPP target data from 2011. Finally, WECANN retrievals are evaluated against other global products and eddy covariance tower data. Results of these comparisons are presented in Sect. 4.

One of the key issues in the design of an ANN to retrieve any geophysical variable is defining a good target dataset. One practice has been to use outputs from a land surface model as the target (Aires et al., 2005; Jiménez et al., 2013; Kolassa et al., 2013; Rodriìguez-Fernández et al., 2015). However, all observations and models contain random errors and biases. Therefore, the retrieval based on the ANN exhibits some of the biases of the original target dataset even if the ANN is able to make corrections to its original target data (e.g., correction of an imperfect seasonal cycle, as demonstrated by Jiménez et al., 2009). To address this issue, we use three datasets, which are sufficiently independent so that the training can learn from each dataset and benefit from all of them, synergistically. We implement a pseudo-Bayesian training by probabilistically weighting the occurrence of each training dataset by its likelihood and define a target dataset. The three datasets are listed in Table 1 for each variable.

To define this prior distribution, we use the TC technique. TC is a method to estimate the RMSE (and, if desired, correlation coefficients) of three spatially and temporally collocated measurements by assuming a linear error model between the measurements (McColl et al., 2014; Stoffelen, 1998). This methodology has been widely used in error estimation of land and ocean parameters, such as wind speed, sea surface temperature, soil moisture, evaporation, precipitation, fAPAR, and in the rescaling of measurement systems to reference system for data assimilation purposes (Alemohammad et al., 2015; D'Odorico et al., 2014; Gruber et al., 2016; Hain et al., 2011; Lei et al., 2015; Miralles et al., 2010, 2011b; Parinussa et al., 2011), as well as in validating categorical variables such as the soil freeze–thaw state (McColl et al., 2016). The relationship between each measurement and the true value is assumed to follow a linear model: Xi=αi+βit+εii=1,2,3, in which Xi is the measurement from the collocated system i (e.g., remote sensing observation, model output), t is the true value, and αi and βi are the intercept and slope of the linear model, respectively. εi is the random error in measurement i and TC estimates the variance of this random variable in each measurement. By further assuming that the errors from the three measurements are uncorrelated Covεi,εj=0,fori≠j and the errors are uncorrelated with the truth Covεi,t=0, the RMSE of each measurement error can be calculated as (McColl et al., 2014) σε1σε2σε3=Q11-Q12Q13Q23Q22-Q12Q23Q13Q33-Q13Q23Q12, in which Qij is the (ith or jth) element of the covariance matrix between the three measurements. Since the triplet of datasets used for training each of the fluxes (see Table 1) is derived through different semiempirical approaches with different sources of errors, the assumption of uncorrelated errors is more likely to be met. In the following, we will calculate the standard deviation of the random error component of Eq. (1) using TC for each of the surface fluxes and use them as TC-based errors of each product.

The TC-estimated errors for the surface fluxes and GPP are shown in Figs. S4–S6. The white regions represent missing retrievals or discarded negative estimates due to an insufficient data record. For LE, high TC errors are found in the Amazon rainforest and tropical Africa for GLEAM, in the Amazon rainforest and the Sahel for ECMWF, on the Indian peninsula for FLUXNET-MTE, and in US Great Plains for ECMWF and FLUXNET-MTE. For H, in addition to the aforementioned regions, high TC errors are also found in Southeast Asia for GLEAM and ECMWF and in northern Canada for FLUXNET-MTE. For GPP, MODIS and ECMWF have the highest errors in the Amazon rainforest, ECMWF and FLUXNET-MTE have relatively higher errors in US Great Plains, and all three products have similar errors in tropical Africa.

There are several likely causes for these errors. For the FLUXNET-MTE data, the regions that are not covered by (many) FLUXNET eddy covariance stations may result in larger uncertainties, and those regions for which interception is a large component of the LE flux as well (Michel et al., 2016). For the GLEAM and ECMWF data, thick vegetation generally induces biases compared to the satellite observations, especially in tropical regions (Anber et al., 2015).

Finally, we use the TC-based RMSE estimates at each pixel to compute the a priori probability (Pi) of selecting a particular dataset in each pixel, if that pixel is used as part of the training dataset: Pi=1σεi2∑i=131σεi2, in which Pi is the probability of selecting dataset i when sampling from three measurements. We assume that these probabilities are time independent as we are limited by the currently available duration of the input data; however, future versions will explore the use of seasonally varying probabilities.

