• Alavi, N., , Berg A. , , Warland J. , , Parkin G. , , Verseghy D. , , and Bartlett P. , 2010: Assimilating soil moisture variability into the class to improve latent heat flux estimation. Can. Water Resour. J., 35, 116.

    • Search Google Scholar
    • Export Citation
  • Aubert, D., , Loumagne C. , , and Oudin L. , 2003: Sequential assimilation of soil moisture and streamflow data in a conceptual rainfall–runoff model. J. Hydrol., 280, 145161.

    • Search Google Scholar
    • Export Citation
  • Berg, A. A., , and Mulroy K. , 2006: Streamflow predictability given macro-scale estimates of the initial soil moisture status. Hydrol. Sci. J., 51, 642654.

    • Search Google Scholar
    • Export Citation
  • Burgers, T., , Van Leeuwen P. J. , , and Evensen G. , 1998: Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev., 126, 17191724.

  • Caparrini, F., , Castelli F. , , and Entekhabi D. , 2003: Mapping of land-atmosphere heat fluxes and surface parameters with remote sensing data. Bound.-Layer Meteor., 107, 605633.

    • Search Google Scholar
    • Export Citation
  • Caparrini, F., , Castelli F. , , and Entekhabi D. , 2004a: Estimation of surface turbulent fluxes through assimilation of radiometric surface temperature sequences. J. Hydrometeor., 5, 145159.

    • Search Google Scholar
    • Export Citation
  • Caparrini, F., , Castelli F. , , and Entekhabi D. , 2004b: Variational estimation of soil and vegetation turbulent transfer and heat flux parameters from sequences of multisensor imagery. Water Resour. Res., 40, W12515, doi:10.1029/2004WR003358.

    • Search Google Scholar
    • Export Citation
  • Champagne, C., , Berg A. , , Belanger J. , , McNairn H. , , and deJeu R. , 2010: Evaluation of soil moisture derived from passive microwave remote sensing over agricultural sites in Canada using ground-based soil moisture monitoring networks. Int. J. Remote Sens., 31, 36693690.

    • Search Google Scholar
    • Export Citation
  • Chemin, Y., , and Honda K. , 2006: Spatiotemporal fusion of rice actual evapotranspiration with genetic algorithms and an agrohydrological model. IEEE Trans. Geosci. Remote Sens., 44, 34623469.

    • Search Google Scholar
    • Export Citation
  • Confesor, R. B., , and Whittaker G. W. , 2007: Automatic calibration of hydrologic models with multi-objective evolutionary algorithm and Pareto optimization. J. Amer. Water Resour. Assoc., 43, 981989.

    • Search Google Scholar
    • Export Citation
  • Crosson, W. L., , Laymon C. A. , , Inguva R. , , and Schamschula M. P. , 2002: Assimilating remote sensing data in a surface flux-soil moisture model. Hydrol. Processes, 16, 16451662.

    • Search Google Scholar
    • Export Citation
  • Crow, W. T., , and Wood E. F. , 2003: The assimilation of remotely sensed soil brightness temperature imagery into a land surface model using ensemble Kalman filtering: A case study based on ESTAR measurements during SGP97. Adv. Water Resour., 26, 137149.

    • Search Google Scholar
    • Export Citation
  • Deb, K., , and Goel T. , 2001: Controlled elitist non-dominated sorting genetic algorithms for better convergence. Evolutionary Multi-Criterion Optimization, E. Zitzler et al., Eds., Lecture Notes in Computer Science, Vol. 1993, Springer, 67–81.

    • Search Google Scholar
    • Export Citation
  • Deb, K., , Agrawal S. , , Pratap A. , , and Meyarivan T. , 2000: A fast elitist non-dominated sorting genetic algorithms for multi-objective optimization: NSGA-II. Parallel Problem Solving from Nature—PPSN VI, M. Schoenauer et al., Eds., Lecture Notes in Computer Science, Vol. 1917, Springer, 849–858.

    • Search Google Scholar
    • Export Citation
  • Deb, K., , Pratap A. , , Agrawal S. , , and Meyarivan T. , 2002: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput., 6, 182197.

    • Search Google Scholar
    • Export Citation
  • Dumedah, G., , Berg A. A. , , Wineberg M. , , and Collier R. , 2010: Selecting model parameter sets from a trade-off surface generated from the non-dominated sorting genetic algorithm-II. Water Resour. Manage., 24, 44694489, doi: 10.1007/s11269-010-9668-y.

    • Search Google Scholar
    • Export Citation
  • Dumedah, G., , Berg A. A. , , and Wineberg M. , 2011: Evaluating auto-selection methods used for choosing solutions from Pareto-optimal set: Does non-dominance persist from calibration to validation phase? J. Hydrol. Eng., in press.

    • Search Google Scholar
    • Export Citation
  • Dunne, S., , and Entekhabi D. , 2005: An ensemble-based reanalysis approach to land data assimilation. Water Resour. Res., 41, W02013, doi:10.1029/2004WR003449.

    • Search Google Scholar
    • Export Citation
  • Eiben, A. E., , and Smith J. E. , 2003: Introduction to Evolutionary Computing. Springer, 299 pp.

  • Galantowicz, J. F., , Entekhabi D. , , and Njoku E. , 1999: Tests of sequential data assimilation for retrieving profile soil moisture and temperature from observed l-band radiobrightness. IEEE Trans. Geosci. Remote Sens., 37, 18601870.

    • Search Google Scholar
    • Export Citation
  • Hodur, R. M., 1997: The Naval Research Laboratory’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). Mon. Wea. Rev., 125, 14141430.

    • Search Google Scholar
    • Export Citation
  • Holmes, T. R. H., , De Jeu R. A. M. , , Owe M. , , and Dolman A. J. , 2009: Land surface temperature from Ka band (37 GHz) passive microwave observations. J. Geophys. Res., 114, D04113, doi:10.1029/2008JD010257.

    • Search Google Scholar
    • Export Citation
  • Houser, P. R., , Shuttleworth W. J. , , Famiglietti J. S. , , Gupta H. V. , , Syed K. H. , , and Goodrich D. C. , 1998: Integration of soil moisture remote sensing and hydrologic modeling using data assimilation. Water Resour. Res., 34, 34053420.

    • Search Google Scholar
    • Export Citation
  • Ines, A. V. M., , and Honda K. , 2005: On quantifying agricultural and water management practices from low spatial resolution RS data using genetic algorithms: A numerical study for mixed-pixel environment. Adv. Water Resour., 28, 856870.

    • Search Google Scholar
    • Export Citation
  • Ines, A. V. M., , and Mohanty B. P. , 2008: Near-surface soil moisture assimilation for quantifying effective soil hydraulic properties under different hydroclimatic conditions. Vadose Zone J., 7, 3952.

    • Search Google Scholar
    • Export Citation
  • Ines, A. V. M., , and Mohanty B. P. , 2009: Near-surface soil moisture assimilation for quantifying effective soil hydraulic properties using genetic algorithms: 2. Using airborne remote sensing during SGP97 and SMEX02. Water Resour. Res., 45, W01408, doi:10.1029/2008WR007022.

    • Search Google Scholar
    • Export Citation
  • Ines, A. V. M., , Honda K. , , Das Gupta A. , , Droogers P. , , and Clemente R. S. , 2006: Combining remote sensing-simulation modeling and genetic algorithm optimization to explore water management options in irrigated agriculture. Agric. Water Manage., 83, 221232.

    • Search Google Scholar
    • Export Citation
  • Khu, S. T., , and Madsen H. , 2005: Multiobjective calibration with Pareto preference ordering: An application to rainfall-runoff model calibration. Water Resour. Res., 41, W03004, doi:10.1029/2004WR003041.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , and Gupta H. V. , 2007: Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework. Water Resour. Res., 43, W07401, doi:10.1029/2006WR005756.

    • Search Google Scholar
    • Export Citation
  • Madsen, H., 2003: Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives. Adv. Water Resour., 26, 205216.

    • Search Google Scholar
    • Export Citation
  • Moradkhani, H., , Hsu K.-L. , , Gupta H. , , and Sorooshian S. , 2005: Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter. Water Resour. Res., 41, W05012, doi:10.1029/2004WR003604.

    • Search Google Scholar
    • Export Citation
  • Njoku, E. G., , and Li L. , 1999: Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz. IEEE Trans. Geosci. Remote Sens., 37, 7993.

    • Search Google Scholar
    • Export Citation
  • Njoku, E. G., , Jackson T. J. , , Lakshmi V. , , Chan T. K. , , and Nghiem S. V. , 2003: Soil moisture retrieval from AMSR-E. IEEE Trans. Geosci. Remote Sens., 41, 215229.

    • Search Google Scholar
    • Export Citation
  • NSIDC, 2008: AMSR-E/Aqua daily L3 surface soil moisture, interpretive parameters, and QC EASE-grids v002. National Snow and Ice Data Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/docs/daac/ae_land3_l3_soil_moisture.gd.html.]

