Assessing the Performance of Separate Bias Kalman Filter in Correcting the Model Bias for Estimation of Soil Moisture Profiles
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摘要
The performance of separate bias Kalman filter(SepKF) in correcting the model bias for the improvement of soil moisture profiles is evaluated by assimilating the near-surface soil moisture observations into a land surface model(LSM). First, an observing system simulation experiment(OSSE) is carried out, where the true soil moisture is known, two types of model bias(i.e., constant and sinusoidal) are specified, and the bias error covariance matrix is assumed to be proportional to the model forecast error covariance matrix with a ratio λ. Second, a real assimilation experiment is carried out with measurements at a site over Northwest China. In the OSSE, the soil moisture estimation with the SepKF is improved compared with ensemble Kalman filter(EnKF) without the bias filter, because SepKF can properly correct the model bias, especially in the situation with a large model bias. However, the performance of SepKF becomes slightly worse if the constant model bias increases or temporal variability of the sinusoidal model bias becomes large. It is suggested that the ratio λ should be increased(decreased) in order to improve the soil moisture estimation if temporal variability of the sinusoidal model bias becomes high(low). Finally, the assimilation experiment with real observations also shows that SepKF can further improve the estimation of soil moisture profiles compared with EnKF without the bias correction.
The performance of separate bias Kalman filter(SepKF) in correcting the model bias for the improvement of soil moisture profiles is evaluated by assimilating the near-surface soil moisture observations into a land surface model(LSM). First, an observing system simulation experiment(OSSE) is carried out, where the true soil moisture is known, two types of model bias(i.e., constant and sinusoidal) are specified, and the bias error covariance matrix is assumed to be proportional to the model forecast error covariance matrix with a ratio λ. Second, a real assimilation experiment is carried out with measurements at a site over Northwest China. In the OSSE, the soil moisture estimation with the SepKF is improved compared with ensemble Kalman filter(EnKF) without the bias filter, because SepKF can properly correct the model bias, especially in the situation with a large model bias. However, the performance of SepKF becomes slightly worse if the constant model bias increases or temporal variability of the sinusoidal model bias becomes large. It is suggested that the ratio λ should be increased(decreased) in order to improve the soil moisture estimation if temporal variability of the sinusoidal model bias becomes high(low). Finally, the assimilation experiment with real observations also shows that SepKF can further improve the estimation of soil moisture profiles compared with EnKF without the bias correction.
The performance of separate bias Kalman filter(SepKF) in correcting the model bias for the improvement of soil moisture profiles is evaluated by assimilating the near-surface soil moisture observations into a land surface model(LSM). First, an observing system simulation experiment(OSSE) is carried out, where the true soil moisture is known, two types of model bias(i.e., constant and sinusoidal) are specified, and the bias error covariance matrix is assumed to be proportional to the model forecast error covariance matrix with a ratio λ. Second, a real assimilation experiment is carried out with measurements at a site over Northwest China. In the OSSE, the soil moisture estimation with the SepKF is improved compared with ensemble Kalman filter(EnKF) without the bias filter, because SepKF can properly correct the model bias, especially in the situation with a large model bias. However, the performance of SepKF becomes slightly worse if the constant model bias increases or temporal variability of the sinusoidal model bias becomes large. It is suggested that the ratio λ should be increased(decreased) in order to improve the soil moisture estimation if temporal variability of the sinusoidal model bias becomes high(low). Finally, the assimilation experiment with real observations also shows that SepKF can further improve the estimation of soil moisture profiles compared with EnKF without the bias correction.
引文
Anderson,J.L.,and S.L.Anderson,1999:A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts.Mon.Wea.Rev.,127,2741-2758,doi:10.1175/1520-0493(1999)127<2741:AMCI-OT>2.0.CO;2.
Ball,J.T.,I.E.Woodrow,and J.A.Berry,1987:A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions.Progress in Photosynthesis Research,J.Biggins,Ed.,Springer,Dordrecht,221-224,doi:10.1007/978-94-017-0519-6_48.
