A generic equation for nitrogen-limited leaf area index and its application in crop growth models for predicting leaf senescence

Appropriate quantification of leaf area index (LAI) is important for accurate prediction of photosynthetic productivity by crop growth models. Estimation of LAI requires accurate modelling of leaf senescence. Many models use empirical turnover coefficients, the relative leaf-death rate determined from frequent field samplings, to describe senescence during growth. In this paper, we first derive a generic equation for nitrogen-determined photosynthetically active LAI (LAI(N)), and then describe a method of using this equation in crop growth models to predict leaf senescence. Based on the theory that leaf-nitrogen at different horizons of a canopy declines exponentially, LAI(N), which is counted from the top of the canopy to the depth at which leaf-nitrogen equals the minimum value for leaf photosynthesis, is calculated analytically as a function of canopy leaf-nitrogen content. At each time-step of crop growth modelling, LAI(N) is compared to an independent calculation of the non-nitrogen-limited LAI assuming no leaf death during that time-step (LAI(NLD)). In early stages, LAI(N) is higher than LAI(NLD); but with the advancement of crop growth, LAI(N) will become smaller than LAI(NLD). The difference between LAI(NLD) and LAI(N), whenever LAI(N) is smaller than LAI(NLD), gives the estimate of leaf area senesced at the time-step; the senesced leaf area divided by specific leaf area (SLA) gives the estimate of senesced leaf mass. The method was incorporated into two crop models and the models adequately accounted for the LAI observed in field experiments for rice and barley. The novel features of the approach are that: (1) it suggests a coherent, biologically reasonable picture of leaf senescence based on the link with photosynthesis and leaf nitrogen content; (2) it avoids the use of empirical leaf-turnover coefficients; (3) it avoids over-sensitivity of LAI prediction to SLA; and (4) it is presumably of sufficient generality as to be applicable to plant types other than crops. The method can be applied to models where leaf-nitrogen is used as an input variable or is simulated explicitly.