    • Search Google Scholar
    • Export Citation
  • Owe, M., , de Jeu R. , , and Walker J. , 2001: A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index. IEEE Trans. Geosci. Remote Sens., 39, 16431654.

    • Search Google Scholar
    • Export Citation
  • Owe, M., , de Jeu R. , , and Holmes T. , 2008: Multisensor historical climatology of satellite-derived global land surface moisture. J. Geophys. Res., 113, F01002, doi:10.1029/2007JF000769.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., 2008: Data assimilation methods in the Earth sciences. Adv. Water Resour., 31, 14111418.

  • Reichle, R. H., , and Koster R. D. , 2005: Global assimilation of satellite surface soil moisture retrievals into the NASA Catchment land surface model. Geophys. Res. Lett., 32, L02404, doi:10.1029/2004GL021700.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Entekhabi D. , , and McLaughlin D. B. , 2001: Downscaling of radio brightness measurements for soil moisture estimation: A four-dimensional variational data assimilation approach. Water Resour. Res., 37, 23532364.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , McLaughlin D. B. , , and Entekhabi D. , 2002a: Hydrologic data assimilation with the ensemble Kalman filter. Mon. Wea. Rev., 130, 103114.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Walker J. P. , , Koster R. D. , , and Houser P. R. , 2002b: Extended versus ensemble Kalman filtering for land data assimilation. J. Hydrometeor., 3, 728740.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Koster R. D. , , Dong J. , , and Berg A. A. , 2004: Global soil moisture from satellite observations, land surface models, and ground data: Implications for data assimilation. J. Hydrometeor., 5, 430442.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Koster R. D. , , Liu P. , , Mahanama S. P. P. , , Njoku E. G. , , and Owe M. , 2007: Comparison and assimilation of global soil moisture retrievals from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) and the Scanning Multichannel Microwave Radiometer (SMMR). J. Geophys. Res., 112, D09108, doi:10.1029/2006JD008033.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Crow W. T. , , Koster R. D. , , Sharif H. O. , , and Mahanama S. P. P. , 2008: Contribution of soil moisture retrievals to land data assimilation products. Geophys. Res. Lett., 35, L01404, doi:10.1029/2007GL031986.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., , Rayner N. A. , , Smith T. M. , , Stokes D. C. , , and Wang W. , 2002: An improved in situ and satellite SST analysis for climate. J. Climate, 15, 16091625.

    • Search Google Scholar
    • Export Citation
  • Schubert, S. D., , Rood R. B. , , and Pfaendtner J. , 1993: An assimilated dataset for earth science applications. Bull. Amer. Meteor. Soc., 74, 23312342.

    • Search Google Scholar
    • Export Citation
  • Schuurmans, J. M., , Troch P. A. , , Veldhuizen A. A. , , Bastiaanssen W. G. M. , , and Bierkens M. F. P. , 2003: Assimilation of remotely sensed latent heat flux in a distributed hydrological model. Adv. Water Resour., 26, 151159.

    • Search Google Scholar
    • Export Citation
  • Tang, Y., , Reed P. , , and Wagener T. , 2006: How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration? Hydrol. Earth Syst. Sci., 10, 289307.

    • Search Google Scholar
    • Export Citation
  • Trenberth, K. E., , and Guillemot C. J. , 1998: Evaluation of the atmospheric moisture and hydrological cycle in the NCEP/NCAR reanalyses. Climate Dyn., 14, 213231.

    • Search Google Scholar
    • Export Citation
  • Troch, P., , Paniconi C. , , and McLaughlin D. , 2003: Catchment-scale hydrological modeling and data assimilation. Adv. Water Resour., 26, 131135.

    • Search Google Scholar
    • Export Citation
  • Verseghy, D. L., 1991: CLASS—A Canadian land surface scheme for GCMs: I. Soil model. Int. J. Climatol., 11, 111133.

  • Verseghy, D. L., 2000: The Canadian Land Surface Scheme (CLASS): Its history and future. Atmos.–Ocean, 38, 113.

  • Verseghy, D. L., , McFarlane N. A. , , and Lazare M. , 1993: CLASS—A Canadian land surface scheme for GCMs: II. Vegetation model and coupled runs. Int. J. Climatol., 13, 347370.

    • Search Google Scholar
    • Export Citation
  • Vrugt, J. A., , Gupta H. V. , , Bastidas L. A. , , Bouten W. , , and Sorooshian S. , 2003: Effective and efficient algorithm for multiobjective optimization of hydrologic models. Water Resour. Res., 39, 1214, doi:10.1029/2002WR001746.

    • Search Google Scholar
    • Export Citation
  • Walker, J. P., , and Houser P. R. , 2004: Requirements of a global near-surface soil moisture satellite mission: Accuracy, repeat time, and spatial resolution. Adv. Water Resour., 27, 785801.

    • Search Google Scholar
    • Export Citation
  • Walker, J. P., , Willgoose G. R. , , and Kalma J. D. , 2002: Three-dimensional soil moisture profile retrieval by assimilation of near-surface measurements: Simplified Kalman filter covariance forecasting and field application. Water Resour. Res., 38, 1301, doi:10.1029/2002WR001545.

    • Search Google Scholar
    • Export Citation
  • Wöhling, T., , Vrugt J. A. , , and Barkle G. F. , 2008: Comparison of three multiobjective optimization algorithms for inverse modeling of vadose zone hydraulic properties. Soil Sci. Soc. Amer. J., 72, 305319.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Soil moisture study area at Brightwater Creek, southern Saskatchewan.

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    Two-step data assimilation framework from brightness temperature to soil moisture. Note that TB denotes brightness temperature, and “TB assimilated soil moisture” is a product of assimilating brightness temperatures from the satellite and LPRM simulation.

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    A time series of the observed in situ soil moisture dataset that was used to evaluate the two assimilation procedures. The error bars represent one standard deviation from the mean daily soil moisture.

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    Time series of daily soil moisture (5-cm depth) estimates from LPRM, CLASS default, and assimilation for data periods 27 Sep–31 Oct 2007, 1 May–23 Jun 2008, and 21 Aug–28 Oct 2008. CLASS default denotes estimate from the calibrated CLASS model.

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    Time series of daily ensemble mean soil moisture (5-cm depth) and its interval, and mean network (in situ) soil moisture for time periods 27 Sep–31 Oct 2007, 1 May–23 Jun 2008, and 21 Aug–28 Oct 2008.

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    Time series of daily soil moisture (20-cm depth) estimates from CLASS default and assimilation for data periods 27 Sep–31 Oct 2007, 1 May–23 June 2008, and 21 Aug–28 Oct 2008. CLASS default denotes estimate from the calibrated CLASS model.

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    Validation for daily soil moisture at 20-cm depth. Comparison between two soil moisture estimates CLASS default and CLASS-LPRM validation for data periods 27 Sep–31 Oct 2007, 1 May–23 Jun 2008, and 21 Aug–28 Oct 2008. CLASS default denotes estimate from the calibrated CLASS model.

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An Integrated Framework for a Joint Assimilation of Brightness Temperature and Soil Moisture Using the Nondominated Sorting Genetic Algorithm II

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  • 1 Department of Geography, University of Guelph, Guelph, Canada
  • 2 Department of Computing and Information Science, University of Guelph, Guelph, Canada
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Abstract

This study has applied the Nondominated Sorting Genetic Algorithm II (NSGA-II) in a two-step assimilation procedure to jointly assimilate brightness temperature into a radiative transfer model and soil moisture into a land surface model. The first assimilation procedure generates a time series of soil moisture by assimilating brightness temperature from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) into the Land Parameter Retrieval Model (LPRM). The second procedure generates assimilated soil moisture by assimilating the soil moisture from LPRM into the Canadian Land Surface Scheme (CLASS). Note that the assimilated soil moisture was generated by merging two soil moisture estimates: one from LPRM and the other from the CLASS simulation. The assimilated soil moisture is better than using the soil moisture determined either from the satellite observation or the land surface scheme alone. This method provides improved model state and parameterizations for both LPRM and CLASS with the aim to facilitate real-time forecasts when satellite information becomes available. Application of this framework to the Brightwater Creek watershed in southern Saskatchewan illustrates the utility of the joint assimilation framework to improve a time series of soil moisture estimates. The estimated soil moisture datasets were evaluated over an agricultural site in southern Saskatchewan using in situ monitoring networks. These results demonstrate that soil moisture generated from assimilation of brightness temperature could be improved by incorporating it into a land surface model. A comparison between the assimilated soil moisture and in situ dataset demonstrates an improvement in accuracy and temporal pattern that is accomplished through the assimilation framework.