In this section, we present and compare the retrievals of LE, H, and GPP for the year 2011, which was not included in the training step of WECANN. Thus, it is used here to evaluate the ANN fit to the target values.

Figure 2 illustrates the annual global average and scatter plots of retrievals vs. target estimates. The spatial patterns of the WECANN retrievals are similar to expectations. The average global values in 2011 are 38.33 W m-2 for LE, 39.44 W m-2 for H, and 2.34 gC m-2 day-1 (or 123.16 PgC yr-1) for GPP. LE has the best R2 (0.95) compared to H (R2=0.89) and GPP (R2=0.90). The root mean squared difference (RMSD) of each of the retrievals with respect to the target estimates is as following: for LE, RMSD = 11.06 W m-2; for H, RMSD = 13.13 W m-2; and for GPP, RMSD = 1.22 gC m-2 day-1.

The seasonal variability in and spatial pattern of the retrievals from 2011 are shown in Figs. 3–5. LE does not exhibit any variability over deserts such as the Sahara and Arabian Peninsula, as expected (Fig. 3). Wet tropical forests exhibit subtle seasonal variability in LE. These spatial variabilities in the seasonal cycle reflect changes in the radiation, temperature, water availability during the dry season, soil nutrients, soil type conditions, and leaf flushing (Anber et al., 2015; Morton et al., 2014, 2016; Restrepo-Coupe et al., 2013; da Rocha et al., 2009; Saleska et al., 2016). In contrast, seasonal variability dominated by radiation availability is noticeable in wet midlatitude regions for both the Northern Hemisphere (NH) and Southern Hemisphere (SH), i.e., East Asia, the eastern US, and the north and east Australian coasts with over 60 W m-2 difference between winter and summer months. One exceptional case is South Asia, where LE does not significantly rise in spring, likely due to the effects of the monsoonal climate. In eastern South America, the ET estimates are relatively high compared to GPP estimates. This difference can be caused by either low water use efficiency or significant rain reevaporation and soil evaporation. Moreover, the SIF relationship with GPP likely changes in C4 plants. However, we did not impose the C4–C3 delimitation in the ANN as it would be highly dependent on the quality of the classification map used. We note that all training products used here include C3–C4 delimitation and therefore the C3–C4 delimitation is implicit in the training dataset; therefore, it can be learned by the network.

Seasonal variabilities in H (Fig. 4) are distributed in an opposite pattern to LE, as expected. Deserts and dry regions, i.e., the Sahara, southwestern US, and Western Australia demonstrate much more seasonal variability than the rest of the world. Given the strong water limitations there, the available energy converted into H becomes dictated by the seasonal cycle of solar radiation. In contrast, tropical rainforests (Amazon, Congo, Indonesian) exhibit limited seasonal variability. In midlatitude energy-limited regions (central and eastern Europe, the eastern US), H also reflects the course of available energy, and in more water-limited regimes (e.g., the western US and Mediterranean Europe), it reflects the interplay between soil dryness and available energy, with a peak between spring and summer for dry regions.

The seasonal variability in GPP (Fig. 5) in northern latitudes follows the availability of radiation in wet regions, with a peak in summer and another in spring for dry regions, corresponding to both soil water availability and high incoming radiation. A clear east–west transition conditioned by water availability is observed in the continental US. In the tropics and subtropics, the response is diverse. The Amazon rainforest exhibits high GPP throughout the year with a peak between September and February in the wetter part of the basin, following the dry season, consistent with the observations at eddy covariance towers near Manaus and Santarém (Restrepo-Coupe et al., 2013; da Rocha et al., 2009). Compared to LE, substantial geographical variability is observed in the Amazon because of the strong variabilities in soil type, green-up, biodiversity, and rooting depth. In the drier part of the basin, water availability controls the seasonal cycle of photosynthesis, and the peak in GPP is observed in the wet season (DJFMA). In the Congo rainforest, GPP exhibits four seasons, with two wet and two dry ones, with a substantial decrease in GPP during those dry spells. In Indonesia, GPP is steadier throughout the year, exhibiting high values year round. Monsoonal climates over India, Southeast Asia, northern Australia, and Central–North America are well captured with rapid rise in GPP following water availability. The highest GPP values are observed in rainforests and the agricultural US Great Plains, in JJA for the latter. Northern latitude regions mainly exhibit substantial GPP in the summer and late spring and small values throughout the rest of the year.

