It is challenging to assimilate the evapotranspiration product (EP) retrieved from satellite data into land surface models (LSMs). In this paper, a perturbed ensemble Kalman filter (PEKF) and à trous wavelet transform (AWT) integrated method are proposed to implement the evapotranspiration assimilation. In this method, the AWT is used to decompose the EPs into multiple channels since it is very powerful in fusing high frequency spatial information of multisource data, and then the Kalman filter is performed in the AWT domain. The proposed method combines the advantages of the PEKF that is capable of accommodating model error and observation error, and the AWT can effectively perform multiresolution fusion. Assimilation experiment conducted with the Noah model and the EP retrieved from the MODIS data shows that the proposed method performs better than the traditional ensemble Kalman filter (EnKF) and PEKF methods. The analysis results fit well with the evapotranspiration observation at two field sites with different land surface conditions. These indicate that the proposed method is promising for assimilating regional scale satellite retrieved EP into LSMs. 1. Introduction Evapotranspiration (ET) is an important component of the water and energy exchanges between the atmosphere and land surface. It is crucial to accurately estimate ET for studying global or regional water and energy balances. Hence, good quality of spatial and temporal ET production (EP) can help to improve comprehension of water and energy cycle. However, this kind of EP is generally difficult to obtain in both dimensions of space and time because ET is influenced by many factors, such as air and skin temperatures, soil moisture, vegetation fraction, and horizontal advection. Up to now, there are two approaches to estimate the ET. One is site observations or remote sensing retrievals. Site observations have high spatial resolutions, but can only provide the EP for limited spatial locations [1]. Remote sensing retrievals have high spatial resolutions and can cover large range, but can only retrieve the instantaneous EP. The other is land surface models (LSMs). LSMs are probably the most efficient approach for continuously estimating ET on a large range [1]. Because of the imperfection of the physics of LSMs and the uncertainties of input and driving data, the EP of the LSMs may contain significant errors. Hence, data assimilation (DA) has been applied to integrate observational ET into LSMs [2]. DA provides a framework for improving the LSMs by updating the state variables of the LSMs
References
[1]
J. Qin, S. Liang, K. Yang, I. Kaihotsu, R. Liu, and T. Koike, “Simultaneous estimation of both soil moisture and model parameters using particle filtering method through the assimilation of microwave signal,” Journal of Geophysical Research D, vol. 114, no. 15, Article ID D15103, 2009.
[2]
C. L. Meng, Z.-L. Li, X. Zhan, J. C. Shi, and C. Y. Liu, “Land surface temperature data assimilation and its impact on evapotranspiration estimates from the common land model,” Water Resources Research, vol. 45, no. 2, Article ID W02421, 2009.
[3]
X. Tian, Z. Xie, and A. Dai, “An ensemble-based explicit four-dimensional variational assimilation method,” Journal of Geophysical Research, vol. 113, article D21124, 2008.
[4]
R. H. Reichle, “Data assimilation methods in the Earth sciences,” Advances in Water Resources, vol. 31, no. 11, pp. 1411–1418, 2008.
[5]
J. P. Pinto, M. C. Bernardino, and A. P. Silva, “A Kalman filter application to a spectral wave model,” Nonlinear Processes in Geophysics, vol. 12, no. 6, pp. 775–782, 2005.
[6]
X. Li, T. Koike, and M. Pathmathevan, “A very fast simulated re-annealing (VFSA) approach for land data assimilation,” Computers and Geosciences, vol. 30, no. 3, pp. 239–248, 2004.
[7]
G. Evensen, “Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics,” Journal of Geophysical Research, vol. 99, no. 5, pp. 10–162, 1994.
[8]
G. Evensen, “The Ensemble Kalman Filter: theoretical formulation and practical implementation,” Ocean Dynamics, vol. 53, pp. 343–367, 2003.
[9]
E. S. Epstein, “Stochastic dynamic prediction,” Tellus, vol. 21, pp. 739–759, 1969.
[10]
G. Burgers, P. J. Van Leeuwen, and G. Evensen, “Analysis scheme in the ensemble Kalman filter,” Monthly Weather Review, vol. 126, no. 6, pp. 1719–1724, 1998.
[11]
J. Qin, R. Liu, S. Liang, H. Zhang, and B. Hu, “A new method based on remote sensing observations and data assimilation for estimation of evapotranspiration over field crops,” New Zealand Journal of Agricultural Research, vol. 50, no. 5, pp. 997–1004, 2007.
[12]
R. C. Pipunic, J. P. Walker, and A. Western, “Assimilation of remotely sensed data for improved latent and sensible heat flux prediction: a comparative synthetic study,” Remote Sensing of Environment, vol. 112, no. 4, pp. 1295–1305, 2008.
[13]
K. Jang, S. Kang, J. Kim et al., “Mapping evapotranspiration using MODIS and MM5 Four-Dimensional Data Assimilation,” Remote Sensing of Environment, vol. 114, no. 3, pp. 657–673, 2010.
[14]
T. Xu, S. Liang, and S. Liu, “Estimating turbulent fluxes through assimilation of geostationary operational environmental satellites data using ensemble Kalman filter,” Journal of Geophysical Research D, vol. 116, no. 9, Article ID D09109, 2011.