Corresponding author address: Aaron Berg, Department of Geography, University of Guelph, Guelph ON N1G 2W1, Canada. E-mail: aberg@uoguelph.ca

Abstract

This study has applied the Nondominated Sorting Genetic Algorithm II (NSGA-II) in a two-step assimilation procedure to jointly assimilate brightness temperature into a radiative transfer model and soil moisture into a land surface model. The first assimilation procedure generates a time series of soil moisture by assimilating brightness temperature from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) into the Land Parameter Retrieval Model (LPRM). The second procedure generates assimilated soil moisture by assimilating the soil moisture from LPRM into the Canadian Land Surface Scheme (CLASS). Note that the assimilated soil moisture was generated by merging two soil moisture estimates: one from LPRM and the other from the CLASS simulation. The assimilated soil moisture is better than using the soil moisture determined either from the satellite observation or the land surface scheme alone. This method provides improved model state and parameterizations for both LPRM and CLASS with the aim to facilitate real-time forecasts when satellite information becomes available. Application of this framework to the Brightwater Creek watershed in southern Saskatchewan illustrates the utility of the joint assimilation framework to improve a time series of soil moisture estimates. The estimated soil moisture datasets were evaluated over an agricultural site in southern Saskatchewan using in situ monitoring networks. These results demonstrate that soil moisture generated from assimilation of brightness temperature could be improved by incorporating it into a land surface model. A comparison between the assimilated soil moisture and in situ dataset demonstrates an improvement in accuracy and temporal pattern that is accomplished through the assimilation framework.

Corresponding author address: Aaron Berg, Department of Geography, University of Guelph, Guelph ON N1G 2W1, Canada. E-mail: aberg@uoguelph.ca

1. Introduction

Soil moisture is an important component of the hydrological cycle as it plays an integral role in mass and energy exchange between the land surface and the atmosphere. As a result, accurate estimation of soil moisture can improve weather and streamflow forecasting in climate and hydrological models (Berg and Mulroy 2006; Reichle et al. 2007, 2008). Remotely sensed soil moisture data have become readily available from a variety of satellite platforms such as the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E). Assimilation of these datasets are necessary to integrate the surface soil moisture into the deeper soil layers. The technique of data assimilation (DA) is an analysis method for merging uncertain model predictions with imperfect observation data in an optimal way that is consistent with the physical descriptions of the system to better estimate and reduce uncertainty (Liu and Gupta 2007; Reichle 2008).

DA methods have been used widely in meteorology and atmospheric sciences (Reynolds et al. 2002; Burgers et al. 1998; Trenberth and Guillemot 1998; Hodur 1997; Schubert et al. 1993) to improve weather forecasts. The methods have focused largely on state estimation or the estimation of initial conditions for atmospheric models. In hydrological applications, DA methods in atmospheric sciences have been adapted and are not only limited to state estimation but also the estimation of errors when merging uncertain data with imperfect hydrological models. DA methods have been used to integrate ground-based, airborne, and satellite observations of near-surface soil moisture and temperature into land surface models (LSMs). Studies have ranged from the assimilation of surface energy flux (Caparrini et al. 2004a,b, 2003; Schuurmans et al. 2003), soil moisture data assimilation (Alavi et al. 2010; Reichle et al. 2007; Reichle and Koster 2005; Reichle et al. 2004, 2002a,b, 2001; Dunne and Entekhabi 2005; Walker and Houser 2004; Walker et al. 2002; Crow and Wood 2003; Crosson et al. 2002; Houser et al. 1998), and streaflow prediction (Moradkhani et al. 2005; Aubert et al. 2003; Troch et al. 2003). The studies have used complex DA methods such as inverse modeling (Wöhling et al. 2008; Vrugt et al. 2003), Kalman filter (Moradkhani et al. 2005; Aubert et al. 2003; Crosson et al. 2002), extended Kalman filter (EKF), ensemble Kalman filter (EnKF) (Reichle et al. 2007, 2002a; Crow and Wood 2003), variational data assimilation (VDA) (Caparrini et al. 2004a,b, 2003; Reichle et al. 2001), and genetic algorithms (Ines and Mohanty 2009, 2008; Chemin and Honda 2006).

The above methods are advanced DA techniques with clear and standard concepts. But the estimation of model state are usually conducted under the precondition of a perfect model structure and accurate model parameters or, at least, under the condition that model structure remains stationary or constant across different time periods. From a general systems standpoint, uncertainties in LSMs can arise from model state, model structure, and the parameterizations of the model (Liu and Gupta 2007). Other sources of uncertainty include inaccuracies in input data (e.g., precipitation) and observation datasets (e.g., soil moisture). It is apparent that these components of model uncertainty can affect the accuracy of model forecasts, and that DA methods should incorporate these uncertainties in their operations.

In assimilating soil moisture, many DA methods have aimed to either determine the Kalman gain function (denoted K) or to minimize the cost (or penalty) function (denoted J) by finding the optimal least squares estimator (or the best estimate) based on the observation dataset, the model estimate, and their associated uncertainties. The determination of K and the minimization of J are usually conducted in a statistical framework using large matrices, and are aimed to integrate errors from model inputs, the model structure, and observation dataset. While several parameter sets are usually evaluated for specific time periods, the resulting solutions do not usually represent an equally competitive set of solutions. That is, it is possible that the resulting solution set has solutions that perform better than other solutions.

Typically, satellite soil moisture data are retrieved using microwave radiative transfer model in an inverse modeling approach. The model associates or relates land surface parameters such as surface temperature, vegetation water content, and soil moisture to the observed brightness temperature (TB) (Njoku et al. 2003; Njoku and Li 1999). Because of uncertainties in land surface parameters in the retrieval algorithms, the satellite TB are sometimes assimilated into LSMs to improve soil moisture estimates (Reichle et al. 2008; Galantowicz et al. 1999).

This study uses an alternative DA method based on genetic algorithms (GAs). GAs employ the concept of natural evolution where candidate solutions to a problem compete among themselves, and the fitter (or high performing) solutions are varied to generate new ones. The competition between solutions and the continuous variation of fitter solutions, which are evaluated under changing conditions, usually results in high-performing solutions to a problem. GAs have been applied in DA studies to estimate soil hydraulic properties by inverting soil moisture (Ines and Mohanty 2009, 2008), explore irrigation water management (Ines et al. 2006; Ines and Honda 2005), and to quantify water consumption by monitoring evapotranspiration (Chemin and Honda 2006). While the study in Ines and Mohanty (2009) explores soil moisture assimilation, the application of GA in a two-step DA framework for improving soil moisture datasets from a satellite-based estimate and a land surface model have not been thoroughly investigated.

Our study applies the Nondominated Sorting Genetic Algorithm II (NSGA-II) in a two-step assimilation procedure to jointly assimilate satellite TB into a radiative transfer model and soil moisture into a land surface model. Our framework generates two sets of soil moisture datasets. The first soil moisture dataset was created by assimilating satellite TB into the Land Parameter Retrieval Model (LPRM)—a microwave radiative transfer model. The assimilated soil moisture data from LPRM are merged with soil moisture simulations from the Canadian Land Surface Scheme (CLASS) to determine an improved soil moisture data.

The rest of the paper is organized as follows. The next section broadly covers materials and methods, which includes a description of the genetic algorithm method and an outline of the joint data assimilation framework for TB and soil moisture. The results of the joint assimilation framework and a time series of the soil moisture data are reported and analyzed in the results and discussion section. The paper concludes with a summary of our findings, a discussion about the effectiveness of our joint assimilation framework, and the utility of the genetic algorithm to improve soil moisture from satellite observations.

2. Materials and method

a. Description of models (LPRM and CLASS), study area, and datasets

The microwave radiative transfer model used, LPRM, was developed by Owe et al. (2001) and was applied in Owe et al. (2008). The LPRM solves for surface soil moisture and vegetation optical depth simultaneously using a nonlinear iterative optimization procedure. The nonlinear iterative procedure employs a forward modeling approach to partition the surface emission into its primary source components—the soil emission and the canopy emission—and then optimizes on the canopy optical depth and the soil dielectric constant. The surface temperature is derived by a procedure using brightness temperature at 36.5 GHz (Holmes et al. 2009). The LRPM requires no field observations of soil moisture and no canopy biophysical properties for calibration purposes. As a result, the LPRM has no regional dependence and is applicable for different microwave frequency channels that are suitable for estimating soil moisture. Assessment of the LPRM over Canada is provided in Champagne et al. (2010). Table 1 shows information about the satellite brightness temperature data and model parameters for the LPRM. Detailed description of the LPRM can be found in Owe et al. (2001, 2008) and Holmes et al. (2009). The satellite observation data used were the AMSR-E, which was provided by the National Snow and Ice Data Center (NSIDC 2008). The AMSR-E dataset has a mean spatial resolution of 56 km, which is completely contained within our study area.

Table 1.

