Abstract
LAI of winter wheat (Triticum aestivum L.) and soil water content of the topsoil (200 mm) and of the subsoil (500 mm) were considered as state variables of a dynamic soil-crop system. This system was assumed to progress according to a Bayesian probabilistic state space model, in which real values of LAI and soil water content were daily introduced in order to correct the model trajectory and reach better future evolution. The chosen crop model was mini STICS which can reduce the computing and execution times while ensuring the robustness of data processing and estimation. To predict simultaneously state variables and model parameters in this non-linear environment, three techniques were used: extended Kalman filtering (EKF), particle filtering (PF), and variational filtering (VF). The significantly improved performance of the VF method when compared to EKF and PF is demonstrated. The variational filter has a low computational complexity and the convergence speed of states and parameters estimation can be adjusted independently. Detailed case studies demonstrated that the root mean square error of the three estimated states (LAI and soil water content of two soil layers) was smaller and that the convergence of all considered parameters was ensured when using VF. Assimilating measurements in a crop model allows accurate prediction of LAI and soil water content at a local scale. As these biophysical properties are key parameters in the crop-plant system characterization, the system has the potential to be used in precision farming to aid farmers and decision makers in developing strategies for site-specific management of inputs, such as fertilizers and water irrigation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Behera, S., & Panda, R. (2009). Integrated management of irrigation water and fertilizers for wheat crop using field experiments and simulation modeling. Agricultural Water Management, 96(11), 1532–1540.
Bellochi, G., Rivington, M., Donatelli, M., & Matthews, K. (2009). Validation of biophysical models: Issues and methodologies. A review. Agronomy for Sustainable Development, 30, 109–130.
Breda, N. (2003). Ground-based measurements of leaf area index: A review of methods, instruments and current controversies. Journal of Experimental Botany, 54(392), 2403–2417.
Brisson, N., Gara, C., Justes, E., Roche, R., Mary, B., Ripoche, D., et al. (2003). An overview of the crop model STICS. European Journal of Agronomy, 18, 309–332.
Calvet, J. (2000). Investigating soil and atmospheric plant water stress using physiological and micrometeorological data. Agricultural and Forest Meteorology, 103(3), 229–247.
Dobriyal, P., Qureshi, A., Badola, R., & Hussain, A. (2012). A review of the methods available for estimating soil moisture and its implications for water resource management. Journal of Hydrology, 458–459, 110–117.
Doucet, A., & Tadic, V. (2003). Parameter estimation in general state-space models using particle methods. Annals of the Institute of Statistical Mathematics, 55(2), 409–422.
Gebbers, R., Ehlert, D., & Adamek, R. (2011). Rapid mapping of the leaf area index in agricultural crops. Agronomy Journal, 103(5), 1532–1541.
Hautala, M., & Hakojarvi, M. (2011). An analytical C3-crop growth model for precision farming. Precision Agriculture, 12, 266–279.
Jonckheere, I., Fleck, S., Nackaerts, K., Muys, B., Coppin, P., Weiss, M., et al. (2004). Review of methods for in situ leaf area index determination. Part I. Theories, sensors and hemispherical photography. Agricultural and Forest Meteorology, 121, 19–35.
Kotecha, J., & Djuric, P. (2003). Gaussian particle filtering. IEEE Transactions on Signal Processing, 51(10), 2592–2601.
Leemans, V., Dumont, B., Destain, M.-F., Vancutsem, F., & Bodson, B. (2012). A method for plant leaf area measurement by using stereo vision. In F. Juste (Ed.) Proceedings of CIGR-AgEng 2012 International Conference on Agricultural Engineering, July 8–12, Valencia (Spain), Paper C-2315.
Lunt, I., Hubbard, S., & Rubin, Y. (2005). Soil water content content estimation using ground-penetrating radar reflection data. Journal of Hydrology, 307, 254–269.
MacKay, D. J. C. (2003). Information Theory, Inference and Learning Algorithms. Cambridge, UK: Cambridge University Press.
Makowski, D., Jeuffroy, M., & Guérif, M. (2004). Bayesian methods for updating crop-model predictions, applications for predicting biomass and grain protein content. In M. van Boekel, A. Stein, & A. van Bruggen (Eds.), Bayesian Statistics and Quality Modelling in the Agro-Food Production Chain (Wageningen UR Frontis Series) (pp. 57–68). Dordrecht: Kluwer Academic.
Mansouri, M., Snoussi, M., & Richard, C. (2009). A nonlinear estimation for target tracking in wireless sensor networks using quantized variational filtering. In IEEE, Proceedings 3rd International Conference on Signals, Circuits and Systems, E-ISBN: 978-1-4244-4398-7, pp. 1–4.
Palosuoa, T., Kersebaumb, K., Angulo, C., Hlavinka, P., Moriondo, M., Olesen, J., et al. (2011). Simulation of winter wheat yield and its variability in different climates of Europe: A comparison of eight crop growth models. European Journal of Agronomy, 35, 103–114.
Sakamoto, T., Gitelson, A., Wardlow, B., Arkebauer, T., Verma, S., Suyker, A., et al. (2012). Application of day and night digital photographs for estimating maize biophysical characteristics. Precision Agriculture, 13, 285–301.
Stacheder, M., Koeniger, F., & Schuhmann, R. (2009). New dielectric sensors and sensing techniques for soil and snow moisture measurements. Sensors, 9(4), 2951–2967.
Sudha, N., Valarmathi, M., Babu, M., & Susan, A. (2011). Energy efficient data transmission in automatic irrigation system using wireless sensor networks. Computers & Electronics in Agriculture, 78(2), 215–221.
Tremblay, M., & Wallach, D. (2004). Comparison of parameter estimation methods for crop models. Agronomie, 24(6–7), 351–365.
Van Der Merwe, R., & Wan, E. A. (2001). The square-root unscented Kalman filter for state and parameter-estimation. In IEEE (Eds), ICASSP, Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 6, pp. 3461–3464.
Van Wijk, M., & Williams, M. (2005). Optical instruments for measuring leaf area index in low vegetation: Application in arctic ecosystems. Ecological Applications, 15(4), 1462–1470.
Vermaak, J., Lawrence, N., & Perez, P. (2003). Variational inference for visual tracking, In IEEE (Ed.) Computer Vision and Pattern Recognition (Vol. 1, pp. 1–773). Proceedings of the 2003 IEEE Computer Society Conference.
Weiss, A., & Wilhem, W. (2006). The circuitous path to the comparison of simulated values from crop models with field observations. Journal of Agricultural Science, 144, 475–488.
Xiao, Z., Liang, S. Wang, J., & Wu, X. (2009). Use of an ensemble Kalman filter for real-time inversion of leaf area index from modis time series data. In IEEE (Ed.), Geoscience and Remote Sensing Symposium, 2009 IEEE International, IGARSS 2009, Vol. 4, pp. 4–73.
Zhang, R., Guo, J., Zhang, L., Zhang, Y., Wang, L., & Wang, Q. (2011). A calibration method of detecting soil water content based on the information-sharing in wireless sensor network. Computers & Electronics in Agriculture, 76(2), 161–168.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mansouri, M., Dumont, B., Leemans, V. et al. Bayesian methods for predicting LAI and soil water content. Precision Agric 15, 184–201 (2014). https://doi.org/10.1007/s11119-013-9332-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11119-013-9332-7