dataesr/scientific-paragraphs-categorization huggingface dataset:
This interpolator became the simulated sensor model, to which the uncertainties characterized in Section 2. 3. 1 were added to produce the Fitted Sensor Model. Very high spectral resolution radiances of the vegetation dataset were convolved using the spectral features simulated at different temperatures producing a retrieval dataset. As in Section 2. 3. 1, the spectral shift was applied to both radiance and irradiance fluxes on a separate basis and then simultaneously. For convenience, a T b of 20 • C was chosen to set the reference spectral features against which SIF retrievals at other temperatures were compared.
Radiometric Calibration Uncertainties In this Section, the relative radiometric calibration uncertainty (u rad ) of the high quality radiance standard, RASTA  [62] , was used to produce the characterization datasets. Radiometric calibration spectra and uncertainties were provided at relatively large spectral intervals (50 nm). Uncertainties were estimated for the whole sensor spectral range by applying a cubic spline interpolation (Figure  3 ). For comparison with uncertainties in Figure  3  notice that in the Vegetation Dataset F ↑ represents the 11. 13% and the 10. 88% of L ↑ app within the O 2 -B and the O 2 -A bands respectively. However, it must be highlighted that the uncertainty estimated in this exercise corresponds to a "best case" scenario, since it is associated with a high-quality standard and does not account for additional uncertainties also present in the calibration procedure.
Realistic cases may present higher values. Thirty radiance spectra with radiometric noise were generated using Monte Carlo sampling from a normal distribution of mean 0 and sigma (σ λ ) scaling with the radiance as σ λ = u rad λ •L λ. The Sensor Simulator optimized the integration time and added random noise to this signal as described in Section 2. 2, producing a Characterization Dataset. The radiometric calibration coefficients and the related uncertainties u g λ were obtained for each band solving g λ in Equation (  3 ). Henceforth, these coefficients and their uncertainties were used in the sensor simulator to convert N λ to L λ when generating other characterization datasets. Uncertainties were propagated via repeated realizations of the conversion including random noise in g λ produced by Monte Carlo sampling from a normal distribution of mean 0 and σ λ = u g λ.
The relative radiometric sensitivity to temperature (ℜT) was defined by the linear model coefficients from reference  [40]. These coefficients predict a given radiance as a function of temperature, which was assumed to correspond to the detector temperature, Td. ℜT corresponds to the ratio between the radiance predicted radiance at a given temperature to the radiance predicted at a reference temperature. The sensor used in reference  [40]  was different to the type of sensor simulated in the present study, but also made of Silicon, thus we assumed that it was a suitable approximation representing changes in Silicon photo-response with temperature. These coefficients were interpolated via cubic splines to the spectral bands of the sensor simulator. The characterization dataset was produced by generating radiances between -10 and 40 °C at 10 °C steps from the interpolated coefficients.
These coefficients were interpolated via cubic splines to the spectral bands of the sensor simulator. The characterization dataset was produced by generating radiances between -10 and 40 • C at 10 • C steps from the interpolated coefficients. RASTA spectral radiance was not used in this case, but RASTA uncertainties were added to these radiances as described in Section 2. 3. 3. These radiances were then processed by the sensor simulator to propagate sensor random noise and radiometric calibration uncertainties. We added also a 2% relative uncertainty to the temperature sensor; which is within the range of uncertainties found in the experiment described in Section 2. The Fitted Sensor Model predicted T between -10 and 40 • C at 10 • C steps. T predictions and propagated uncertainties were used to bias the vegetation dataset therefore producing the retrieval dataset.
Non-Linearity A synthetic simulated sensor model representing grey-level related non-linearity ( N )  [50]  was generated using the non-linearity coefficients of a QE Pro spectroradiometer. The characterization dataset was produced from the RASTA radiance spectra. First, the sensor simulator optimized t int at the saturation level (scaled value: 200,000 DN). In the next step, the observations of this radiance were generated as in previous sections, reducing the optimized t int by the following factors: 1. 000, 0. 975, 0. 950, 0. 900, 0. 850, 0. 800, and then up to, 0. 100 with 0. 100 steps. Thirty realizations with random noise of different uncertainties were produced for each t int. The sensor simulator converted L λ to N λ. We then used the simulated sensor model to bias N λ as a function of the digital value in DN, producing in this way the characterization dataset.