Information about the AMSR-E data, and model parameter values for the LPRM.

Table 1.

The land surface model used, CLASS, was developed at Environment Canada by Verseghy (1991), and has been updated by Verseghy et al. (1993) and Verseghy (2000). CLASS integrates the energy and water balances of the land surface forward in time from an initial starting point, making use of atmospheric forcing data to drive the simulation. Data required to run CLASS include atmospheric forcing data, surface vegetation data, soil data, and initial values for prognostic variables. At the beginning of the simulation, initialization is conducted for several variables including the temperatures and the liquid and frozen moisture contents of the soil layers; temperature, density, and albedo of snowpack if present; the temperature and intercepted rain and snow on the vegetation canopy; the temperature and depth of ponded water on the soil surface; and an empirical vegetation growth index.

State variables that are modified between different modeling time steps are shown in Table 2. Soil moisture for the initial time step has a low value because moisture recharge in the soil typically occurs on shorter scales than soil moisture loss. Additionally, Table 3 shows CLASS model parameters and their descriptions. These parameters are modified in the subsequent modeling time steps as part of model calibration and data assimilation steps to be described below. Note that upper and lower bounds of forcing variables were determined based on the distribution of weather stations in the study area. Forcing data were obtained from eight stations—Elbow, Last Mountain, Lucky Lake, Moose Jaw Airport, Moose Jaw, Outlook Prairie Farm Rehabilitation Administration (PFRA), Saskatoon Diefenbaker International Airport, and Watrous East—and averaged using inverse distance weighting. Data from these stations were collected from the National Climate Data and Information Archive available from Environment Canada.

Table 2.

CLASS state variables that were initialized between time steps (TS).

Table 2.
Table 3.

CLASS model parameters, their intervals and description. The parameter intervals are defined using the CLASS manual and based on the soil, vegetation, and meteorological conditions in the study area.

Table 3.

The CLASS output includes surface energy fluxes and associated state variables describing temperatures and moisture conditions. CLASS estimates the volumetric water content at each time step for each soil layer. The standard operational configuration for CLASS consists of three soil layers at depths 0.10, 0.25, and 3.75 m. The layer thicknesses can be changed to suit the needs for a specific application. In this study, we are interested in the near-surface soil moisture, which approximates to the top 5-cm thickness. As a result, the soil layers in CLASS were modified accordingly to generate soil moisture data at depths 0.05, 0.20, and 0.50 m.

This study was applied in the Brightwater Creek (BWC) watershed (location: 51.9°N, 106.6°W) in Saskatchewan (Fig. 1). The study area has 16 in situ monitoring stations with continuous soil moisture measurements at 5-, 20-, and 50-cm depths established over a 60 × 60 km2 area (Champagne et al. 2010). The site is generally flat (representative of the Canadian Prairie) and the installed sensors capture the expected variability (elevation, vegetation, soil, and landuse types) suitable for passive-microwave-derived soil moisture. In situ data were collected for growing seasons (April–October) in 2007 and 2008.

Fig. 1.
Fig. 1.

Soil moisture study area at Brightwater Creek, southern Saskatchewan.

Citation: Journal of Hydrometeorology 12, 6; 10.1175/JHM-D-10-05029.1

b. Data assimilation approach

Our DA method uses a genetic algorithm applied in a multiobjective fashion. Multiobjective genetic algorithms are analysis tools that are capable of evaluating multiple objectives simultaneously while searching through a population of candidate solutions to a problem. One such tool is the NSGA-II. NSGA-II was developed by Deb et al. (2002) and is a widely applied algorithm (Dumedah et al. 2010; Wöhling et al. 2008; Confesor and Whittaker 2007; Tang et al. 2006; Khu and Madsen 2005; Madsen 2003) with advanced and standard concepts capable of providing diverse solutions to a problem. Typically, the outcome to multiobjective problems is a set of solution(s) usually referred to as Pareto set (or Pareto frontier), which forms a trade-off between objective functions under evaluation (Deb et al. 2002; Deb and Goel 2001; Deb et al. 2000). The Pareto set is a set of incomparable solutions, as each solution has a competing accuracy when compared to other solutions and a distinct trade-off between the objectives.

In this study, the soil moisture DA problem is aimed at finding several optimal solutions for each simulation period and evaluating these solutions for subsequent simulation periods to provide a better model state for future simulations. The distribution and deviation of simulation from observation are used as a penalty function to properly merge background information with the observation dataset. To address the soil moisture assimilation problem, the task is threefold. First, estimate model parameters for a simulation period—for example, using bias [in Eq. (1)] and root-mean-square error (RMSE) [in Eq. (2)] to tune model parameters. A good parameter estimation will provide an improved model state for future simulations. Second, apply a DA procedure to improve model estimates by using the distribution and the deviation of simulation from observation as a penalty function. Third, merge background information with observation based on information from the penalty function and known uncertainties from both observation and background information using J [Eq. (3)]:
e1
e2
e3
where xb,i is background value (e.g., soil moisture) for the ith data point in the current window, xo,i is observed value (e.g., soil moisture) for the ith data point in the current window, is error variance of xb,i for the ith data point in the current window, is error variance of xo,i for the ith data point in the current window, xi is the analysis (i.e., the searched) value (e.g., soil moisture) for the ith data point in the current window that minimizes J(xi), and k is duration of the current time window or number of data points in the time window.

The evolution of several solutions is important as information from competing parameter sets could provide unique properties about simulation–observation dynamics for other modeling periods or be used to improve future model states. Usually, one optimum solution is inadequate to provide information about simulation–observation dynamics for different modeling periods all at the same time. Information about several solutions that are equally competitive for different simulation periods are needed to properly merge simulation with observation.

Our method uses a two-step assimilation procedure (shown in Fig. 2) to generate an improved soil moisture data from microwave satellite observation. First, we assimilate satellite TB into LPRM to provide a time series of soil moisture data. The independent assimilation of TB has no input from the LSM; as a result, it generates a soil moisture dataset that is subject to errors only from the satellite TB and the radiative transfer model. Second, we merge the estimated soil moisture from TB assimilation with soil moisture simulation from the LSM to provide an improved soil moisture that is better than using the individual soil moisture estimates either from the satellite observation or the LSM alone.

Fig. 2.
Fig. 2.

Two-step data assimilation framework from brightness temperature to soil moisture. Note that TB denotes brightness temperature, and “TB assimilated soil moisture” is a product of assimilating brightness temperatures from the satellite and LPRM simulation.

Citation: Journal of Hydrometeorology 12, 6; 10.1175/JHM-D-10-05029.1

c. NSGA-II framework for data assimilation

The NSGA-II uses advanced and standard multiobjective concepts such as incomparability, also known as nondominance. Incomparability assumes that when two or more independent objectives are optimized for a problem, there exist some solutions that are not comparable as it is uncommon to find a single solution with the best performance across all objectives. As a result, the solution to such problems is usually a set of incomparable solutions representing trade-offs between the objectives being optimized. The set of incomparable solutions is usually called the Pareto-optimal set. To draw comparison between solutions, the concept of nondominance is applied by comparing two candidate solutions to determine if one solution dominates the other or not. A candidate solution x1 is said to dominate solution x2 for a problem with k objectives if and only if (Deb et al. 2002, 2000; Deb and Goel 2001)

  • solution x1 performs as well as x2 in all objectives, and
  • solution x1 performs better than x2 in at least one objective.

Incomparability and nondominance are applied in NSGA-II to assign candidate solutions to different nondomination frontiers. Solution x1 is placed at a greater or more fit nondomination frontier as it dominates solution x2 in our description above. In cases where neither solution dominates the other—that is, solution x1 does not dominate x2, and x2 does not dominate x1—then the two solutions are incomparable and they are placed at the same nondomination frontier.

The NSGA-II method has been applied in the calibration of hydrological models (Dumedah et al. 2010; Wöhling et al. 2008; Confesor and Whittaker 2007; Tang et al. 2006; Khu and Madsen 2005; Madsen 2003). The NSGA-II method uses evolution and natural selection to solve problems that are based on stochastic trial-and-error or generate-and-test problems (Eiben and Smith 2003). The dynamics of randomly selecting and evolving a population of candidate solutions through time is appealing to the computational mechanics of DA.

In a DA context, a candidate solution is any single parameter set or a possible model state, and a population represents a number of possible parameter sets or ensemble of model states to evaluate. The computational procedure of DA involves a repeated search through massive combinations of parameters and model states for scenarios that provide a better merge between model outputs and observation data for different simulation periods. To address this task using NSGA-II, the randomized selection of model states–scenarios enables stochastic properties and capabilities, whereas the evolution of the population ensures that high-performing model states–scenarios survive to reproduce for subsequent populations.