Direct validation of the WECANN retrievals is challenged by the fact that no global, error-free estimates of LE, H, and GPP are available. Remote sensing or model products such as those used for training have their own errors. When three datasets with uncorrelated errors (commonly assumed to be true if the sources of error in each dataset have no common physical origin) are available, TC provides a valuable technique to evaluate large-scale datasets in the absence of a known truth. However, WECANN's use of different training datasets will cause the presence of some correlated errors between WECANN retrievals and any of the datasets used for the training. Instead, we evaluate the retrievals by comparing them to data from a set of FLUXNET eddy covariance towers. WECANN uses three training datasets, one of which (FLUXNET-MTE) is based on upscaling FLUXNET eddy covariance tower estimates. This might cause some dependence between WECANN retrievals and the tower estimates. However, WECANN learns from all three training datasets collectively and uses remote sensing observations as input. Therefore, this dependence is negligible. In situ estimates from eddy covariance towers with a footprint of a few hundred meters to kilometers may not be representative of the entire 1∘ × 1∘ pixel and are known to have problems with energy closure (Foken et al., 2010). However, in the comparison against tower data the impact of large-scale climate variability and seasonality can still be seen even on different spatial scales. For instance, the phenology has a strong impact on the seasonal cycle of the LE, H, and GPP and in the following examples; it is clearly highlighted when comparing different products to flux tower estimates.

A summary of statistics across 85 FLUXNET sites is provided in Tables S2–S4. Overall, WECANN performs better than other alternative global products. In particular, WECANN has the highest correlation for 76 % of sites for LE, 58 % of sites for H, and 55 % of sites for GPP. This high R2 reflects the capacity of WECANN to correctly capture the seasonal cycle and interannual variability, as it is largely imposed by the remote sensing observations rather than by the statistical retrieval (Jiménez et al., 2009). One of the reasons for this is the presence of the SIF information in the ANN retrieval, which is directly related to GPP and plant transpiration (Frankenberg et al., 2011). The RMSE of WECANN is lower than all other products at 71 % of sites for LE, 46 % of sites for H, and 51 % of the sites for GPP. The bias is also reduced compared to other retrievals, even if some variability can be seen from site to site.

Figure 6 shows a summary of the correlation coefficients presented in Tables S2–S4 for each group of plant functional types (PFTs). Each class has between 6 and 22 sites. WECANN has the best mean within each PFT class, and the smallest variability in most of the classes for all three variables.

Figure 7 shows the comparison of monthly WECANN retrievals and three other global products' estimates with the tower estimates across five select sites that span a range of climatic and vegetation coverage conditions. At the Oklahoma agricultural site (US-ARM), H and LE are reproduced well, yet dry year H is underestimated (Fig. 7a). The GPP reported at the site very rapidly decays at the end of the spring, whereas the region is highly agricultural with sustained agriculture in the summer. The difference between the reported GPP and WECANN retrievals might again be due to the difference in the footprint of the two estimates.

At the Brasschaat, Belgium, site (BE-Bra) (Fig. 7b), LE is very well captured by WECANN, which captures the seasonal cycle well, yet misses some of the interannual variability. WECANN outperforms the other retrievals of LE and GPP and captures the GPP seasonal cycle very well compared to other products, which display a too-early GPP rise and overestimate summer GPP. Again, the SIF data provide independent useful data compared to other environmental information (radiation, temperature, vegetation indices) used by the other retrieval schemes. All retrievals strongly underestimate the reported eddy covariance H. At this humid site though, the magnitude of the measured H is often higher or on the same order in the summer as LE. Given the high degree of urbanization around the site, it is most likely a reflection of the footprint of the eddy covariance and the fact that it observes urbanized surfaces with high H. Indeed, the surface energy budget is not locally balanced and turbulent fluxes are higher than the observed net radiation minus ground heat flux.

At the cold Finland site (FI-Hyy), WECANN captures the seasonal cycle of GPP and LE very well, as well as H to a lesser extent. WECANN reproduces the seasonality, amplitude, and interannual variability better compared to other retrievals (Fig. 7c). It also reflects the difficulties of retrieving fluxes in snow-dominated regions. SIF has the great advantage that it is not directly sensitive to snow compared to vegetation indices, for instance, which incorrectly attribute snowmelt and changes in observed ground color to photosynthesis onset (Jeong et al., 2017).