N was calculated as the rate (N λ -N 0λ )/t int -a variable proportional to L λ (Equation (  3 ))- normalized by the maximum value of this rate found in each pixel  [51]. In order to reduce the effect of noise on the calculation of N , we used the averaged radiance of the 30 samples produced at each t int to compute the maximum rate (N λ -N 0λ )/t int. Next, a 7th degree polynomial was fitted to predict N as a function of N scaled ; where N scaled is N λ -N 0,λ scaled after subtracting the mean and dividing by the standard deviation to prevent bad conditioning  [63]. Figure  4  shows the simulated and fitted sensor models. Remote Sens. 2019, 11, 960 10 of 29 random noise of different uncertainties were produced for each tint. The sensor simulator converted Lλ to Nλ. We then used the simulated sensor model to bias Nλ as a function of the digital value in DN, producing in this way the characterization dataset.
ℜ N was calculated as the rate  -  ⁄ -a variable proportional to Lλ (Equation (3)normalized by the maximum value of this rate found in each pixel  [51]. In order to reduce the effect of noise on the calculation of ℜ N , we used the averaged radiance of the 30 samples produced at each tint to compute the maximum rate  -  ⁄. Next, a 7th degree polynomial was fitted to predict ℜN as a function of Nscaled; where Nscaled is Nλ -N0,λ scaled after subtracting the mean and dividing by the standard deviation to prevent bad conditioning  [63]. Figure  4  shows the simulated and fitted sensor models. Once characterized, the fitted sensor model was applied to the vegetation dataset. First, the sensor simulator optimized tint according to L ↑ app and L ↓ tot spectra of the vegetation dataset. Then radiances in the vegetation dataset were modified by a factor (fL) of 0.
20, 0. 40, 0. 60, 0. 80, 1. 00, 1. 02, 1. 06 and 1. 10. Scaled radiances were transferred to the sensor simulator, which, without modifying the value of the optimized tint, transformed Lλ to Nλ. The digital signal Nλ was biased (and noised) by the fitted sensor model and converted back to Lλ units to produce the retrieval dataset.
Directional Response Characterization The characterized DR of an opaline glass cosine diffuser (Ocean Optics, Dunednin, FL, USA)  [53]  was used as the base to generate a simulated sensor model. A 4th degree polynomial was fitted for each illumination angle simulated in the experimental data to smooth the response. Cubic spline interpolation was used subsequently to predict the DR at the spectral bands of the simulated sensor at different illumination angles (θs), which became the Simulated Sensor Model (DRsim,λ). A synthetic dataset for the characterization of DR was generated using RASTA radiance for θs equal 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, 80° and 85°. An absolute uncertainty of 0. 25° was assumed for these angles. For each of them, we produced 30 synthetic radiance spectra including random noise corresponding to lamp, calibration and sensor simulator uncertainties.
This was the characterization dataset. Then we computed the relative deviation of irradiance (assuming  =   ⁄ ) from of the cosine response ( ) as follows: Once characterized, the fitted sensor model was applied to the vegetation dataset. First, the sensor simulator optimized t int according to L ↑ app and L ↓ tot spectra of the vegetation dataset. Then radiances in the vegetation dataset were modified by a factor (f L ) of 0. 20, 0. 40, 0. 60, 0. 80, 1. 00, 1. 02, 1. 06 and 1. 10. Scaled radiances were transferred to the sensor simulator, which, without modifying the value of the optimized t int , transformed L λ to N λ. The digital signal N λ was biased (and noised) by the fitted sensor model and converted back to L λ units to produce the retrieval dataset. 𝛽 = , • , , • , • , (5).
Directional Response Characterization The characterized DR of an opaline glass cosine diffuser (Ocean Optics, Dunednin, FL, USA)  [53]  was used as the base to generate a simulated sensor model. A 4th degree polynomial was fitted for each illumination angle simulated in the experimental data to smooth the response. Cubic spline interpolation was used subsequently to predict the DR at the spectral bands of the simulated sensor at different illumination angles (θ s ), which became the Simulated Sensor Model (DR sim,λ ). A synthetic dataset for the characterization of DR was generated using RASTA radiance for θ s equal 0 • , 10  , 70 • , 80 • and 85 •. An absolute uncertainty of 0. 25 • was assumed for these angles. For each of them, we produced 30 synthetic radiance spectra including random noise corresponding to lamp, calibration and sensor simulator uncertainties.