Additionally, the NSGA-II has an adaptive capability to accommodate complex and nonlinear relationships under varying conditions caused by several model states–scenarios for the different simulation periods. The adaptive capacity of the NSGA-II method is most appealing in DA operations because the distribution and deviation of simulation from observation are used continuously to update the penalty function to properly merge future simulation to observation. In sum, the stochastic and adaptive capabilities of the NSGA-II and its memory capacity to search using population-based analysis makes the NSGA-II method suitable for applications in DA.

d. A joint data assimilation framework for brightness temperature and soil moisture

Our DA framework is designed to find an optimal estimate of soil moisture that is consistent with two soil moisture datasets. To achieve this objective, the framework uses NSGA-II in two separate assimilations. The first assimilation generates a time series of soil moisture through the assimilation of satellite TB into LPRM. The second assimilation merges two soil moisture estimates—one estimated from LPRM and the other simulated from CLASS—to determine an improved soil moisture that is better than using either LPRM or CLASS alone. These two assimilations are described in detail in the following sections.

1) Assimilation of satellite brightness temperature into LRPM

This component assimilates satellite TB into LPRM to generate a time series of soil moisture. The time series is based on a sequence of data points where each data point represents one day. For any data point, the NSGA-II randomly generates r number of solutions (for LPRM), which constitute a population (denoted Pr). For this study r = 20 was used; the NSGA-II actually evaluates 2r parameter sets for each iteration where both parent and child solutions compete for survival. Note that Pr represents an ensemble of LPRM solutions composed of unique parameter sets (or unique model parameterizations). The candidate solutions in Pr are evaluated using the objective functions: bias, RMSE, and J. The bias and RMSE minimizes error in daily TB (satellite observation and LPRM simulation). The LPRM uses an inverse modeling approach to simulate TB by optimizing for soil moisture. The J merges TB for satellite observation and LPRM simulation while incorporating uncertainties from observation (i.e., satellite TB), model (i.e., LPRM), and background information (i.e., first guess from LPRM). Note that although LPRM does not simulate state variables, the assimilation procedure ensures that soil moisture for previous day and current satellite TB are incorporated into determining the assimilated soil moisture. That is, the assimilated LPRM soil moisture cannot be worse than using either the satellite TB alone or the previous parameterization of LPRM.

The result is a Pareto set of TB found in objective space and the corresponding values in parameter space and soil moisture values that produce the TB. The m (where mr) number of soil moisture values (in the Pareto set) for the current data point are used to estimate the average soil moisture and its error variance. At the current data point, the parameter values in the Pareto set are used to predict m number of TB for the next (i.e., future) data point. The m number of TB values for the current data point are used to estimate the average TB and its error variance. The average TB and its error variance are used as background information for the future data point. These procedures are repeated to assimilate satellite TB into LPRM, and to generate soil moisture values and its error variance for subsequent data points.

The result is a time series of soil moisture values and their error variances, which represent the retrieved soil moisture from the satellite observation to be merged with soil moisture simulated from CLASS. It is worth noting that the m number of soil moisture values retrieved for each data point represent an ensemble of solutions that are generated based on different parameterizations of LPRM, and are equally competitive and consistent with past predictions (i.e., background information) of LPRM. These procedures are applied to estimate soil moisture using LPRM (results in section 3a).

2) Assimilation of satellite soil moisture into CLASS: A merger between two soil moisture estimates

This component assimilates the estimated satellite soil moisture (from LPRM) into CLASS. Using the generated time series of soil moisture from LPRM and a simulation of soil moisture from CLASS, the NSGA-II method merges the two soil moisture datasets. The merging procedure incorporates errors from observation (LPRM soil moisture), simulation, and CLASS inputs. The procedure is conducted over a moving time window that is defined as a series of data points—for example, 20 data points for one time window. That is, the framework chooses a size for a moving time window, w (e.g., w = 20 days), where t1, t2, t3, … , tn denote the first, second, and third time windows to the nth time window. To make the time windows a truly overlapping moving window, the windows are separated by (w/2) such that if t1 starts from 1 to 20 then t2 will start from 10 to 30. The overlapping moving window ensures that soil moisture for each data point is estimated twice, starting from all data points in the second window to the penultimate window.

The NSGA-II randomly generates a population of solutions (denoted Pq) of size q specifically for CLASS. Again, NSGA-II evaluates 2q parameter sets of CLASS for each iteration; q was set to 50. The Pq is an ensemble of CLASS parameter sets (defined in Table 3), each of which produces an estimate of soil moisture. For any time window, Pq undergoes evolution to merge the two soil moisture datasets by estimating model parameters and inputs for CLASS through the minimization of three objectives: bias, RMSE, and J. As in the assimilation of TB, bias and RMSE minimize the error in daily soil moisture, whereas J determines a soil moisture that provides an optimal compromise between soil moisture estimates from LPRM and CLASS. The J incorporates uncertainties from observation (LPRM soil moisture), model (CLASS) and its inputs, and background information (i.e., first guess from CLASS). Note that the background soil moisture and its error variance for the first time window is based on a default (open loop) run of CLASS. For subsequent time windows, the background soil moisture and its error variance are determined from the previous model state and parameterizations (i.e., the best solutions obtained so far). For each time step, state variables for CLASS remained unchanged but are updated between time steps, whereas CLASS model parameters are optimized to minimize the objectives within time steps.

The resulting output is a merged soil moisture value for each data point in the current time window, and a Pareto set with z (zq) number of solutions representing a competitive ensemble of solutions for initiating CLASS. These solutions are carried over as seed population for the next (or future) time window: t2. Before simulation for the next time window begins, the Pareto set for the current time window, t1, is used to predict for the future time window: t2. The prediction for t2 generates z number of soil moisture values for each data point in the future time window; these are used to compute the average soil moisture and its error variance for each data point. This information is used as the background for the next time window: t2.

At t2, the above procedure for t1 is repeated to generate a time series of soil moisture values for t2 by first assimilating satellite TB into LPRM to estimate soil moisture. The LPRM-estimated soil moisture is merged with simulated soil moisture from CLASS. This is achieved through the evolution of the population Pq to minimize bias, RMSE, and J. This integrated procedure of jointly assimilating TB and soil moisture is repeated for subsequent time windows until the last time window tn or the referenced number n of time windows is reached.

In combination with the first assimilation, the key output of this framework is twofold. First, the framework generates a time series of soil moisture values retrieved specifically by assimilating satellite TB into LPRM. Second, a time series of soil moisture values is generated by merging two soil moisture estimates—one from LPRM and the other from CLASS—such that the assimilated soil moisture is better than using either LPRM or CLASS alone. Note that the final assimilated soil moisture is based on improved model state and parameterization of CLASS.

3. Results and discussion

This study has estimated surface soil moisture using two different models: one through the assimilation of satellite TB using LPRM and the other through the assimilation of the retrieved soil moisture from LPRM into CLASS. These soil moisture estimates are compared to in situ data. Note that the in situ dataset has not been used in either assimilation procedure. A time series of the in situ dataset is shown in Fig. 3, where the error bars represent one standard deviation from the average daily soil moisture. The in situ dataset has three continuous time periods: 27 September–31 October 2007, 1 May–23 June 2008, and 21 August–28 October 2008. As a result, the two assimilation procedures are evaluated specifically for these periods where in situ data were available. Note that the assimilations are run continuously from August 2007 to October 2008, and results are evaluated over the periods where the in situ data is available.

Fig. 3.
Fig. 3.

A time series of the observed in situ soil moisture dataset that was used to evaluate the two assimilation procedures. The error bars represent one standard deviation from the mean daily soil moisture.

Citation: Journal of Hydrometeorology 12, 6; 10.1175/JHM-D-10-05029.1

a. Assimilation of brightness temperature for ascending and descending orbits

Radiative models for retrieving soil moisture from satellite TB usually generate varying outcomes based on the satellite acquisition time either ascending pass [about 1330 local time (LT)] or descending pass (about 0130 LT). We evaluate the AMSR-E dataset for both ascending and descending passes to determine which overpass to include in this case study for future assimilation into CLASS. A suitable satellite pass time was identified based on its comparison to the in situ soil moisture. The 6.9-GHz frequency was used to retrieve the soil moisture (using horizontal polarization). Note that radio frequency interference (RFI) was not detected in our study area for the period of data used and only the 6.9-GHz brightness temperature was used. If RFI were detected, we would have to had a second simulation and an assimilation of brightness temperature at 10.7 GHz so as to include this data as a replacement for the data at 6.9 GHz.

The NSGA-II uses the LPRM to retrieve soil moisture by assimilating TB for the two orbits. The assimilation for ascending orbit is denoted LPRM-AssimAsc, and descending orbit is denoted LPRM-AssimDesc. Results from the default approach of retrieving soil moisture using LPRM for both ascending and descending passes are also compared. The comparisons between the retrieved soil moisture values and the in situ data are shown in Table 4 for various evaluation measures.