At the monsoonal grassland site of Santa Rita, AZ, WECANN correctly captures the complex dynamics of H and LE at the site, with some rain periods preceding the monsoon period (Fig. 7d). However, WECANN slightly underestimates LE and overestimates GPP. In fact, all products overestimate GPP in the dry and cold seasons. The landscape in the region is highly heterogeneous, with denser vegetation in riparian zones, away from the tower location, which may explain the lower GPP value at the site compared to estimates of the larger-scale values.

Finally, at the South African Mediterranean site, ZA-Kru, WECANN reproduces some of the dynamics of the observed H, yet is typically smoother (Fig. 7e). It reasonably captures the LE dynamics, except for the suspect cold season increase reported at the tower in 2013 (like other products). All products overestimate the reported GPP, though WECANN is closest to the observations and captures the seasonal dynamics better compared to other products.

Overall, across the different sites, the WECANN retrieval performs better than other products, especially in terms of the seasonality of LE, H, and GPP. Several factors contribute to the improved retrieval of WECANN compared to other products, even at those smaller footprint sites. First, the SIF measurements that are directly correlated with GPP provide a better constraint on estimating LE, H, and GPP. The ANN approach in WECANN also uses a novel training technique based on probabilistically merging different datasets to remove outliers from its target dataset. Therefore, WECANN retrievals learn collectively from the different datasets (and remote sensing observations) and are closer to the truth than each of the individual target datasets.

In this section, we compare the WECANN-based estimates to other datasets used in the training to better understand how WECANN differs from those training data. Figure 8 shows the comparisons for LE and indicates that our product has a relatively similar R2 with the three products (R2=0.96 with FLUXNET-MTE and ECMWF and R2=0.94 with GLEAM). However, the scatter plot with FLUXNET-MTE is more concentrated and aligned along the 1:1 line, further emphasizing the consistency between the two datasets (RMSD of 6.42 W m-2 for FLUXNET MTE versus 8.47 and 9.72 W m-2 for GLEAM and ECMWF, respectively). Differences in spatial patterns shown in Fig. 8a–c reflect that WECANN exhibits smaller spatial differences with FLUXNET-MTE than GLEAM or ECMWF and such differences exhibit a narrower range between -10 and 10 W m-2. FLUXNET-MTE overestimates LE compared to WECANN in transitional tropical and subtropical regions and particularly over India, which are regions with few eddy covariance towers. GLEAM exhibits substantial differences with our product, particularly in regions dominated by seasonal water stress such as Brazilian savannas, the Horn of Africa, Central America, India, and the subtropical humid part of Africa south of the Congo. In the Sahel, GLEAM LE is higher than our estimate and FLUXNET-MTE. The LE estimate of ECMWF is nearly always higher than our estimate, with much higher values in the Congo, the Amazon, southern Brazil, and northern Canada. In Europe, where the ECMWF estimate should be best because of the frequent weather operational forecast checks and model adjustment in the region, the estimates are more similar. The differences and similarities of WECANN retrievals with the three target datasets are consistent with the error estimates from TC. For example, Fig. S4 shows that FLUXNET-MTE has the smallest error in LE estimates globally compared to GLEAM and ECMWF, other than across India. WECANN retrievals also have better agreement with FLUXNET-MTE.

The differences in H estimates are more complex (Fig. 9). First, the R2 values between WECANN and the other datasets are slightly lower than for LE. ECMWF and FLUXNET-MTE yield a higher R2 with WECANN (0.92) while GLEAM has an R2 of 0.87. GLEAM exhibits lower H in most of the NH, especially in seasonally dry regions, potentially due to its simple formulation of ground heat flux (G). H estimates are relatively higher over the Amazon and Congo but lower over Indonesia for GLEAM. In the southern Sahara and northern Sahel as well as in eastern Asia and Canada, GLEAM has lower H compared to WECANN and FLUXNET-MTE. ECMWF exhibits higher values in seasonal dry regions such as the western US, Brazilian savannas, southern Congo, and the Sahel compared to WECANN and smaller values in the Amazon, Indonesia, over desert areas of the Sahara and Arabian Peninsula, and Southeast Asia. The GLEAM and ECMWF H difference maps show many similar patterns: the Sahara, eastern Europe, and East Asia are underestimated, while southern Africa and the eastern part of the Amazon are overestimated. Similarly the errors patterns estimated from TC (Fig. S5) are consistent with the comparison of WECANN and the target datasets. Figure S5 shows that ECMWF has higher errors in the Sahel, southern Congo, and Brazilian savanna, and GLEAM has higher errors in the Amazon, East Asia, and Central Africa.

