## 1 Introduction  
Accurate estimates of Gross Primary Production (GPP, i.e., an ecosystem's ground-area based photosynthetic rate) are needed to better assess ecosystem function and stress, as well as the role of terrestrial ecosystems in the global carbon cycle [1]. The eddy covariance technique provides a relatively direct measure of GPP at scales of a few hundred meters, but the cost and time required to operate eddy covariance sites precludes the deployment of the large network of homogenously-instrumented towers needed to accurately sample global GPP. Remote sensing provides a cost-effective strategy to extrapolate the GPP observations from eddy covariance towers to larger spatial and longer temporal scales. Remote sensing approaches for GPP extrapolation range from simple empirical relationships to complex models [2; 3]. Recent developments using Solar-Induced Fluorescence (SIF) provide a promising approach for extrapolating GPP [4], but the satellite records required for SIF retrieval are brief and/or at coarse spatial resolution (a few years at 10 km or larger; longer at coarser resolution). Vegetation Indices (VIs) provide an alternative, simple approach to extrapolate GPP, which often performs as well as comparatively complex strategies [5; 6; 7; 8; 9]. Time series of satellite-based VI observations extend back to at least the mid-1980s, and are available at high spatial (30 m) and temporal resolution (bi-weekly to daily), providing a useful tool for exploring GPP. Previous analyses have shown strong correlations between selected VIs and GPP, and the resulting empirical relationships are frequently used to extrapolate GPP [5; 6; 8; 10]. Vegetation Indices have been shown to respond to ecosystem attributes such as Leaf Area Index (LAI), fractional vegetation cover and light interception, chlorophyll density and leaf morphology [11; 12], which are also related to GPP [13; 14; 15], but current understanding is mostly qualitative and often links VIs to poorly defined concepts such as \"greening\" [16; 17]. The quantitative, mechanistic linkages between VIs and GPP remain inadequately understood and publications that trace the causal chain from VIs to spectral reflectance to ecosystem biophysical properties to ecosystem metabolism are surprisingly sparse. Moreover, hundreds of alternative VIs have been proposed over the last decades ([[https://www.indexdatabase.de/](https://www.indexdatabase.de/)]([https://www.indexdatabase.de/](https://www.indexdatabase.de/))), raising questions about whether the current knowledge is sufficient to fully understand the advantages and disadvantages of various VIs, and underscoring the need for more detailed efforts to explore and compare the links between VIs, ecosystem biophysical properties and GPP. Several key issues remain unresolved, especially related to the mechanisms that link VIs and GPP, and the implications of these mechanisms for the interpretation, generality, advantages, and limitations of specific VIs. We explored these issues for three commonly used VIs: the Normalized Difference Vegetation Index (NDVI), the Enhanced Vegetation Index (EVI), and the Near Infrared Vegetation (NIR\({}_{\text{v}}\)) index:  
\[NDVI\ =\ \frac{NIR-Red}{NIR+Red} \tag{1}\]  
\[EVI\ =\ 2.5\frac{NIR-Red}{NIR+6\cdot Red-7.5\cdot Blue+1} \tag{2}\]  
\[NIR_{v}\ =\ NDVI\text{-}NIR \tag{3}\]  
where _Blue_, _Red_, and _NIR_ refer to the reflectance in the blue, red, and Near InfraRed (NIR) wavelengths. Currently, there is no consensus on which of these VIs provides the most universal predictions of GPP, with some studies showing stronger relationships with EVI and NIR\({}_{\text{v}}\)[5; 6; 7; 18] while others suggest that no single vegetation index performs best in all cases and that relationships are site-specific [8; 10]. Likewise, understanding of the causal links between these VIs and GPP remains incomplete, and tends to emphasize the importance of LAI, with less attention to a VI's sensitivity to biophysical attributes related to leaf level metabolism.