Brunsell,N.A.,S.J.Schymanski,and A.Kleidon,2011:Quantifying the thermodynamic entropy budget of the land surface:Is this useful?Earth Syst.Dyn.,2,87-103,doi:10.5194/esd-2-87-2011.
Cai,X.T.,Z.L.Yang,C.H.David,et al.,2014:Hydrological evaluation of the Noah-MP land surface model for the Mississippi River Basin.J.Geophys.Res.Atmos.,119,23-38,doi:10.1002/2013JD020792.
Crow,W.T.,R.D.Koster,R.H.Reichle,et al.,2005:Relevance of time-varying and time-invariant retrieval error sources on the utility of spaceborne soil moisture products.Geophys.Res.Lett.,32,L24405,doi:10.1029/2005GL024889.
De Lannoy,G.J.M.,R.H.Reichle,P.R.Houser,et al.,2007:Correcting for forecast bias in soil moisture assimilation with the ensemble Kalman filter.Water Resour.Res.,43,W09410,doi:10.1029/2006WR005449.
Dee,D.P.,and A.M.Da Silva,1998:Data assimilation in the presence of forecast bias.Quart.J.Roy.Meteor.Soc.,124,269-295,doi:10.1002/qj.49712454512.
Drécourt,J.P.,and H.Madsen,2002:Uncertainty estimation in groundwater modelling using Kalman filtering.Proceedings of the 4th International Conference on Calibration and Reliability in Groundwater Modelling,Acta Universitatis Carolinae,Prague,Czech Republic,306-309.
Drécourt,J.P.,H.Madsen,and D.Rosbjerg,2006:Bias aware Kalman filters:Comparison and improvements.Adv.Water Resour.,29,707-718,doi:10.1016/j.advwatres.2005.07.006.
Evensen,G.,1994:Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics.J.Geophys.Res.Oceans,99,10,143-10,162,doi:10.1029/94JC00572.
Friedland,B.,1969:Treatment of bias in recursive filtering.IEEETrans.Autom.Control,14,359-367,doi:10.1109/TAC.1969.1099223.
Hamill,T.M.,and J.S.Whitaker,2005:Accounting for the error due to unresolved scales in ensemble data assimilation:Acomparison of different approaches.Mon.Wea.Rev.,133,3132-3147,doi:10.1175/MWR3020.1.
Hamill,T.M.,J.S.Whitaker,and C.Snyder,2001:Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter.Mon.Wea.Rev.,129,2776-2790,doi:10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2.
Huang,J.P.,W.Zhang,J.Q.Zuo,et al.,2008:An overview of the semi-arid climate and environment research observatory over the Loess Plateau.Adv.Atmos.Sci.,25,906,doi:10.1007/s00376-008-0906-7.
Jazwinski,A.H.,1970:Stochastic Processes and Filtering Theory.Academic Press,New York,1-103.
Kollat,J.B.,P.M.Reed,and D.M.Rizzo,2008:Addressing model bias and uncertainty in three dimensional groundwater transport forecasts for a physical aquifer experiment.Geo-phys.Res.Lett.,35,L17402,doi:10.1029/2008GL035021.
Kollat,J.B.,P.M.Reed,and R.M.Maxwell,2011:Many-objective groundwater monitoring network design using bias-aware ensemble Kalman filtering,evolutionary optimization,and visual analytics.Water Resour.Res.,47,W02529,doi:10.1029/2010WR009194.
Meyers,T.P.,and S.E.Hollinger,2004:An assessment of storage terms in the surface energy balance of maize and soybean.Agric.For.Meteor.,125,105-115,doi:10.1016/j.agr-formet.2004.03.001.
Montzka,C.,H.Moradkhani,L.Weihermüller,et al.,2011:Hydraulic parameter estimation by remotely-sensed top soil moisture observations with the particle filter.J.Hydrol.,399,410-421,doi:10.1016/j.jhydrol.2011.01.020.
Montzka,C.,V.R.N.Pauwels,H.J.H.Franssen,et al.,2012:Multivariate and multiscale data assimilation in terrestrial systems:A review.Sensors,12,16291-16333,doi:10.3390/s121216291.