Table 4.

A comparison between soil moisture [m3 (m3)−1] estimated through the assimilation of satellite TB into LPRM and soil moisture from LPRM default using both ascending and descending passes. Here, R = pairwise correlation coefficient, = degree of agreement, and xs,i and xo,i denote simulated and observed soil moisture for ith day.

Table 4.

The evaluation results show that assimilation of TB has improved soil moisture estimates compared with the ones generated from the LPRM by default, denoted LPRM-Asc for ascending orbit and LPRM-Desc for descending orbit. Overall, the LPRM-default has the highest error ranging from 8% to 12% and has very low correlation to the in situ soil moisture. Note that the LPRM-default soil moisture dataset was generated for our study area based on the study by Owe et al. (2008). As a result, our study has no control of the parameterizations of LPRM that were used to generate this dataset.

The comparison between ascending and descending passes is not straight forward. Generally, the descending pass has a better accuracy but with a low correlation to the in situ data. The ascending pass, in contrast, has a temporal pattern more similar to the in situ soil moisture (based on correlation coefficient) but with a higher error margin. For the purpose of this study we used LPRM-AssimDesc in the LPRM to retrieve the soil moisture by assimilating TB.

The evaluation measures in Table 4 have illustrated how the assimilation of satellite TB into LPRM has improved soil moisture estimates. To quantify the differences between the estimated soil moisture datasets, we test their residuals from the in situ dataset. The residuals of each estimated soil moisture dataset were compared to determine whether the means of the residuals are the same using analysis of variance (ANOVA). The residuals are determined as the difference between the in situ soil moisture and each of the four soil moisture datasets: LPRM-AssimAsc, LPRM-AssimDesc, LPRM-Asc, and LPRM-Desc. The comparisons have a significance of 0.000 [degrees of freedom (df) = 3596 and F = 72.28), suggesting that at least one of the datasets is different.

To identify which means of the residuals are different, Tukey’s test was conducted on the residuals. The Tukey’s test (using mean differences) showed that LPRM-AssimDesc has the lowest residual, followed by LPRM-AssimAsc. Using the significance, soil moisture estimates from LPRM-AssimDesc and LPRM-AssimAsc are statistically similar (p = 0.160) but LPRM-AssimDesc has an added benefit of being closer to the in situ dataset. Both LPRM-AssimDesc and LPRM-AssimAsc are statistically different from LPRM-Asc and LPRM-Desc, with p < 0.0001.

b. A comparison between soil moisture estimates from LPRM, CLASS default, and assimilation

This section presents outputs for the joint assimilation of TB and soil moisture for LRPM and CLASS using the NSGA-II framework. The results are presented for the assimilation of TB into the LPRM (LPRM-AssimDesc) to retrieve soil moisture, and for the merger of soil moisture estimates from LPRM and CLASS.

A time series comparison of estimated soil moisture (at 5-cm depth) between various models is shown in Fig. 4. The assimilated (or merged) soil moisture data points are closely located to the in situ soil moisture when compared to individual estimates from LPRM and CLASS default. As a merger between LPRM and CLASS soil moisture estimates, the assimilation framework simultaneously combines both estimates and incorporates model state from previous assimilation periods. Performance of the assimilation in the spring season (May–June 2008) is noticeably improved even though it generally overestimates the observation. The assimilation (and simulation from other models: LPRM and CLASS) overestimates the observation in the summer–fall season. Although the assimilation overestimates the in situ data in all three periods it provides an improved data compared to estimates from LPRM and CLASS default. In other words, when presented with the three output options, one would choose the CLASS–LPRM output. The ensemble mean of the assimilation and its daily standard deviation are shown in Fig. 5 in comparison to the network (i.e., in situ) mean soil moisture.

Fig. 4.
Fig. 4.

Time series of daily soil moisture (5-cm depth) estimates from LPRM, CLASS default, and assimilation for data periods 27 Sep–31 Oct 2007, 1 May–23 Jun 2008, and 21 Aug–28 Oct 2008. CLASS default denotes estimate from the calibrated CLASS model.

Citation: Journal of Hydrometeorology 12, 6; 10.1175/JHM-D-10-05029.1

Fig. 5.
Fig. 5.

Time series of daily ensemble mean soil moisture (5-cm depth) and its interval, and mean network (in situ) soil moisture for time periods 27 Sep–31 Oct 2007, 1 May–23 Jun 2008, and 21 Aug–28 Oct 2008.

Citation: Journal of Hydrometeorology 12, 6; 10.1175/JHM-D-10-05029.1

Furthermore, we compared soil moisture data at 20-cm depth for the default simulation from CLASS and the estimate from our evaluation to the in situ dataset. The comparison is shown in Figs. 6 and 7 for the two soil moisture estimates. Both datasets are well distributed around the in situ soil moisture, but the evaluation dataset shows a better match as its plotted points spread closely to the in situ soil moisture. In contrast, the estimate from CLASS default is scattered far away from the in situ dataset. The estimate from CLASS default has been calibrated based on the information in the study area. As a result, CLASS estimates (both at 5- and 20-cm depths) were not any random model output but finely tuned as best as possible to the study area.

Fig. 6.
Fig. 6.

Time series of daily soil moisture (20-cm depth) estimates from CLASS default and assimilation for data periods 27 Sep–31 Oct 2007, 1 May–23 June 2008, and 21 Aug–28 Oct 2008. CLASS default denotes estimate from the calibrated CLASS model.

Citation: Journal of Hydrometeorology 12, 6; 10.1175/JHM-D-10-05029.1

Fig. 7.
Fig. 7.

Validation for daily soil moisture at 20-cm depth. Comparison between two soil moisture estimates CLASS default and CLASS-LPRM validation for data periods 27 Sep–31 Oct 2007, 1 May–23 Jun 2008, and 21 Aug–28 Oct 2008. CLASS default denotes estimate from the calibrated CLASS model.

Citation: Journal of Hydrometeorology 12, 6; 10.1175/JHM-D-10-05029.1

An evaluation for the various models is shown in Table 5. Generally, as assimilation period increases the various models have consistently improved their performance. This is partly due to an improved estimate of the model state from past periods, which is incorporated into merging the two soil moisture estimates. The merged soil moisture from LPRM and CLASS (referred to as “assimilated” in Table 5) is better than the individual soil moisture estimates generated from either model. The assimilation shows improvement in the evaluation measures including accuracy, bias, degree of agreement, and a better temporal pattern that is more similar to the in situ soil moisture. The level of accuracy for soil moisture estimates from LPRM and CLASS have a direct impact on the level of improvement in the assimilated soil moisture. Particularly, improvement in soil moisture retrieval from LPRM has considerable influence on the assimilation as the penalty to the LRPM estimates is generally low for most time steps compared to the penalty for CLASS simulations.

Table 5.

A comparison between soil moisture [m3 (m3)−1] estimates generated from LPRM, CLASS default, and assimilated (merged soil moisture). The assimilation framework is validated for soil moisture at 20-cm depth. Here, R = pairwise correlation coefficient, = degree of agreement, and xs,i and xo,i denote simulated and observed soil moisture for ith day.

Table 5.

Based on Figs. 46 and Table 5 it is clear that the assimilated versions of CLASS and LPRM are improving through time. Note that the assimilations were run continuously over and between the three evaluation time periods with consistent assimilation of data. Therefore we should expect some continuous improvement to the assimilated version of the modes as more data is available. Whether these model improvements through time are an artifact of differing micrometeorological conditions or caused by different vegetation stages is difficult to isolate. However, it is worth noting that improvement through time is limited to the assimilated models (LPRM and CLASS) and is not reflected in the LPRM and CLASS default simulations.

The results in Table 5 have demonstrated the performance of the assimilation framework to improve soil moisture estimates. However, it is important to show that the soil moisture datasets are statistically different and that the improved soil moisture generated from the assimilation framework is not due to some random effect. To illustrate that there are differences between the soil moisture datasets, we evaluate the residuals of each of the soil moisture datasets from the in situ dataset. ANOVA was applied on residuals of the soil moisture datasets to determine whether the means of the residuals are different. The residuals are computed for the three soil moisture datasets: the assimilated soil moisture (i.e., Assim), LPRM-AssimDesc, and the CLASS simulation. The residuals were determined by finding the difference between the in situ soil moisture and each of the three soil moisture datasets. The comparisons showed p < 0.0001 (df = 2447 and F = 9.574) where at least one mean of the residuals is different.

Tukey’s test was applied on the residuals to specify which means of the residuals are different. The Tukey’s test (based on mean difference) revealed that the Assim has the lowest mean of the residuals while the CLASS soil moisture estimate has the largest residual. Residuals from Assim and LPRM-AssimDesc are statistically identical (p = 0.42) but the Assim is much closer to the in situ dataset as indicated by its small residual.