This was the characterization dataset. Then we computed the relative deviation of irradiance (assuming L λ = E λ /π) from of the cosine response (β λ ) as follows: β λ = L 1,λ •DR sim,λ -L 2,λ • cos θ s L 2,λ • cos θ s , (4) where L 1,λ and L 2,λ represent RASTA radiances at θ s = 0 • but with different random uncertainties. Figure  5a  presents the simulated DR function versus θ s at different wavelengths, and compares them with the cosine response. As can be seen, the simulated sensor model overestimates irradiance at short wavelengths and θ s ; and underestimates it at large θ s and wavelengths. Figure  5b  shows the relative deviation of the cosine response corresponding to the DR curves in the contiguous subplot. β λ strongly decreases when θ s becomes larger than 70 • ; which is in part explained by the low values of cos θ s at large angles (Equation (  4 )).
Low cos θ s values make β λ also very sensitive at to uncertainties at large θ s. However, no measurements for SIF retrieval are expected to be reliable at such angles and in the case of the diffuse radiation coming from this angular region, the overall effect is expected to be low since the contribution of diffuse irradiance to the signal is also weighted by cos θ s (Equation (  5 )). Fitted sensor model parameters and uncertainties were estimated for each band by fitting a 6th degree polynomial on the characterization dataset, describing β λ as a function of θ s. Remote Sens. 2019, 11, 960 11 of 29 relative deviation of the cosine response corresponding to the DR curves in the contiguous subplot. strongly decreases when θs becomes larger than 70°; which is in part explained by the low values of cos  at large angles (Equation (  5 ).
Low cos  values make βλ also very sensitive at to uncertainties at large θs. However, no measurements for SIF retrieval are expected to be reliable at such angles and in the case of the diffuse radiation coming from this angular region, the overall effect is expected to be low since the contribution of diffuse irradiance to the signal is also weighted by cos  (Equation (  6 )). Fitted sensor model parameters and uncertainties were estimated for each band by fitting a 6th degree polynomial on the characterization dataset, describing  as a function of θs. The fitted sensor model was used to bias and noise E ↓ tot in the vegetation dataset using the approach in reference  [54]. The vegetation dataset was generated from the Matrix-Operator Model (MOMO) irradiance spectra provided at θs = 0. 00°, 2.
61 mW/m 2 /sr/nm to 0. 19 mW/m 2 /sr/nm in the O2-A band. For each wavelength and solar angle, the fitted sensor model predicted the relative deviation from the cosine response  -which was the factor biasing E ↓ dir-, and the related uncertainties. Similarly, the mean cosine-weighted response error αλ, Equation (  6 ) was computed to bias the diffuse flux, E ↓ diff, which was always assumed isotropic. 𝛼 = 𝛽 𝜃 ) 𝜇 𝑑𝜃𝜇 , ( 6 ) where μs is cos. E ↓ tot in the retrieval dataset (E ↓ tot,DR ) was computed as (Equation (  7 ): The fitted sensor model was used to bias and noise E ↓ tot in the vegetation dataset using the approach in reference  [54]. The vegetation dataset was generated from the Matrix-Operator Model (MOMO) irradiance spectra provided at θ s = 0. 00  ; and L ↑ app and F ↑ were generated as described in Section 2.
Similarly, the mean cosine-weighted response error α λ , Equation (  5 ) was computed to bias the diffuse flux, E ↓ diff , which was always assumed isotropic. 𝐸 , ↓ = ↓ • • , (7) α λ = 0 1 β λ (θ s )µ s dθµ s , (5) where µ s is cos θ s. E ↓ tot in the retrieval dataset (E ↓ tot,DR ) was computed as (Equation (  6 )): E ↓ tot,DR = E ↓ tot 1 -β λ • f dir -α λ • f diff , (6).
Uncertainty Estimation and Propagation Uncertainties in the sensor simulator and the radiance sources were assumed to be uncorrelated and were propagated via a Monte Carlo approach. In order to generate the characterization datasets, we simulated 30 experimental replicates of each observation, adding normal noise to the different quantities or parameters involved in their computation: radiances, radiometric calibration coefficients, dark current, temperature sensors, illumination angle, etc. Fitted sensor model parameters and related uncertainties were estimated by fitting different models to the characterization datasets. Uncertainties were summarized by the covariance matrix of the parameter estimators (Cov p ), which was linearly approximated as Equation (  7 ): Cov p ≈ MSE•                J T                1 σ 2 meas,1.
