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u ≤ -v	daylength=0
-v<u<v	daylength=24 · arccos(-u/v) · 1/π
u ≥ v	daylength=24

PAR is Photosynthetically Active Radiation [Wm^-2]. It is assumed to be 50% of shortwave incoming solar radiation (Prentice et al., 1993; Haxeltine and Prentice, 1996).
FPAR is the Fraction of absorbed PAR, dimensionless [0-1]
APAR = PAR · FPAR

according to Prentice et al. 1993, daily short-wave radiation is
and par is
,
because

in LPJmL code is implemented as:

u ≤ -v	par=0
-v<u<v	par=w · (u · arccos(-u/v)+v · sin(arccos(-u/v))) · k
u ≥ v	par=w · u · π · k

The evapotranspiration rate from a reference surface, not short of water, is called the reference crop evapotranspiration or reference evapotranspiration and is denoted as ET0. The reference surface is a hypothetical grass reference crop with specific characteristics. The use of other denominations such as potential ET is strongly discouraged due to ambiguities in their definitions (however in LPJmL it is called potential ET, and in this page as well : ) ). The concept of the reference evapotranspiration was introduced to study the evaporative demand of the atmosphere independently of crop type, crop development and management practices (Allen et al., 1998).

Meteorologists have developed a wide variety of formulae for estimating Potential Evapotranspiration (e.g., Thornthwaite, 1948; Penman, 1948; Turc, 1954; Priestley and Taylor, 1972), based entirely on weather variables (Jarvis and McNaughton, 1986).

In LPJmL code, pet (kg H₂O m^^-2 d^-1 or mm d^-1) equation is in the form of the Priestley-Taylor equation:

Where γ_t (Pa K^-1) is the psychrometer constant, approximately 65 Pa K^-1; λ (J kg^-1) is the latent heat of vaporization of water, approximately 2.5 times 10^6 J kg^-1; par (MJ d^-1) is multiplied by 2, because it is assumed to be 50% of shortwave incoming solar radiation (2 · par = rs_day, daily total net radiation flux); s (Pa K^-1) is the rate of increase of saturated vapor pressure with temperature T, computed as:

source:trunk/src/numeric/petpar.c

source:trunk/src/soil/waterbalance.c
source:trunk/src/lpj/interception.c

Evapotranspiration about actual evapotranspiration (AET)

Priestley, C. H. B., & Taylor, R. J. (1972). On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly weather review, 100(2), 81-92.

Jarvis, P.G., McNaughton, K.G. (1986). Stomatal control of transpiration: scaling up from leaf to region. Advances in ecological research 15, 49.

Prentice, I. C., Sykes, M. T., & Cramer, W. (1993). A simulation model for the transient effects of climate change on forest landscapes. Ecological modelling, 65(1), 51-70.

Monteith, J. L. (1995). Accommodation between transpiring vegetation and the convective boundary layer. Journal of Hydrology, 166(3), 251-263.

Haxeltine, A., & Prentice, I. C. (1996). BIOME3: An equilibrium terrestrial biosphere model based on ecophysiological constraints, resource availability, and competition among plant functional types. Global Biogeochemical Cycles, 10(4), 693-709.

Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. FAO, Rome, 300(9), D05109. (http://www.fao.org/docrep/x0490e/x0490e04.htm).

Sitch, S., Smith, B., Prentice, I. C., Arneth, A., Bondeau, A., Cramer, W., … & Venevsky, S. (2003). Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model. Global Change Biology, 9(2), 161-185.

Gerten, D., Schaphoff, S., Haberlandt, U., Lucht, W., Sitch, S. (2004). Terrestrial vegetation and water balance—hydrological evaluation of a dynamic global vegetation model. Journal of Hydrology 286, 249–270. doi:10.1016/j.jhydrol.2003.09.029