Evaluation of normalized root length density distribution models

Abstract The root length density (RLD) distribution is an essential parameter for modeling crop growth and root uptake in soil–plant systems, but it is difficult to measure under field conditions. Several RLD models contain many parameters that vary with the crop growth season and they are difficult to measure, and thus they have limited applicability. The normalized RLD (NRLD) distribution models are independent of the growing season and they can be used to easily and accurately estimate the RLD distribution in different growing stages. Power, exponential, and polynomial models are commonly used to describe the NRLD distributions. However, it’s still not clear whether different models can be used to simulate NRLD profiles, and if there was the most suitable distribution model for NRLD distribution measurements from different crops. In this study, observational cotton RLD data obtained from a field experiment and RLD distribution data for other crops (wheat, maize, and rice) reported in previous studies were all transformed into NRLD distributions. We fitted power, exponential, and polynomial models to each crop NRLD profile distribution based on 1041 data points. The results showed that the power model had the highest root mean squared error (RMSE) and lowest coefficient of determination (R2) for wheat, maize, and rice, whereas the exponential model had the highest RMSE and lowest R2 for cotton. The polynomial model had the lowest RMSE and highest R2 for all four crops, but it was physically meaningless because the value of NRLD(zr = 1) could not reach zero. Thus, we proposed an improved polynomial model to ensure that the simulation was precise and with physical meaning and simplify the fitting coefficients. Our results showed that the improved polynomial model was the most flexible and suitable for fitting the observed NRLD distributions for the four crops.