1 σ 2 meas,n                J                -1 (7) where MSE is the Mean Squared Error, J is the Jacobian matrix evaluated at the solution of the model inversion, and superscript T stands for transposed. J is a matrix of n observations and m parameters. Cov p allowed uncertainty propagation following the approach in reference [64]. To do so, each time the fitted sensor model was used to predict sensor responses affecting the vegetation dataset, we generated 500 realizations of the model parameters sampling from multivariate normal distributions centered on the parameters values and constrained by Cov p. Therefore, the retrieval datasets presented 500 spectra per simulated observation from which F ↑ was estimated.
Spectral Calibration Uncertainties Uncertainties in the location of λ c and size of FWHM were 0. 59•10 -3 nm and 1. 34•10 -3 nm, respectively. These values describe the incertitude on the determination of these parameters; they do not represent a difference between the nominal and the characterized features or any variation induced by external factors. These uncertainties led to very small errors in the retrieved SIF. In the O 2 -A band, the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) were both 0. 003 mW/m 2 /sr/nm; whereas in the O 2 -B band MAE and RMSE were 0. 008 mW/m 2 /sr/nm and 0. 010 mW/m 2 /sr/nm, respectively. Absolute errors were always lower than 0. 020 mW/m 2 /sr/nm (95% confidence interval). Figure  6  shows the difference between F ↑ retrieved from the Retrieval Dataset and simulated in the Vegetation Dataset (∆F ↑ = F ↑ ret -F ↑ sim ) in the two O 2 bands.
Temperature-Induced Changes in Photo-response Figure  10  shows the predicted ℜT used to modify L ↑ app and L ↓ tot in the Vegetation Dataset As can be seen, ℜT ~ 0 around 764. 4 nm, decreased with increasing Td for shorter wavelengths and increased at higher wavelengths. In the simulated Td range of explored temperatures, average predicted ℜT ranged between 0. 996 and 1. 000 in the O2-A band, and between 0. 954 and 1. 000 O2-B band. Table  A2  compares F ↑ and the R RRMSE with and without uncertainty propagation. RRMSE are lower and most similar between F ↑ and R when the spectral variations equally affect both fluxes. Otherwise there are much larger relative errors in the retrieved F ↑. In most of the cases, model uncertainties increased RRMSE.
Temperature-Induced Changes in Photo-Response Figure  10  shows the predicted T used to modify L ↑ app and L ↓ tot in the Vegetation Dataset As can be seen, T ~0 around 764. 4 nm, decreased with increasing T d for shorter wavelengths and increased at higher wavelengths. In the simulated T d range of explored temperatures, average predicted T ranged between 0. 996 and 1. 000 in the O 2 -A band, and between 0. 954 and 1. 000 O 2 -B band. Table  B2  compares F ↑ and the R RRMSE with and without uncertainty propagation. RRMSE are lower and most similar between F ↑ and R when the spectral variations equally affect both fluxes. Otherwise there are much larger relative errors in the retrieved F ↑. In most of the cases, model uncertainties increased RRMSE.
Temperature-Induced Changes in Photo-response Figure  10  shows the predicted ℜT used to modify L ↑ app and L ↓ tot in the Vegetation Dataset As can be seen, ℜT ~ 0 around 764. 4 nm, decreased with increasing Td for shorter wavelengths and increased at higher wavelengths. In the simulated Td range of explored temperatures, average predicted ℜT ranged between 0. 996 and 1. 000 in the O2-A band, and between 0. 954 and 1. 000 O2-B band. Figure  11  shows ∆F ↑ induced by temperature dependence of detector responsivity, the impact of T was low in both O 2 bands. Dispersion induced by propagated uncertainties is presented in boxes. For comparison, the errors induced by the Fitted Sensor Model with no propagation of uncertainties are shown in circles. Median ∆F 687 ↑ (Figure  11a ) was inversely related to T d , ranging between 0.
We simulated observations of a sensor not optimizing integration time under varying radiation levels, and SIF relative errors ranged between 10-15% still at the optimization level (Figure  12 , Table  A4 ). During the simulation of the non-linearity characterization, we found a misfit between the simulated and the fitted sensor model, which overestimated non-linearity in the extremes of the radiometric range of the sensor (Figure  4 ). Inaccuracy of the polynomial fit might be in part induced by noise present in the characterization dataset and by the inherent sensitivity of the method to random noise. This is because the highest photo-response used to normalize the rate of DN/ms can often be found in the noisiest measurements  [50, 51]. A second reason could be the heterogeneous distribution of the data, which prioritizes the fitting in the central region of the radiometric range, but not in the extremes.
