## Appendix A Methodological Detail
### Kriging and Trend-Surface-Only Prediction for Validation Comparisons
We model the spatial variation across the locations associated with \(\mathbf{R}_{a1}^{*(-A)}\) by the covariance matrix  
\[\mathbf{\Sigma}_{a1}^{\text{kr}}=\mathbf{C}_{a1}+\frac{\sigma_{\omega,1}^{2}} {\hat{S}_{R,1}^{2}}\mathbf{I}+\text{diag}(\mathbf{\sigma}_{e,a1}^{*}), \tag{12}\]  
where \(\mathbf{C}_{a1}\) is a 150 \(\times\) 150 covariance matrix having elements given by \(C_{1}(\cdot)\) from Equation (11) with estimated parameters \(\widehat{\theta}\) substituted in; \(\mathbf{I}\) is the 150 \(\times\) 150 identity matrix; \(\mathbf{\sigma}_{e,a1}^{*}\) is a 150-dimensional vector with elements \(\{\sigma_{e,a1}^{2}/\hat{S}_{R,1}^{2}:l=1,\dots,150\}\) corresponding to locations associated with \(\mathbf{R}_{a1}^{*(-A)}\); and \(\text{diag}(\mathbf{\sigma}_{e,a1}^{*})\) is a diagonal matrix with the elements of \(\mathbf{\sigma}_{e,a1}^{*}\) along the diagonal. Similarly, we define the vector \(\mathbf{c}_{a1}^{\text{kr}}\equiv\left(\text{cov}\left(\psi_{1}^{*}(\mathbf{s} _{a}),\;R_{a1l}^{*(-A)}\right):l=1,\dots,150\right)^{T}\), where  
\[\text{cov}\left(\psi_{1}^{*}(\mathbf{s}_{a}),\;R_{a1l}^{*(-A)}\right)=C_{1}(h_ {al})+\frac{\sigma_{\omega,1}^{2}}{\hat{S}_{R,1}^{2}}\mathbf{1}\{h_{al}=0\}, \tag{13}\]  
for \(h_{al}=||\mathbf{s}_{a}-\mathbf{s}_{l}||\), \(\mathbf{s}_{l}\) the spatial location associated with \(R_{a1l}^{*(-A)}\); \(||\cdot||\) denotes chordal distance; and \(\mathbf{1}\{\cdot\}\) is the indicator function. After updating through (see also Equations (11) and (12))\[\widehat{\psi}_{1}^{*(\mathrm{kr})}(\mathbf{s}_{a}) =\Big{(}\mathbf{c}_{a1}^{\mathrm{kr}}\Big{)}^{T}\Big{(}\mathbf{z}_ {a1}^{\mathrm{kr}}\Big{)}^{-1}\mathbf{R}_{a1}^{*(-A)}, \tag{11}\] \[MSPE\Big{(}\widehat{\psi}_{1}^{*(\mathrm{kr})}(\mathbf{s}_{a}) \Big{)} =\frac{\sigma_{\omega,1}^{2}}{\widehat{S}_{R,1}^{2}}+C_{1}(0)- \Big{(}\mathbf{c}_{a1}^{\mathrm{kr}}\Big{)}^{T}\Big{(}\mathbf{z}_{a1}^{\mathrm{ kr}}\Big{)}^{-1}\mathbf{c}_{a1}^{\mathrm{kr}}, \tag{12}\]  
we obtain the kriging validation prediction, \(\widehat{Z}_{1a}^{\mathrm{kr}}\), and its root-mean-squared prediction error, \(RMSPE\Big{(}\widehat{Z}_{1a}^{\mathrm{kr}}\Big{)}\), using Equations (13)-(15). It should be noted that the kriging predictor, \(\widehat{Z}_{1a}^{\mathrm{kr}}\), can be considered a special case of cokriging where the XCO\({}_{2}\) residuals, \(\mathbf{R}_{a2}^{*}\), are given zero weight; hence, kriging is a _simplification_ of cokriging. As a further simplification, the trend-surface-only prediction at validation location \(\mathbf{s}_{a}\in A\), \(\widehat{Z}_{1a}^{\mathrm{tr}}\), and the corresponding root-mean-squared prediction error, \(RMSPE\Big{(}\widehat{Z}_{1a}^{\mathrm{tr}}\Big{)}\), use only the SIF data \(\mathbf{Z}_{1}\) but assume no spatial dependence in \(\psi_{1}^{*}(\cdot)\). In particular, the trend-surface-only prediction is simply given by \(\widehat{Z}_{1a}^{\mathrm{tr}}=\widehat{\mu}_{1}(\mathbf{s}_{a})\), for \(a=1,\ldots,n_{A}\), where \(\widehat{\mu}_{1}(\cdot)\) is defined in Equation (4) when \(i=1\). Since the trend-surface-only predictions do not account for spatial dependence, their associated prediction errors depend only on the micro-scale variation \(\omega_{1}(\cdot)\) and the measurement errors \(\{\epsilon_{1a}\}_{a}\), and consequently the covariance as a function of distance from prediction location to data locations is identically zero. Recall that \(\omega_{1}(\cdot)\) is a process uncorrelated at the grid scale with mean zero and variance \(\sigma_{\omega,1}^{2}\), and that \(\{\epsilon_{1a}\}_{a}\) is a set of (non-stationary) independent measurement errors with mean zero and variances \(\{\sigma_{\epsilon,1a}^{2}\}_{a}\); see Equation (1). To obtain an estimate of \(\sigma_{\omega,1}^{2}\), we take an average of the squared residuals given in Equation (6). Define  
\[\widehat{\tau}_{1}^{2}\equiv\frac{1}{n_{1}}\sum_{l=1}^{n_{1}}R_{1I}^{*2}, \tag{13}\]  
which is an estimate of the total variation at data locations.