Update leaf maintenance respiration section to include Atkin et al. 2017 model

docs/source/CLM50_Tech_Note_References.rst

@@ -127,6 +127,18 @@ studies, Ecological Applications, 14, 280-298, 10.1890/01-6019.
 Asner, G. P., Knapp, D. E., Broadbent, E. N., Oliveira, P. J. C., Keller, M., and Silva, J. N. 2005.
 Selective Logging in the Brazilian Amazon, Science, 310, 480.
 
+
+.. _atkin2017:
+
+|br|
+
+Atkin, O.K., Bahar, N. H. A., Bloomfield, K.J., Griffin, K.L., Heskel, M.A., Huntingford, C., 
+Martinez de la Torre, A., Turnbull, M.H.,. 2017. Leaf Respiration in Terrestrial Biosphere Models. In: 
+Tcherkez, G., Ghashghaie, J. (eds) 
+Plant Respiration: Metabolic Fluxes and Carbon Balance. Advances in Photosynthesis and Respiration, 
+vol 43. Springer, Cham. 10.1007/978-3-319-68703-2_6
+
+
 .. _Atondo-Bueno2016:
 
 |br|
@@ -149,12 +161,6 @@ fertilization. Tree Phys. 2:189-204.
 
 Atkin OK, Bloomfield KJ, Reich PB, Tjoelker MG, Asner GP, Bonal D et al (2015) Global variability in leaf respiration in relation to climate, plant functional types and leaf traits. New Phytologist 206:614–636
 
-.. _Atkin2017:
-
-|br|
-
-Leaf Respiration in Terrestrial Biosphere Models. In Plant Respiration: Metabolic Fluxes and Carbon Balance, Advances
-in Photosynthesis and Respiration 43, G. Tcherkez, J. Ghashghaie (eds.) Springer International Publishing AG 2017
 
 .. _BadgerandDirmeyer2015:
 
@@ -1090,6 +1096,17 @@ Henderson-Sellers, A., Yang, Z.-L., and Dickinson, R.E. 1993. The
 project for intercomparison of land-surface parameterization schemes.
 Bull. Amer. Meteor. Soc. 74: 1335-1349.
 
+.. _Heskel2016:
+
+|br|
+
+Heskel, M.A. O'Sullivan, O.S., Reich, P.B., Tjoelker, M.G., Weerasinghe, L.K., Penillard, A., 
+Egerton, J.J.G., Creek, D., Bloomfield, K.J., Xiang, J., Sinca, F., Stangl, Z.R., Martinez de la Torre, A., 
+Griffen, K.L., Huntingford, C., Hurry, V., Meir, P., Turnbull, M.H., Atkin, O.K. .2016.
+Convergence in the temperature response of leaf respiration across biomes and plant functional types. 
+Proc. Natl Acad. Sci. USA 113, 3832–3837.
+
+
 .. _HostetlerBartlein1990:
 
 |br|

docs/source/fates_tech_note.rst

@@ -1957,8 +1957,57 @@ s\ :math:`^{-1}`) .
 
 .. math:: R_{m,coh} = R_{m,leaf,coh}+ R_{m,froot,coh}+R_{m,croot,coh}+R_{m,stem,coh}
 
-To calculate canopy leaf respiration, which varies through we canopy, we
-first determine the top-of-canopy leaf respiration rate
+Leaf maintenance respiration - Atkin et al. 2017
+------------------------------------------------
+The :ref:`Atkin et al. 2017<atkin2017>` leaf maintenance respiration (Rdark) model
+includes temperature acclimation. We first determine the
+top-of-canopy Rdark rate.
+
+.. math:: r_{tref} = max(0, r_0 + r_1 * lnc_{top} + r_2 * max(0, tgrowth))
+
+where :math:`r_0` is the PFT-dependent base Rdark rate,
+:math:`r_1` is a parameter that determines the effects of nitrogen availability
+on Rdark, :math:`r_2` is a parameter that determines the effects of temperature
+on Rdark, and :math:`tgrowth` is the lagged vegetation temperature averaged over
+the acclimation timescale. We use :math:`r_1` = 0.2061 and :math:`r_2` = -0.0402
+following :ref:`Atkin et al. 2017<atkin2017>`.
+
+At very high temperatures, and with low values of
+:math:`r_0`, the whole term can become negative, and we therefore cap it at 0 to prevent negative Rdark.
+
+
+We scale vertically through the canopy based on nitrogen availability following
+:ref:`Lloyd et al. 2010<Lloydetal2010>`, in the same way that :math:`V_{c,max}`
+values are scaled uisng :math:`V_{above}`, described above.
+
+.. math:: r_{tref} = nscaler * r_{tref}
+
+where 
+
+.. math:: nscaler = exp(-kn * cumulativelai)
+
+and
+
+.. math:: kn =  exp(0.00963 * vcmax25top - 2.43) 
+
+where :math:`vcmax25top` is PFT-dependent maximum carboxylation rate of rubisco at the top 
+of the canopy at 25 degrees C, and :math:`cumulativelai` is the cumulative LAI, top down,
+to the leaf layer of interest. 
+
+We then adjust Rdark for current vegetation temperature (:math:`veg_{temp}`).
+
+.. math:: R_{m,leaf,coh} = r_{tref} * exp(b * (veg_{temp} - TrefC) + c * (veg_{temp}^{2} - TrefC^{2}))
+
+where :math:`TrefC` is the reference temperature of 25 degrees C, and :math:`b`
+and :math:`c` are parameters from :ref:`Heskel et al. 2016<Heskel2016>`, set as
+:math:`b` = 0.1012 and :math:`c` = -0.0005.
+
+
+
+Leaf maintenance respiration - Ryan 1991
+----------------------------------------
+To calculate canopy leaf respiration following :ref:`Ryan et al. 1991<ryan1991>`,
+we first determine the top-of-canopy leaf respiration rate
 (:math:`r_{m,leaf,ft,0}`, gC s\ :math:`^{-1}` m\ :math:`^{-2}`) is
 calculated from a base rate of respiration per unit leaf nitrogen
 derived from :ref:`Ryan et al. 1991<ryan1991>`. The base rate for leaf