Data assimilation of photosynthetic light-use efficiency using multi-angular satellite data: I. Model formulation

Forest photosynthetic exchange rates at landscape scales have proven difficult to either accurately measure or estimate. Recent developments (Hall et al., 2011, 2008; Hilker et al., 2011a, 2010a) permit us to infer photosynthetic forest light use efficiency ($\epsilon$) using multi-angle measurements of photochemical reflectance index (PRI) from the CHRIS/PROBA satellite imaging spectrometer, thus completing a long sought-after capability to remotely sense the major inputs driving gross primary production GPP i.e., $\epsilon$ and absorbed photosynthetically active radiation (APAR). In this first of two companion papers we introduce the theoretical underpinnings of an innovative approach that utilizes our recent developments to produce remotely sensed and spatially explicit maps of $\epsilon$ and GPP from space, and a data assimilation approach to extend the spatially explicit maps to diurnal, daily and annual time scales. We quantify GPP using the traditional radiation-limited approach of Monteith (1972); however we apply it in an innovative way. [I] Using CHRIS/PROBA we quantify $\epsilon$ at each satellite overpass for a 625km2 area at 30m resolution. [II] We use a novel physiologically-based multivariate function of APAR, temperature and water vapor pressure deficit model (described herein) and use it to down-regulate $\epsilon$ at 30 minute intervals. [III] We use the CHRIS/PROBA images of spatial variation in $\epsilon$, and NDVI to quantify APAR, hence produce snapshots of GPP. We use a data assimilation approach to extend $\epsilon$ and GPP to temporally continuous and spatially contiguous maps of vegetation carbon uptake. In the second part of this study (Hilker et al., 2011b) we demonstrate and validate our approach over eight different forest flux tower sites in North America