The comparison between the GPP estimates shows significant differences (Fig. 10). WECANN compares the best against FLUXNET-MTE (R2= 0.93), with MODIS (R2= 0.91) and ECMWF (R2= 0.90) following. While all three products have a similar R2, their spatial differences are distinct. In the Amazon, ECMWF and FLUXNET-MTE have larger GPP estimates compared to WECANN, while MODIS estimates are much smaller. In cold northern latitude regions of Siberia and northern Canada, all three products have a higher GPP than WECANN. In Congo, MODIS and FLUXNET-MTE have higher GPP, while ECMWF has a lower one. In central and the southwestern US, all three products tend to yield lower GPP. Comparison of these findings with the error estimates from TC (Fig. S6) shows that FLUXNET-MTE has the lowest errors globally, while ECMWF has the largest errors in the Amazon.

Finally, we compare annual anomalies of WECANN retrievals and the three training datasets globally and in different climatic zones. The zones are defined as polar (90–60∘ N), NH midlatitude (60–10∘ N), tropics (10–15∘ S), and SH midlatitude (15–60∘ S). Results are presented in Fig. S7. WECANN anomalies are derived from the mean values between 2007 and 2015. However, not all the training products are available for this period. Therefore, their anomalies are calculated from their respective temporal domain, which is 2007–2011 for FLUXNET-MTE, GLEAM, and MODIS and 2008–2011 for ECMWF. Anomalies from the four products have similar patterns in general, while their absolute values differ. Anomalies in GPP have better agreement across different products compared to LE and H. Evaluation of the discrepancies between these anomalies is beyond the scope of this paper and will be characterized in detail in a future study.

In order to further assess WECANN on regional scales, we analyze its capacity to capture extreme events. We thus selected three major heat wave and drought events that occurred during the temporal coverage of the WECANN product. These events are the 2010 Russia heat wave, 2011 Texas drought, and 2012 US Corn Belt drought. Figure 11 shows the percentage of average monthly anomalies with respect to mean values, for LE, H, and GPP, in each of the three cases. The patterns reveal significant anomalies in all fluxes, which is consistent with reported patterns. In summer 2010, a historical heat wave occurred over western Russia and resulted in an all-time maximum temperature record in many locations (Dole et al., 2011). The extent of reduction in LE and increase in H derived from WECANN retrievals is consistent with estimates reported in the literature (Lau and Kim, 2012), with a 10–15 % increase in H and a 15–20 % reduction in LE. In early 2011, drought conditions developed in the southern US, particularly in the states of Texas and Louisiana (Luo and Zhang, 2012). By April, most of Texas, Oklahoma, Louisiana, and Arkansas was classified in the D4 drought condition (exceptional drought), and the situation continued throughout the summer and fall of 2011 as reported by the US Drought Monitor (Svoboda et al., 2002). As Fig. 11 reveals, the same spatial pattern is pronounced in the monthly anomalies derived from WECANN retrievals, emphasizing massive reduction in LE and GPP accompanied by high H over the region.

Finally, an intense drought in the central US, particularly in the Corn Belt, occurred in 2012 and reduced maize yields by about 25 % and increased prices by 17–24 % (Boyer et al., 2013; USDA, 2013). By mid-September 2012 almost two-thirds of the continental US was covered by drought, and different parts of the US Corn Belt were categorized as either D3 (extreme drought) or D4 (exceptional drought) conditions. Figure 11 shows similar patterns in LE, H, and GPP, with a significant positive anomaly in H (∼ 20 %) and reductions in LE and GPP (∼ 20 %), consistent with crop yield decrease.

We also assess the accuracy of WECANN ET retrievals using ET estimates from the independent water budget closure model introduced in Sect. 2.3.2. The analysis is carried out for the years 2007 to 2010, which overlap between WECANN retrievals and the water budget closure study. Figure 12 shows the relative absolute difference in ET estimates from WECANN compared to the ET estimates from the water budget study for each of the five basins (mean value and 1 standard deviation across 48 months). Mean absolute differences vary between a low of 5 % in the Amazon and a larger 24 % value in Colorado, while the other three basins have mean differences of 9, 17, and 20 %. While the differences vary between a low and moderate range, it should be noted that the coarse spatial resolution of the WECANN product causes a difference in the spatial averaging to get the basin-level estimates of ET. Moreover, in the budget closure estimates only a single runoff (at the outlet of the considered basin) is used over the entire basin; therefore, large heterogeneous basins such as the Colorado and Mississippi have large uncertainties associated with them, as runoff does not correctly constrain the flux distribution over the entire basin. It is over those basins that the WECANN retrieval compares less favorably with these large-scale estimates. Downscaled version of those estimates would further help in the evaluation of ET products.