Alternatively, diffuse irradiance could be assumed isotropic and estimated inverting atmospheric radiative transfer codes from the observed down-welling irradiance  [68]. Furthermore, the consequences of such an assumption on the retrieval of SIF are still not well understood. In practice, diffusers and panels featuring DR close enough to the cosine response would be preferable if this allowed avoiding any correction; however this point remains to be validated. DR characterization and the framework of uncertainty propagation provided in this article might also help to stablish θ s and diffuse fraction thresholds above which SIF retrievals cannot be trusted. The fraction of diffuse irradiance is usually low in remote sensing applications (cloudy data are discarded), but can be large in the case of automated proximal sensing  [36].
Acknowledgments: Authors are grateful to the  COST Action ES1309  " Innovative optical Tools for proximal sensing of ecophysiological processes " (OPTIMISE) for their primacy in facilitating the scientific networking that resulted in this work. We are also grateful to  FLUSS project (Atmospheric Corrections for Fluorescence Signal and Surface Pressure Retrieval over Land ) and the  Freie Universität Berlin  for providing the very high spectral resolution dataset generated with MOMO. We also acknowledge  COST Action   CA17134  " Optical synergies for spatiotemporal SENsing of Scalable ECOphysiological traits" (SENSECO)  for its support on networking and dissemination.
Study Area, Climate Data, and Vegetation Mapping This study was conducted in Aosta Valley, an inner-alpine valley located in north western Italy. The large elevation range between 300 and 4800 m (mean: 2100 m), over a relatively small surface (3262 km 2 ), produces steep temperature gradients, with mean annual temperatures of 14 • C at 500 m down to -3 • C at 3000 m for the period 2000-2018. The continental character of the valley results in pronounced precipitation gradients, with cumulative values of more than 1800 mm year -1 in peripheral areas (west and south-east boundaries), and local minima of 500 mm year -1 in the center of the region. Daily gridded temperature, precipitation, and evapotranspiration data at 100 m spatial resolution were used as climatic descriptors for the period 2000-2018.
Precipitation and temperature are derived from geostatistical interpolation of ground data from the regional network of automatic weather stations  [26]. Daily temperature (precipitation, evapotranspiration) maps were averaged (cumulated) to a long-term annual product, as well as seasonally, considering meteorological seasons. A simplified water balance was estimated as the difference between precipitation and evapotranspiration. Evapotranspiration was computed using the hydrological model Continuum  [26, 27]. The model is distributed and solves the conservation equation for mass and energy at the soil on a regular grid with 100 m resolution. It estimates latent and sensible heat fluxes using a bulk transfer approach based on bulk transfer formula  [28]. It is used operationally in the region for flood forecasting and water managements.
Maps of snow water equivalent (SWE, 500 m spatial, 15 days temporal resolution) were obtained from a statistical model combining MODIS snow covered area, snow depth data from a ground meteorological network, manual SWE measurements, and topographical attributes in a multiple-regression-krieging framework. These data were used to describe the snow climatology of the study area, by means of two average maps: mean maximum SWE and mean snow melt date for the period 2002-2018. Vegetation types were mapped by photo-interpretation of aerial photographs collected in the years 2005 and 2006. Vegetation mapping was performed according to the habitats defined in Annex I of the Habitats Directive  [29]  and described in detail in  [30]. The final product, digitized in the form of polygons at a scale ranging between 1:5000 and 1:10,000, was then rasterized at 250 m to match the spatial resolution of the satellite products.
Satellite Data All satellite data cover the period from February 2000 to December 2018. MODIS Terra surface reflectance images (MOD09Q1) collection 6 at 250 spatial and 8 days temporal resolution  [31]  were downloaded from National Aeronautics and Space Administration (NASA) ftps using the MODIStsp R package  [32]. The same was used to compute NDVI maps, which were then masked according to the MOD09Q1 quality flags; only pixels classified as of "best quality" were retained. NDVI was preferred over the enhanced vegetation index (EVI) for consistency with the majority of studies on global greening trends, which considered NDVI only. The MOD10A2 collection 6 snow covered area (SCA) standard product was also downloaded and re-sampled at 250 m spatial resolution using the nearest neighbor interpolation method.