Niu,G.Y.,Z.L.Yang,K.E.Mitchell,et al.,2011:The community Noah land surface model with multiparameterization options(Noah-MP):1.Model description and evaluation with local-scale measurements.J.Geophys.Res.Atmos.,116,D12109,doi:10.1029/2010JD015139.
Pauwels,V.R.N.,and G.J.M.De Lannoy,2015:Error covariance calculation for forecast bias estimation in hydrologic data assimilation.Adv.Water Resour.,86,284-296,doi:10.1016/j.advwatres.2015.05.013.
Reichle,R.H.,and R.D.Koster,2004:Bias reduction in short records of satellite soil moisture.Geophys.Res.Lett.,31,L19501,doi:10.1029/2004GL020938.
Reichle,R.H.,D.Entekhabi,and D.B.McLaughlin,2001:Downscaling of radio brightness measurements for soil moisture estimation:A four-dimensional variational data assimilation approach.Water Resour.Res.,37,2353-2364,doi:10.1029/2001WR000475.
Sakaguchi,K.,and K.B.Zeng,2009:Effects of soil wetness,plant litter,and under-canopy atmospheric stability on ground evaporation in the Community Land Model(CLM3.5).J.Geophys.Res.Atmos.,114,D01107,doi:10.1029/2008JD010834.
Seuffert,G.,H.Wilker,P.Viterbo,et al.,2003:Soil moisture analysis combining screen-level parameters and microwave brightness temperature:A test with field data.Geophys.Res.Lett.,30,1498,doi:10.1029/2003GL017128.
Walker,J.P.,and P.R.Houser,2004:Requirements of a global near-surface soil moisture satellite mission:Accuracy,repeat time,and spatial resolution.Adv.Water Resour.,27,785-801,doi:10.1016/j.advwatres.2004.05.006.
Walker,J.P.,G.R.Willgoose,and J.D.Kalma,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.
Yan,H.X.,C.M.DeChant,and H.Moradkhani,2015:Improving soil moisture profile prediction with the particle filter-Markov chain Monte Carlo method.IEEE Trans.Geosci.Remote Sens.,53,6134-6147,doi:10.1109/TGRS.2015.2432067.
Yang,K.,T.Watanabe,T.Koike,et al.,2007:Auto-calibration system developed to assimilate AMSR-E data into a land surface model for estimating soil moisture and the surface energy budget.J.Meteor.Soc.Japan,85A,229-242,doi:10.2151/jmsj.85A.229.
Zhang,F.,C.Snyder,and J.Z.Sun,2004:Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter.Mon.Wea.Rev.,132,1238-1253,doi:10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.
Zhang,S.W.,H.R.Li,W.D.Zhang,et al.,2005:Estimating the soil moisture profile by assimilating near-surface observations with the ensemble Kalman filter(EnKF).Adv.Atmos.Sci.,22,936-945,doi:10.1007/BF02918692.
Zhang,S.W.,X.B.Zeng,W.D.Zhang,et al.,2010:Revising the ensemble-based Kalman filter covariance for the retrieval of deep-layer soil moisture.J.Hydrometeorol.,11,219-227,doi:10.1175/2009JHM1146.1.
Zhang,S.W.,D.Q.Li,and C.J.Qiu,2011:A multimodel ensemble-based Kalman filter for the retrieval of soil moisture profiles.Adv.Atmos.Sci.,28,195-206,doi:10.1007/s00376-010-9200-6.
Zhang,S.W.,Y.H.Liu,and W.D.Zhang,2013:Ensemble square root filter assimilation of near-surface soil moisture and reference-level observations into a coupled land surface-boundary layer model.Acta Meteor.Sinica,27,541-555,doi:10.1007/s13351-013-0402-6.
Zhou,Y.H.,D.McLaughlin,and D.Entekhabi,2006:Assessing the performance of the ensemble Kalman filter for land surface data assimilation.Mon.Wea.Rev.,134,2128-2142,doi:10.1175/MWR3153.1.
Ball,J.T.,I.E.Woodrow,and J.A.Berry,1987:A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions.Progress in Photosynthesis Research,J.Biggins,Ed.,Springer,Dordrecht,221-224,doi:10.1007/978-94-017-0519-6_48.