As exemplified in the above results, our method provides an integrated approach and an improved estimate of soil moisture. Note that our assimilation framework has been illustrated for a single study area: Brightwater Creek watershed. The method can be easily adapted to multiple sites (or grids) with varying physiographic conditions in large scale applications. In particular, the continuous estimation of model state and parameterizations of both LPRM and CLASS would facilitate real-time soil moisture forecasts when satellite data becomes available. Future study should explore robustness–sensitivity of parameter sets obtained from the assimilation results following work conducted by Dumedah et al. (2010, 2011), which examines model parameterizations and solution robustness using evolutionary strategies.

4. Conclusions

This study has illustrated a two-step assimilation procedure to jointly assimilate satellite TB into a microwave radiative transfer model and soil moisture into a land surface model. The first assimilation incorporates satellite TB from AMSR-E into LPRM to generate a time series of soil moisture data. The second procedure generates a time series of improved soil moisture by merging soil moisture estimates from LPRM and CLASS simulation. We have demonstrated that the assimilation of TB can improve soil moisture retrieval for microwave radiative transfer models (e.g., LRPM). The retrieved satellite soil moisture has been shown to be accurate and has a temporal pattern that is more similar to the in situ soil moisture. The two satellite acquisition passes—ascending and descending—were evaluated for retrieving soil moisture using LPRM for our study area. The assimilation of satellite TB into LPRM for both passes has been shown to improve the soil moisture dataset compared to the estimate from LPRM default.

The soil moisture from LPRM retrieved independently by assimilating TB was incorporated into an assimilation framework that merges the LPRM soil moisture to the soil moisture generated from CLASS. The assimilation incorporates independent errors from both LPRM and CLASS to generate an improved soil moisture that is better than using either model alone. Our results show that an improvement in the assimilation of TB for LPRM has a direct impact on the merged soil moisture, emphasizing the importance of assimilating TB. The method demonstrates that soil moisture generated from assimilation of satellite brightness temperature could be improved by incorporating it into a land surface model.

Application of this framework to the Brightwater Creek watershed in Saskatchewan illustrates the utility of our joint assimilation framework to improve a time series of soil moisture estimates. The retrieved soil moisture dataset was evaluated over an agricultural site in Saskatchewan using in situ monitoring networks. A comparison between the assimilated soil moisture and in situ data demonstrates an improvement in accuracy and temporal pattern that is accomplished through our assimilation framework. These improvements were based on improved estimate of model state and parameterizations for LPRM and CLASS, which are important drivers for efficient forecasting systems.

Acknowledgments

This work is supported by the Natural Sciences and Engineering Research Council of Canada and the Canadian Foundation for Climate and Atmospheric Sciences. The authors acknowledge the work of all people involved in installing and maintaining the soil moisture monitoring networks, particularly Jonathan Belanger, Ingrid Volet, Haily Ashworth, Matt Reid, Mark Cliffe-Phillips, Kristian Imgrund, and Brenda Toth. The authors thank Gordon Drewitt for providing the meteorological forcing data, Bruce Davidson for providing information about CLASS, and Thomas Holmes and Richard de Jeu for providing source code for the Land Parameter Retrieval Model (LPRM). We thank the anonymous reviewers for their comments.

REFERENCES

  • Alavi, N., , Berg A. , , Warland J. , , Parkin G. , , Verseghy D. , , and Bartlett P. , 2010: Assimilating soil moisture variability into the class to improve latent heat flux estimation. Can. Water Resour. J., 35, 116.

    • Search Google Scholar
    • Export Citation
  • Aubert, D., , Loumagne C. , , and Oudin L. , 2003: Sequential assimilation of soil moisture and streamflow data in a conceptual rainfall–runoff model. J. Hydrol., 280, 145161.

    • Search Google Scholar
    • Export Citation
  • Berg, A. A., , and Mulroy K. , 2006: Streamflow predictability given macro-scale estimates of the initial soil moisture status. Hydrol. Sci. J., 51, 642654.

    • Search Google Scholar
    • Export Citation
  • Burgers, T., , Van Leeuwen P. J. , , and Evensen G. , 1998: Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev., 126, 17191724.

  • Caparrini, F., , Castelli F. , , and Entekhabi D. , 2003: Mapping of land-atmosphere heat fluxes and surface parameters with remote sensing data. Bound.-Layer Meteor., 107, 605633.

    • Search Google Scholar
    • Export Citation
  • Caparrini, F., , Castelli F. , , and Entekhabi D. , 2004a: Estimation of surface turbulent fluxes through assimilation of radiometric surface temperature sequences. J. Hydrometeor., 5, 145159.

    • Search Google Scholar
    • Export Citation
  • Caparrini, F., , Castelli F. , , and Entekhabi D. , 2004b: Variational estimation of soil and vegetation turbulent transfer and heat flux parameters from sequences of multisensor imagery. Water Resour. Res., 40, W12515, doi:10.1029/2004WR003358.

    • Search Google Scholar
    • Export Citation
  • Champagne, C., , Berg A. , , Belanger J. , , McNairn H. , , and deJeu R. , 2010: Evaluation of soil moisture derived from passive microwave remote sensing over agricultural sites in Canada using ground-based soil moisture monitoring networks. Int. J. Remote Sens., 31, 36693690.

    • Search Google Scholar
    • Export Citation
  • Chemin, Y., , and Honda K. , 2006: Spatiotemporal fusion of rice actual evapotranspiration with genetic algorithms and an agrohydrological model. IEEE Trans. Geosci. Remote Sens., 44, 34623469.

    • Search Google Scholar
    • Export Citation
  • Confesor, R. B., , and Whittaker G. W. , 2007: Automatic calibration of hydrologic models with multi-objective evolutionary algorithm and Pareto optimization. J. Amer. Water Resour. Assoc., 43, 981989.

    • Search Google Scholar
    • Export Citation
  • Crosson, W. L., , Laymon C. A. , , Inguva R. , , and Schamschula M. P. , 2002: Assimilating remote sensing data in a surface flux-soil moisture model. Hydrol. Processes, 16, 16451662.

    • Search Google Scholar
    • Export Citation
  • Crow, W. T., , and Wood E. F. , 2003: The assimilation of remotely sensed soil brightness temperature imagery into a land surface model using ensemble Kalman filtering: A case study based on ESTAR measurements during SGP97. Adv. Water Resour., 26, 137149.

    • Search Google Scholar
    • Export Citation
  • Deb, K., , and Goel T. , 2001: Controlled elitist non-dominated sorting genetic algorithms for better convergence. Evolutionary Multi-Criterion Optimization, E. Zitzler et al., Eds., Lecture Notes in Computer Science, Vol. 1993, Springer, 67–81.

    • Search Google Scholar
    • Export Citation
  • Deb, K., , Agrawal S. , , Pratap A. , , and Meyarivan T. , 2000: A fast elitist non-dominated sorting genetic algorithms for multi-objective optimization: NSGA-II. Parallel Problem Solving from Nature—PPSN VI, M. Schoenauer et al., Eds., Lecture Notes in Computer Science, Vol. 1917, Springer, 849–858.

    • Search Google Scholar
    • Export Citation
  • Deb, K., , Pratap A. , , Agrawal S. , , and Meyarivan T. , 2002: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput., 6, 182197.

    • Search Google Scholar
    • Export Citation
  • Dumedah, G., , Berg A. A. , , Wineberg M. , , and Collier R. , 2010: Selecting model parameter sets from a trade-off surface generated from the non-dominated sorting genetic algorithm-II. Water Resour. Manage., 24, 44694489, doi: 10.1007/s11269-010-9668-y.

    • Search Google Scholar
    • Export Citation
  • Dumedah, G., , Berg A. A. , , and Wineberg M. , 2011: Evaluating auto-selection methods used for choosing solutions from Pareto-optimal set: Does non-dominance persist from calibration to validation phase? J. Hydrol. Eng., in press.

    • Search Google Scholar
    • Export Citation
  • Dunne, S., , and Entekhabi D. , 2005: An ensemble-based reanalysis approach to land data assimilation. Water Resour. Res., 41, W02013, doi:10.1029/2004WR003449.

    • Search Google Scholar
    • Export Citation
  • Eiben, A. E., , and Smith J. E. , 2003: Introduction to Evolutionary Computing. Springer, 299 pp.

  • Galantowicz, J. F., , Entekhabi D. , , and Njoku E. , 1999: Tests of sequential data assimilation for retrieving profile soil moisture and temperature from observed l-band radiobrightness. IEEE Trans. Geosci. Remote Sens., 37, 18601870.

    • Search Google Scholar
    • Export Citation
  • Hodur, R. M., 1997: The Naval Research Laboratory’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). Mon. Wea. Rev., 125, 14141430.