[15]
A. French, D. Hunsaker, and T. Clarke, “forecasting spatially distributed cotton evapotranspiration by assimilating remotely sensed and ground-based observations,” Journal of Irrigation and Drainage Engineering, vol. 138, no. 11, pp. 984–992, 2012.
[16]
M. Holdschneider, R. Kronland-martinet, J. Morlet, and P. Tchamitchian, “A real time algorithm for signal analysis with the help of the wavelet transform,” in Proceedings of the International Conference on Time-Frequency Methods and Phase Space, J. M. Combes, A. Grossman, and P. Tchamitchian, Eds., p. 286, Springer, Marseille, France, 1987.
[17]
P. Dutilleux, “An implementation of the “algorithme à trous” to compute the wavelet transform,” in Wavelet. Proceedings of the International Conference on Time-Frequency Methods and Phase Space, J. M. Combes, A. Grossman, and P. Tchamitchian, Eds., pp. 298–304, Springer, Marseille, France, 1987.
[18]
T.-M. Tu, W.-C. Cheng, C.-P. Chang, P. S. Huang, and J.-C. Chang, “Best tradeoff for high-resolution image fusion to preserve spatial details and minimize color distortion,” IEEE Geoscience and Remote Sensing Letters, vol. 4, no. 2, pp. 302–306, 2007.
[19]
S. Chen, R. Zhang, H. Su, J. Tian, and J. Xia, “SAR and multispectral image fusion using generalized IHS transform based on trous wavelet and EMD decompositions,” IEEE Sensors Journal, vol. 10, no. 3, pp. 737–745, 2010.
[20]
A. Deckmyn and L. Berre, “A wavelet approach to representing background error covariances in a limited-area model,” Monthly Weather Review, vol. 133, no. 5, pp. 1279–1294, 2005.
[21]
O. Pannekoucke, L. Berre, and G. Desroziers, “Filtering properties of wavelets for local background-error correlations,” Quarterly Journal of the Royal Meteorological Society, vol. 133, no. 623, pp. 363–379, 2007.
[22]
A. Tangborn, “Wavelet approximation of error covariance propagation in data assimilation,” Tellus, vol. 56, no. 1, pp. 16–28, 2004.
[23]
J. Nú？ez, X. Otazu, and O. Fors, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Transactions on Geoscience and Remote Sensing, vol. 37, no. 3, pp. 1204–1211, 1999.
[24]
Y. Chibani and A. A. Houacine, “Redundant versus orthogonal wavelet decomposition for multisensor image fusion,” Pattern Recognition, vol. 36, no. 4, pp. 879–887, 2002.
[25]
M. González-Audícana, X. Otazu, O. Fors, and A. Seco, “Comparison between the Mallat’s and the à trous discrete wavelet transform based algorithms for the fusion of multispectral and panchromatic images,” International Journal of Remote Sensing, vol. 26, no. 3, pp. 595–614, 2005.
[26]
R. Zhang, J. Tian, H. Su, X. Sun, S. Chen, and J. Xia, “Two improvements of an operational two-layer model for terrestrial surface heat flux retrieval,” Sensors, vol. 8, no. 10, pp. 6165–6187, 2008.
[27]
F. Chen and J. Dudhia, “Coupling and advanced land surface-hydrology model with the Penn State-NCAR MM5 modeling system—part I: model implementation and sensitivity,” Monthly Weather Review, vol. 129, no. 4, pp. 569–585, 2001.
[28]
J. Tian, R. Zhang, X. Sun, Z. Zhu, and Y. Zhou, “Study of a model for correcting the effects of horizontal advection on surface fluxes measurement based on remote sensing,” Science in China, vol. 49, no. 2, pp. 273–280, 2006.
[29]
M. B. Ek, K. E. Mitchell, Y. Lin et al., “Implementation of Noah land surface model advances in the National Centers for Environmental Prediction operational mesoscale Eta model,” Journal of Geophysical Research D, vol. 108, no. 22, pp. 1–16, 2003.
[30]
K. E. Mitchell, D. Lohmann, and P. R. Houser, “The multi-institution North American Land Data Assimilation System (NLDAS): utilizing multiple GCIP products and partners in a continental distributed hydrological modeling system,” Journal of Geophysical Research, vol. 109, 2004.
[31]
K. L. Verdin and S. K. Greenlee, “Development of continental scale digital elevation models and extraction of hydrographic features,” in Proceedings of 3rd International Conference/Workshop on Integrating GIS and Environmental Modeling, National Center for Geographic Information and Analysis, pp. 21–26, Santa Fe, NM, USA, 1996.
[32]
M. C. Hansen, R. S. Defries, J. R. G. Townshend, and R. Sohlberg, “Global land cover classification at 1 km spatial resolution using a classification tree approach,” International Journal of Remote Sensing, vol. 21, no. 6-7, pp. 1331–1364, 2000.
[33]
D. A. Miller and R. A. A. White, “Conterminous United States multi-layer soil characteristics data set for regional climate and hydrology modeling,” Earth Inter, vol. 2, no. 2, 1998.
[34]
G. Gutman and A. Ignatov, “The derivation of the green vegetation fraction from NOAA/AVHRR data for use in numerical weather prediction models,” International Journal of Remote Sensing, vol. 19, no. 8, pp. 1533–1543, 1998.
