# Measurement of Diurnal Variation in Needle PRI and Shoot Photosynthesis in a Boreal Forest
## 1 Introduction  
Successful quantification of the terrestrial carbon cycle requires determination of the efficiency with which the absorbed photosynthetically active radiation (PAR) is utilized in the fixation of carbon by plants [1; 2]. This efficiency, known as the light use efficiency (LUE), depends on the amount of vegetation cover and is constrained by various environmental factors, such as temperature and the availability of water. Commonly, the constraints are inferred from climatological or meteorological data. However, remote sensing of LUE, or its variations with time, could improve global estimations of photosynthetic productivity [1]. Although many unresolved issues exist, a potential tool for achieving this is the photochemical reflectance index (PRI) [3; 4], a narrowband spectral index which can be easily calculated from remotely sensed data. It is defined as follows [5]:  
\[\text{PRI}=\frac{R(531)-R(570)}{R(531)+R(570)} \tag{1}\]  
where \(R(\lambda)\) is the reflectance at the wavelength \(\lambda\) given in nanometers. PRI depends explicitly on the fraction of absorbed PAR that is dissipated as heat [6] and its use has been shown to improve the estimates of carbon fluxes in leaves and canopies using remotely-sensed data [7; 8]. Recently, the power of this index has been demonstrated empirically using MODIS ocean band 11 (526-536 nm) [9; 10] and has been shown to be a useful proxy for tracking phenology in the boreal ecosystem [10]. MODIS is currently the only space-based instrument which is providing global data in this spectral region on a near daily basis. Although MODIS lacks the reference band at 570 nm, it has been demonstrated that other spectral channels have been successfully used [9; 11; 12], for example, those at 551 and 667 nm. Furthermore, hyperspectral missions which fully satisfy the spectral requirements for calculating PRI are under preparation at the ESA [6] and NASA [13]. Two types of leaf PRI changes with time can be distinguished [14; 15; 16]: constitutive and facultative ones. Constitutive changes, also referred to as sustainable, occur on a time scale of weeks to months and are associated with pigment pools [17; 18]. The reversible facultative changes are caused by the interconversion of xanthophyll cycle pigments [15] and occur on time scales from seconds to hours. Due to the involvement of xanthophylls in non-photosynthetic quenching of absorbed PAR, facultative PRI changes are directly related to LUE. The link between PRI and LUE, therefore, provides an opportunity to improve the mapping of carbon sequestration by vegetation from remote sensing data. The processes involved are extensively documented in the literature and the reader is referred to [PERSON] et al. [7] and [PERSON] et al. [19]. Earth observation satellites are mostly in sun-synchronous orbits and revisit each location at a specific and constant local time. The power of satellite-measured PRI in measuring terrestrial photosynthesis, compared with other narrowband spectral indices, lies in its ability to capture dynamic changes in LUE. However, to relate remotely-detected changes in instantaneous photosynthetic downregulation to changes in daily or seasonal productivity, the daily baseline curve for PRI (or, equivalently, LUE) is one of the variables that needs to be known for the observed vegetation type. The need to take into account the daily cycle of forest PRI for an improved remote estimate of LUE was recently demonstrated using the two satellites with the MODIS sensor on Aqua and Terra, with different overpass times [9]. The remotely-sensed PRI values corresponding to a specific vegetation type is strongly affected by vegetation structure, observation geometry and the spectral composition of diffuse sky radiation [9; 20; 21; 22; 23; 24; 25] and, hence, not direct measures of leaf PRI.