Brunsell,N.A.,S.J.Schymanski,and A.Kleidon,2011:Quantifying the thermodynamic entropy budget of the land surface:Is this useful?Earth Syst.Dyn.,2,87-103,doi:10.5194/esd-2-87-2011.
Cai,X.T.,Z.L.Yang,C.H.David,et al.,2014:Hydrological evaluation of the Noah-MP land surface model for the Mississippi River Basin.J.Geophys.Res.Atmos.,119,23-38,doi:10.1002/2013JD020792.
Crow,W.T.,R.D.Koster,R.H.Reichle,et al.,2005:Relevance of time-varying and time-invariant retrieval error sources on the utility of spaceborne soil moisture products.Geophys.Res.Lett.,32,L24405,doi:10.1029/2005GL024889.
De Lannoy,G.J.M.,R.H.Reichle,P.R.Houser,et al.,2007:Correcting for forecast bias in soil moisture assimilation with the ensemble Kalman filter.Water Resour.Res.,43,W09410,doi:10.1029/2006WR005449.
Dee,D.P.,and A.M.Da Silva,1998:Data assimilation in the presence of forecast bias.Quart.J.Roy.Meteor.Soc.,124,269-295,doi:10.1002/qj.49712454512.
Drécourt,J.P.,and H.Madsen,2002:Uncertainty estimation in groundwater modelling using Kalman filtering.Proceedings of the 4th International Conference on Calibration and Reliability in Groundwater Modelling,Acta Universitatis Carolinae,Prague,Czech Republic,306-309.
Drécourt,J.P.,H.Madsen,and D.Rosbjerg,2006:Bias aware Kalman filters:Comparison and improvements.Adv.Water Resour.,29,707-718,doi:10.1016/j.advwatres.2005.07.006.
Evensen,G.,1994:Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics.J.Geophys.Res.Oceans,99,10,143-10,162,doi:10.1029/94JC00572.
Friedland,B.,1969:Treatment of bias in recursive filtering.IEEETrans.Autom.Control,14,359-367,doi:10.1109/TAC.1969.1099223.
Hamill,T.M.,and J.S.Whitaker,2005:Accounting for the error due to unresolved scales in ensemble data assimilation:Acomparison of different approaches.Mon.Wea.Rev.,133,3132-3147,doi:10.1175/MWR3020.1.
Hamill,T.M.,J.S.Whitaker,and C.Snyder,2001:Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter.Mon.Wea.Rev.,129,2776-2790,doi:10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2.
Huang,J.P.,W.Zhang,J.Q.Zuo,et al.,2008:An overview of the semi-arid climate and environment research observatory over the Loess Plateau.Adv.Atmos.Sci.,25,906,doi:10.1007/s00376-008-0906-7.
Jazwinski,A.H.,1970:Stochastic Processes and Filtering Theory.Academic Press,New York,1-103.
Kollat,J.B.,P.M.Reed,and D.M.Rizzo,2008:Addressing model bias and uncertainty in three dimensional groundwater transport forecasts for a physical aquifer experiment.Geo-phys.Res.Lett.,35,L17402,doi:10.1029/2008GL035021.
Kollat,J.B.,P.M.Reed,and R.M.Maxwell,2011:Many-objective groundwater monitoring network design using bias-aware ensemble Kalman filtering,evolutionary optimization,and visual analytics.Water Resour.Res.,47,W02529,doi:10.1029/2010WR009194.
Meyers,T.P.,and S.E.Hollinger,2004:An assessment of storage terms in the surface energy balance of maize and soybean.Agric.For.Meteor.,125,105-115,doi:10.1016/j.agr-formet.2004.03.001.
Montzka,C.,H.Moradkhani,L.Weihermüller,et al.,2011:Hydraulic parameter estimation by remotely-sensed top soil moisture observations with the particle filter.J.Hydrol.,399,410-421,doi:10.1016/j.jhydrol.2011.01.020.
