Review of the Kalman-type hydrological data assimilation

Figures & data

Figure 1. Types of estimation problem: (i) prediction, (ii) filtering, (iii) smoothing.

Figure 2. Schematic of the EnKF with perturbed observations (Moradkhani et al. 2005b). Reprinted from Dual state–parameter estimation of hydrological models using ensemble Kalman filter. H. Moradkhani, S. Sorooshian, H. V. Gupta, P. R. Houser. Advances in Water Resources 28 (2005), 135–147. Copyright (2005), with permission from Elsevier.

Table 1. Literature summary of state and parameter(s) selection.

Reference	Method	Model	State	Parameter(s)	Observations
Reichle et al. (2002a)	EnKF	Reichle et al. (2001)	Soil moisture and soil temperature	–	L-band microwave radio brightness
Madsen et al. (2003)	EnKF	MIKE 11	Water level and flux	–	Water level and flux
Moradkhani et al. (2005b)	EnKF	HyMOD	Water storage	Rq, Rs, α, bexp, Cmax	Streamflow
Vrugt et al. (2006)	EnKF	SAC-SMA	Six soil-zone reservoir variables, three routing variables	14 time-invariant parameters	Streamflow
Weerts and El Serafy (2006)	EnKF, PF	HBV96	Soil moisture, snow water, interception storage, lower and upper zone, etc.	–	Discharge
Clark et al. (2008)	EnKF	Topnet	Soil storage, aquifer storage, surface storage, streamflow prediction	–	Streamflow
Xie and Zhang (2010)	EnKF	SWAT	Runoff, water storage, evapotranspiration, etc.	CN2	Streamflow, soil water content, evapotranspiration
Dechant and Moradkhani (2011)	EnKF, PF	Snow 17, SAC-SMA	SWE	All model parameters	Microwave radiance
Chen et al. (2011)	EnKF	SWAT	Soil moisture	–	Surface soil moisture
Cammalleri and Ciraolo (2012)	EnKF	SVAT	Soil moisture	All model parameters	Surface temperature, latent heat flux, soil water content
Han et al. (2012)	EnKF	SWAT	Soil moisture	–	Surface soil moisture
Trudel et al. (2014)	EnKF	CATHY	Pressure head, incoming and outgoing discharge	–	Streamflow
Samuel et al. (2014)	EnKF	SAC-SMA	Soil moisture content, SWE, etc.	10 time-variant parameters	Streamflow, soil moisture
Kitanidis and Bras (1980b)	EKF	NWS	Soil water content, additional impervious storage, channel storage, routing coefficient	–	Streamflow
Puente and Bras (1987)	EKF	Conceptual lumped model	Water equivalent mass in cloud, soil water content, channel reservoir storage, etc.	–	Discharge, precipitation
Francois et al. (2003)	EKF	GRKAL	Soil moisture	–	Surface soil moisture
Aubert et al. (2003)	EKF	GR4J	Water level in soil reservoir and water level in routing reservoir	–	Soil moisture, streamflow
Kumar and Kaleita (2003)	EKF	LSM	Soil temperature	–	Near-surface soil temperature
Jonsdottir et al. (2006)	EKF, maximum likelihood	Stochastic model similar to HBV and NAM	Temperature, snow, upper and lower water content	All model parameters	Discharge
Lü et al. (2011)	EKF, PSO	1-D Richards’ equation	Soil moisture content	Ks, θr, θs, α, n	Surface soil moisture

PSO, particle swarm optimization.

Moradkhani, H., et al., 2005b. Dual state–parameter estimation of hydrological models using ensemble Kalman filter. Advances in Water Resources, 28 (2), 135–147. doi:10.1016/j.advwatres.2004.09.002

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Clark, M.P., et al., 2008. Hydrological data assimilation with the ensemble Kalman filter: use of streamflow observations to update states in a distributed hydrological model. Advances in Water Resources, 31 (10), 1309–1324. doi:10.1016/j.advwatres.2008.06.005

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Xie, X. and Zhang, D., 2010. Data assimilation for distributed hydrological catchment modeling via ensemble Kalman filter. Advances in Water Resources, 33 (6), 678–690. doi:10.1016/j.advwatres.2010.03.012

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Dechant, C. and Moradkhani, H., 2011. Radiance data assimilation for operational snow and streamflow forecasting. Advances in Water Resources, 34 (3), 351–364. doi:10.1016/j.advwatres.2010.12.009

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Chen, F., et al., 2011. Improving hydrologic predictions of a catchment model via assimilation of surface soil moisture. Advances in Water Resources, 34 (4), 526–536. doi:10.1016/j.advwatres.2011.01.011

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Cammalleri, C. and Ciraolo, G., 2012. State and parameter update in a coupled energy/hydrologic balance model using ensemble Kalman filtering. Journal of Hydrology, 416–417, 171–181. doi:10.1016/j.jhydrol.2011.11.049

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Han, E., Merwade, V., and Heathman, G.C., 2012. Implementation of surface soil moisture data assimilation with watershed scale distributed hydrological model. Journal of Hydrology, 416–417, 98–117. doi:10.1016/j.jhydrol.2011.11.039

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Puente, C.E. and Bras, R.L., 1987. Application of nonlinear filtering in the real time forecasting of river flows. Water Resources Research, 23 (4), 675–682. doi:10.1029/WR023i004p00675

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Francois, C., Quesney, A., and Ottlé, C., 2003. Sequential assimilation of ERS-1 SAR data into a coupled land surface-hydrological model using an extended Kalman filter. Journal of Hydrometeorology, 4 (2), 473–487. doi:10.1175/1525-7541(2003)4<473:SAOESD>2.0.CO;2

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Aubert, D., Loumagne, C., and Oudin, L., 2003. Sequential assimilation of soil moisture and streamflow data in a conceptual rainfall–runoff model. Journal of Hydrology, 280 (1–4), 145–161. doi:10.1016/S0022-1694(03)00229-4

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Kumar, P. and Kaleita, A.L., 2003. Assimilation of near-surface temperature using extended Kalman filter. Advances in Water Resources, 26 (1), 79–93. doi:10.1016/S0309-1708(02)00098-2

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Jonsdottir, H., Madsen, H., and Palsson, O.P., 2006. Parameter estimation in stochastic rainfall-runoff models. Journal of Hydrology, 326 (1–4), 379–393. doi:10.1016/j.jhydrol.2005.11.004

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Lü, H., et al., 2011. Dual state-parameter estimation of root zone soil moisture by optimal parameter estimation and extended Kalman filter data assimilation. Advances in Water Resources, 34 (3), 395–406. doi:10.1016/j.advwatres.2010.12.005

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