    • Search Google Scholar
    • Export Citation
  • Holmes, T. R. H., , De Jeu R. A. M. , , Owe M. , , and Dolman A. J. , 2009: Land surface temperature from Ka band (37 GHz) passive microwave observations. J. Geophys. Res., 114, D04113, doi:10.1029/2008JD010257.

    • Search Google Scholar
    • Export Citation
  • Houser, P. R., , Shuttleworth W. J. , , Famiglietti J. S. , , Gupta H. V. , , Syed K. H. , , and Goodrich D. C. , 1998: Integration of soil moisture remote sensing and hydrologic modeling using data assimilation. Water Resour. Res., 34, 34053420.

    • Search Google Scholar
    • Export Citation
  • Ines, A. V. M., , and Honda K. , 2005: On quantifying agricultural and water management practices from low spatial resolution RS data using genetic algorithms: A numerical study for mixed-pixel environment. Adv. Water Resour., 28, 856870.

    • Search Google Scholar
    • Export Citation
  • Ines, A. V. M., , and Mohanty B. P. , 2008: Near-surface soil moisture assimilation for quantifying effective soil hydraulic properties under different hydroclimatic conditions. Vadose Zone J., 7, 3952.

    • Search Google Scholar
    • Export Citation
  • Ines, A. V. M., , and Mohanty B. P. , 2009: Near-surface soil moisture assimilation for quantifying effective soil hydraulic properties using genetic algorithms: 2. Using airborne remote sensing during SGP97 and SMEX02. Water Resour. Res., 45, W01408, doi:10.1029/2008WR007022.

    • Search Google Scholar
    • Export Citation
  • Ines, A. V. M., , Honda K. , , Das Gupta A. , , Droogers P. , , and Clemente R. S. , 2006: Combining remote sensing-simulation modeling and genetic algorithm optimization to explore water management options in irrigated agriculture. Agric. Water Manage., 83, 221232.

    • Search Google Scholar
    • Export Citation
  • Khu, S. T., , and Madsen H. , 2005: Multiobjective calibration with Pareto preference ordering: An application to rainfall-runoff model calibration. Water Resour. Res., 41, W03004, doi:10.1029/2004WR003041.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , and Gupta H. V. , 2007: Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework. Water Resour. Res., 43, W07401, doi:10.1029/2006WR005756.

    • Search Google Scholar
    • Export Citation
  • Madsen, H., 2003: Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives. Adv. Water Resour., 26, 205216.

    • Search Google Scholar
    • Export Citation
  • Moradkhani, H., , Hsu K.-L. , , Gupta H. , , and Sorooshian S. , 2005: Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter. Water Resour. Res., 41, W05012, doi:10.1029/2004WR003604.

    • Search Google Scholar
    • Export Citation
  • Njoku, E. G., , and Li L. , 1999: Retrieval of land surface parameters using passive microwave measurements at 6-18 GHz. IEEE Trans. Geosci. Remote Sens., 37, 7993.

    • Search Google Scholar
    • Export Citation
  • Njoku, E. G., , Jackson T. J. , , Lakshmi V. , , Chan T. K. , , and Nghiem S. V. , 2003: Soil moisture retrieval from AMSR-E. IEEE Trans. Geosci. Remote Sens., 41, 215229.

    • Search Google Scholar
    • Export Citation
  • NSIDC, 2008: AMSR-E/Aqua daily L3 surface soil moisture, interpretive parameters, and QC EASE-grids v002. National Snow and Ice Data Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/docs/daac/ae_land3_l3_soil_moisture.gd.html.]

    • Search Google Scholar
    • Export Citation
  • Owe, M., , de Jeu R. , , and Walker J. , 2001: A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index. IEEE Trans. Geosci. Remote Sens., 39, 16431654.

    • Search Google Scholar
    • Export Citation
  • Owe, M., , de Jeu R. , , and Holmes T. , 2008: Multisensor historical climatology of satellite-derived global land surface moisture. J. Geophys. Res., 113, F01002, doi:10.1029/2007JF000769.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., 2008: Data assimilation methods in the Earth sciences. Adv. Water Resour., 31, 14111418.

  • Reichle, R. H., , and Koster R. D. , 2005: Global assimilation of satellite surface soil moisture retrievals into the NASA Catchment land surface model. Geophys. Res. Lett., 32, L02404, doi:10.1029/2004GL021700.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Entekhabi D. , , and McLaughlin D. B. , 2001: Downscaling of radio brightness measurements for soil moisture estimation: A four-dimensional variational data assimilation approach. Water Resour. Res., 37, 23532364.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , McLaughlin D. B. , , and Entekhabi D. , 2002a: Hydrologic data assimilation with the ensemble Kalman filter. Mon. Wea. Rev., 130, 103114.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Walker J. P. , , Koster R. D. , , and Houser P. R. , 2002b: Extended versus ensemble Kalman filtering for land data assimilation. J. Hydrometeor., 3, 728740.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Koster R. D. , , Dong J. , , and Berg A. A. , 2004: Global soil moisture from satellite observations, land surface models, and ground data: Implications for data assimilation. J. Hydrometeor., 5, 430442.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Koster R. D. , , Liu P. , , Mahanama S. P. P. , , Njoku E. G. , , and Owe M. , 2007: Comparison and assimilation of global soil moisture retrievals from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) and the Scanning Multichannel Microwave Radiometer (SMMR). J. Geophys. Res., 112, D09108, doi:10.1029/2006JD008033.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Crow W. T. , , Koster R. D. , , Sharif H. O. , , and Mahanama S. P. P. , 2008: Contribution of soil moisture retrievals to land data assimilation products. Geophys. Res. Lett., 35, L01404, doi:10.1029/2007GL031986.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., , Rayner N. A. , , Smith T. M. , , Stokes D. C. , , and Wang W. , 2002: An improved in situ and satellite SST analysis for climate. J. Climate, 15, 16091625.

    • Search Google Scholar
    • Export Citation
  • Schubert, S. D., , Rood R. B. , , and Pfaendtner J. , 1993: An assimilated dataset for earth science applications. Bull. Amer. Meteor. Soc., 74, 23312342.

    • Search Google Scholar
    • Export Citation
  • Schuurmans, J. M., , Troch P. A. , , Veldhuizen A. A. , , Bastiaanssen W. G. M. , , and Bierkens M. F. P. , 2003: Assimilation of remotely sensed latent heat flux in a distributed hydrological model. Adv. Water Resour., 26, 151159.

    • Search Google Scholar
    • Export Citation
  • Tang, Y., , Reed P. , , and Wagener T. , 2006: How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration? Hydrol. Earth Syst. Sci., 10, 289307.

    • Search Google Scholar
    • Export Citation
  • Trenberth, K. E., , and Guillemot C. J. , 1998: Evaluation of the atmospheric moisture and hydrological cycle in the NCEP/NCAR reanalyses. Climate Dyn., 14, 213231.

    • Search Google Scholar
    • Export Citation
  • Troch, P., , Paniconi C. , , and McLaughlin D. , 2003: Catchment-scale hydrological modeling and data assimilation. Adv. Water Resour., 26, 131135.

    • Search Google Scholar
    • Export Citation
  • Verseghy, D. L., 1991: CLASS—A Canadian land surface scheme for GCMs: I. Soil model. Int. J. Climatol., 11, 111133.

  • Verseghy, D. L., 2000: The Canadian Land Surface Scheme (CLASS): Its history and future. Atmos.–Ocean, 38, 113.

  • Verseghy, D. L., , McFarlane N. A. , , and Lazare M. , 1993: CLASS—A Canadian land surface scheme for GCMs: II. Vegetation model and coupled runs. Int. J. Climatol., 13, 347370.

    • Search Google Scholar
    • Export Citation
  • Vrugt, J. A., , Gupta H. V. , , Bastidas L. A. , , Bouten W. , , and Sorooshian S. , 2003: Effective and efficient algorithm for multiobjective optimization of hydrologic models. Water Resour. Res., 39, 1214, doi:10.1029/2002WR001746.

    • Search Google Scholar
    • Export Citation
  • Walker, J. P., , and Houser P. R. , 2004: Requirements of a global near-surface soil moisture satellite mission: Accuracy, repeat time, and spatial resolution. Adv. Water Resour., 27, 785801.

    • Search Google Scholar
    • Export Citation
  • Walker, J. P., , Willgoose G. R. , , and Kalma J. D. , 2002: Three-dimensional soil moisture profile retrieval by assimilation of near-surface measurements: Simplified Kalman filter covariance forecasting and field application. Water Resour. Res., 38, 1301, doi:10.1029/2002WR001545.

    • Search Google Scholar
    • Export Citation
  • Wöhling, T., , Vrugt J. A. , , and Barkle G. F. , 2008: Comparison of three multiobjective optimization algorithms for inverse modeling of vadose zone hydraulic properties. Soil Sci. Soc. Amer. J., 72, 305319.

    • Search Google Scholar
    • Export Citation
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