One of the advantages of a statistical retrieval algorithm, in particular of ANNs, is that the run time is extremely fast after the training step. This enables us to characterize the uncertainty of the retrievals by propagating the uncertainties in the input variables through the network. For this purpose, we set up a 10 000-bootstrap experiment and run the WECANN retrieval by adding error to input variables. The errors are normally distributed with a mean of zero and a standard deviation that depends on the input variable. For SIF, air temperature, and soil moisture, we use the error estimates or standard deviations reported in their associated products. These errors vary spatially and temporally and we used the associated value for each time and space data point. For net radiation, we use a constant standard deviation of 34.58 W m-2 based on the analysis by Pan et al. (2015). For precipitation and SWE estimates, we use a conservative 10 % of the estimates themselves as a standard deviation for error. For each bootstrap replicate, we sample from the error distribution of each input variable and add that to the input.

Figure 13 shows the results of the bootstrap for each of the LE, H, and GPP values globally and in different climatic zones (defined in Sect. 4.3). Each panel in Fig. 13 shows the uncertainty derived from the bootstrap experiment, relative to the interannual variability in the retrievals. GPP estimates are provided in units of petagrams of carbon per year as total productivity in each region. LE and H are provided in units of watts per square meter as an average rate of flux in each region.

On a global scale the GPP ranges between a minimum of 117.15 ± 2.379 PgC yr-1 in 2015 and a maximum of 124.82 ± 2.482 PgC yr-1 in 2007. Similarly, LE has a minimum of 37.40 ± 0.54 W m-2 in 2015 and a maximum of 38.33 ± 0.53 W m-2 in 2011. H has a maximum of 41.00 ± 0.54 W m-2 in 2015 and a minimum of 39.43 ± 0.52 W m-2 in 2011.

The interannual variations in surface fluxes and GPP show distinct patterns. For example, in the year 2015, which was an El Niño year, LE and GPP decreased notably, and H increased to an extreme value in the 9 years of the WECANN product. Moreover, from 2011 to 2015 both LE and GPP have a consistent decreasing trend on a global scale. The interannual variability in GPP and LE is similar on a global scale, while their regional patterns are different. For example, in the year 2015, GPP on a global scale and in all regions has decreased with respect to 2014, while LE in polar and NH mid-latitudes has increased, and LE on a global scale has decreased. As expected, the variability in LE and H is anticorrelated. We note that while WECANN is trained on three independent estimates of LE, H, and GPP, its interannual variability is driven by remote sensing observations that are input into the ANN.

Satellite SIF observations are relatively new and have not been previously used to estimate LE and H on a global scale. Therefore, we want to assess the information content of SIF observations in the WECANN retrievals by replacing them with more typical optical and/or near-infrared indices of vegetation (normalized difference vegetation index, NDVI, or enhanced vegetation index, EVI).

To do so, we trained two different ANNs with NDVI and EVI instead of SIF data on each of the three variables (LE, H, and GPP) and evaluated the retrievals against the same FLUXNET tower measurements used in Sect. 4.2 for evaluating WECANN retrievals. Tables S5–S7 show the results of evaluations of these three retrievals against the tower measurements for LE, H, and GPP. In terms of the correlation coefficient, on average all three retrievals have a relatively similar performance except in regions such as Spain where phenology (and incident radiation) is not the main contributor to the flux variability (ES-LgS). Indeed, in such regions, changes in canopy structure are more limited and changes in response to water stress (through changes in light- and water-use efficiency) are the primary reason for the seasonal variability. This emphasizes, similar to current thinking on the SIF signal, that the monthly SIF signal is dominated by incident radiation and canopy structure but that in some conditions light-use efficiency changes are detected by SIF but not optical vegetation indices (Lee et al., 2013). We also point out that current SIF retrievals (such as those from GOME-2 used here) are still noisy as they were not obtained by satellites designed to measure SIF. Future SIF-designated missions such as Fluorescence Explorer (FLEX) will have higher accuracy and finer spatial and temporal resolution (Drusch et al., 2016). We expect they will further enhance the retrievals of surface fluxes and GPP such as those from WECANN.