Coupled models of water and carbon cycles from leaf to global: A retrospective and a prospective

• Key developments in the coupled model of water-carbon cycle are identified. • These developments shaped how we model those two cycles from leaf to global scales. • Large divergence among different approaches remains unabated among different approaches. • Application of machine learning will increase significantly in the future. Our understanding of water and carbon cycles and their coupling has advanced significantly over the last six decades. In this review, we will examine the progress made since the 1960s and explore how key developments in the studies of water and carbon cycles on land have influenced the way we model these two cycles from leaf to global scales. We will particularly focus on the Penman-Monteith equation for calculating evapotranspiration, the biochemical model of leaf photosynthesis, and the model of stomatal conductance. These three models developed over three decades ago have been widely adopted in the studies of water and carbon cycle from leaf to global scales. The success of these models lie in their sound representation of the basic biophysical and biochemical processes with relative simplicity. Their wide adoption was also assisted by the rapid development of portable leaf gas exchange instruments and field deployment of eddy covariance techniques, which provide the data for estimating the key model parameters and for model evaluation and improvement. Over the last two decades, rapid advances in remote sensing, global eddy flux networks, and computation have led to a rapid growth of different approaches for estimating water and carbon fluxes. This review compares the simulated global gross primary production, evapotranspiration and ecosystem water use efficiency and their trends using these different approaches, and finds that significant progress has been made in understanding their spatial patterns, interannual variations and trends. However, significant divergences remain among them. Looking ahead, we identify several key areas where significant progress is likely, particularly through the applications of machine learning and ecological forecasting. We also anticipate the development of new theories by integrating theoretical understanding with increasing observations from ground and space.