## 1. Introduction

[2] Climate models are now used to predict future oceanic and terrestrial carbon storage and hence how much will remain in the atmosphere and contribute to global warming [e.g., *Dickinson*, 2012; *Friedlingstein et al.*, 2006; *Fung et al.*, 2005; *Sarmiento et al.*, 2010]. Carbon enters the terrestrial ecosystem through leaf stomata, which also transpire water extracted from soil. Therefore, a coupled photosynthesis and stomatal conductance (inverse of stomatal resistance) model is often used within a general land surface modeling framework to simulate terrestrial gross primary production (GPP) and transpiration at various time and spatial scales [e.g., *Bonan et al.*, 2011; *Dai et al.*, 2004; *Sellers et al.*, 1996]. GPP is the initial step of terrestrial carbon cycling [*Beer et al.*, 2010; *Zhao and Running*, 2010]. It fuels the growth of plants, which in turn provide organic matter to soil [*Dickinson*, 2012]. Transpiration is a key component of evapotranspiration (ET) that by balancing absorbed solar radiation determines land surface temperature and other climate features [*Dickinson et al.*, 2002]. Thus a robust solution of the coupled photosynthesis (*A*) and stomatal conductance (*g*_{s}) process (denoted as *A*– *g*_{s}) is needed for accurate predictions of terrestrial carbon and water fluxes in climate models.

[3] A widely used framework of the coupled process of the CO_{2} and water vapor flow through the stomata was first implemented by *Collatz et al.* [1991], a variant version of which now is a component of the Community Land Model (CLM) [*Oleson et al.*, 2010]. This *A*– *g*_{s} model encompasses a suite of nonlinear equations that in general must be solved iteratively, although under certain simplified conditions, analytical solutions are possible [*Baldocchi*, 1994].

[4] Various iteration methods are available for solving such nonlinear equations, with their own strengths and limitations for specific applications. Choosing an appropriate such scheme is of particular importance when it is applied for global simulations. We emphasize this point for a couple of reasons. First, in a global modeling framework, there are 10^{3}–10^{6} land grids (depending on the simulation resolution), each of which can consist of mixed patches of various plant types that are forced by different environmental conditions. These vegetation and climatic conditions in turn strongly affect the behavior of the nonlinear equations involved and therefore the validity of their numerical treatment. Second, iterative calculations must be computationally inexpensive for global applications. However, we are not aware of any previous effort to examine these numerical issues in depth for the *A*– *g*_{s} model, although the coupling between carbon and water vapor fluxes is at the core of land surface modeling.

[5] We have found that the iteration approach used in CLM to solve the *A*– *g*_{s}model (and likely other such models of similar heritage) does not converge, hence introduces errors to the modeled carbon and water fluxes. We examine why this nonconvergence occurs and introduce a more robust iteration framework to remedy this numerical problem. This new approach is based on an in-depth analysis of the numerical behavior of the*A*– *g*_{s} model. We demonstrate that our new treatment corrects substantial biases in the GPP and transpiration simulated by the latest released version of CLM, i.e., CLM4 [*Oleson et al.*, 2010].