Because Farquhar's photosynthesis model is only directly applicable to individual leaves instantaneously, considerable skill is needed to use this model for regional plant growth and carbon budget estimations. In many published models, Farquhar's equations were applied directly to plant canopies by assuming a plant canopy to function like a big-leaf. This big-leaf approximation is found to be acceptable for estimating seasonal trends of canopy photosynthesis but inadequate for simulating its day-to-day variations, when compared with eddy-covariance and gas-exchange chamber measurements from two boreal forests. The daily variation is greatly dampened in big-leaf simulations because the original leaf-level model is partially modified through replacing stomatal conductance with canopy conductance. Alternative approaches such as separating the canopy into sunlit and shaded leaf groups or stratifying the canopy into multiple layers can avoid the problem. Because of non-linear response of leaf photosynthesis to meteorological variables (radiation, temperature and humidity), considerable errors exist in photosynthesis calculation at daily steps without considering the diurnal variability of the variables. To avoid these non-linear effects, we have developed an analytical solution to a simplified daily integral of Farquhar's model by considering the general diurnal patterns of meteorological variables. This daily model not only captures the main effects of diurnal variations on photosynthesis but is also computationally efficient for large area applications. Its application is then not restricted by availability of sub-daily meteorological data. This scheme has been tested using measured CO 2 data from the Boreal Ecosystem-Atmosphere Study (BOREAS), which took place in Manitoba and Saskatchewan in 1994 and1996.

We perform Langevin simulations on the depinning dynamics of two-dimensional magnetized colloids on a random substrate. On increasing the magnetic field strength, we find for the first time a crossover from plastic to smectic flows as well as a crossover from smectic to elastic crystal flows above depinning. For both the smectic and elastic crystal flows, a power-law scaling relationship could be obtained between the average velocity and applied driving force. The scaling exponent is found to be larger than 1 for smectic flow. But, for the elastic crystal flow, the scaling exponent is found to be less than 1. For the plastic flow, no power-law scaling relationship between the average velocity and applied driving force can be derived and history dependence of the depinning occurs. Within the crossover from plastic to smectic flows, a sudden decrease in the critical driving force is observed, and a sudden increase is found in the critical driving force across the crossover from smectic to elastic crystal flows, accompanied by a crossing of the curves of average velocity versus driving force.