Montzka,C.,V.R.N.Pauwels,H.J.H.Franssen,et al.,2012:Multivariate and multiscale data assimilation in terrestrial systems:A review.Sensors,12,16291-16333,doi:10.3390/s121216291.
Niu,G.Y.,Z.L.Yang,K.E.Mitchell,et al.,2011:The community Noah land surface model with multiparameterization options(Noah-MP):1.Model description and evaluation with local-scale measurements.J.Geophys.Res.Atmos.,116,D12109,doi:10.1029/2010JD015139.
Pauwels,V.R.N.,and G.J.M.De Lannoy,2015:Error covariance calculation for forecast bias estimation in hydrologic data assimilation.Adv.Water Resour.,86,284-296,doi:10.1016/j.advwatres.2015.05.013.
Reichle,R.H.,and R.D.Koster,2004:Bias reduction in short records of satellite soil moisture.Geophys.Res.Lett.,31,L19501,doi:10.1029/2004GL020938.
Reichle,R.H.,D.Entekhabi,and D.B.McLaughlin,2001:Downscaling of radio brightness measurements for soil moisture estimation:A four-dimensional variational data assimilation approach.Water Resour.Res.,37,2353-2364,doi:10.1029/2001WR000475.
Sakaguchi,K.,and K.B.Zeng,2009:Effects of soil wetness,plant litter,and under-canopy atmospheric stability on ground evaporation in the Community Land Model(CLM3.5).J.Geophys.Res.Atmos.,114,D01107,doi:10.1029/2008JD010834.
Seuffert,G.,H.Wilker,P.Viterbo,et al.,2003:Soil moisture analysis combining screen-level parameters and microwave brightness temperature:A test with field data.Geophys.Res.Lett.,30,1498,doi:10.1029/2003GL017128.
Walker,J.P.,and P.R.Houser,2004:Requirements of a global near-surface soil moisture satellite mission:Accuracy,repeat time,and spatial resolution.Adv.Water Resour.,27,785-801,doi:10.1016/j.advwatres.2004.05.006.
Walker,J.P.,G.R.Willgoose,and J.D.Kalma,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.
Yan,H.X.,C.M.DeChant,and H.Moradkhani,2015:Improving soil moisture profile prediction with the particle filter-Markov chain Monte Carlo method.IEEE Trans.Geosci.Remote Sens.,53,6134-6147,doi:10.1109/TGRS.2015.2432067.
Yang,K.,T.Watanabe,T.Koike,et al.,2007:Auto-calibration system developed to assimilate AMSR-E data into a land surface model for estimating soil moisture and the surface energy budget.J.Meteor.Soc.Japan,85A,229-242,doi:10.2151/jmsj.85A.229.
Zhang,F.,C.Snyder,and J.Z.Sun,2004:Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter.Mon.Wea.Rev.,132,1238-1253,doi:10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.
Zhang,S.W.,H.R.Li,W.D.Zhang,et al.,2005:Estimating the soil moisture profile by assimilating near-surface observations with the ensemble Kalman filter(EnKF).Adv.Atmos.Sci.,22,936-945,doi:10.1007/BF02918692.
Zhang,S.W.,X.B.Zeng,W.D.Zhang,et al.,2010:Revising the ensemble-based Kalman filter covariance for the retrieval of deep-layer soil moisture.J.Hydrometeorol.,11,219-227,doi:10.1175/2009JHM1146.1.
Zhang,S.W.,D.Q.Li,and C.J.Qiu,2011:A multimodel ensemble-based Kalman filter for the retrieval of soil moisture profiles.Adv.Atmos.Sci.,28,195-206,doi:10.1007/s00376-010-9200-6.
Zhang,S.W.,Y.H.Liu,and W.D.Zhang,2013:Ensemble square root filter assimilation of near-surface soil moisture and reference-level observations into a coupled land surface-boundary layer model.Acta Meteor.Sinica,27,541-555,doi:10.1007/s13351-013-0402-6.
Zhou,Y.H.,D.McLaughlin,and D.Entekhabi,2006:Assessing the performance of the ensemble Kalman filter for land surface data assimilation.Mon.Wea.Rev.,134,2128-2142,doi:10.1175/MWR3153.1.