Skip to main content
SpringerLink
Log in

Comparison of ensemble Kalman filter application to a prediction model of soil solute transfer into surface runoff by updating different parameters

  • ORIGINAL PAPER
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

Raindrop impact causes soil erosion and the transfer of solutes into surface runoff, leading to soil solute loss and water pollution. Accurately modelling this process in complex agricultural environments is challenging. A new prediction model was applied to illustrate mechanisms of soil solute transfer into surface runoff, addressing the underestimation of solute concentration in surface runoff but limited by uncertain model parameters. Two laboratory experiments were conducted, studying solute loss from soil to surface runoff under initially saturated and unsaturated soil conditions. An elasticity sensitivity analysis was used to identify crucial parameters. To improve prediction results, the ensemble Kalman filter (EnKF) method was coupled with the model during the early stage of the simulation, assimilating observed solute concentrations in surface runoff to update model parameters. After the early stage, the model generated predicted solute concentrations in surface runoff without the observed data until the simulation ended. Four model parameters, including incomplete mixing parameters α and γ, soil mixing layer depth hmix,t(t), and moving rate of the soil mixing layer front imix, were updated. The inflation method was used to prevent filter divergence caused by the EnKF. The simulation results showed that the EnKF significantly improved the model's prediction accuracy, even when applied during specific periods throughout the simulation. Updating α, γ, hmix,t(t) and imix resulted in better predictions compared to updating only α, γ and imix. This further demonstrated that the hmix,t(t) must be updated using the EnKF.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

The experimental data of this study are available by contacting the authors.

References

  • Ahuja LR (1990) Modeling soluble chemical transfer to runoff with rainfall impact as a diffusion process. Soil Sci Soc Am J 54(2):312–321

    Google Scholar 

  • Ahuja LR, Lehman OR (1983) The extent and nature of rainfall soil interaction in the release of soluble chemicals to runoff. J Environ Qual 12(1):34–40

    Google Scholar 

  • Ahuja LR, Sharpley AN, Yamamoto M, Menzel RG (1981) The depth of rainfall-runoff-soil interaction as determined by 32P. Water Resour Res 17(4):969–974

    Google Scholar 

  • Assumaning GA, Chang SY (2016) Application of sequential data-assimilation techniques in groundwater contaminant transport modeling. J Environ Eng 142(2):04015073

    Google Scholar 

  • Bauser HH, Berg D, Klein O, Roth K (2018) Inflation method for ensemble Kalman filter in soil hydrology. Hydrol Earth Syst Sci 22(9):4921–4934

    Google Scholar 

  • Bostic JT, Nelson DM, Sabo RD, Eshleman KN (2022) Terrestrial nitrogen inputs affect the export of unprocessed atmospheric nitrate to surface waters: insights from triple oxygen isotopes of nitrate. Ecosystems 25(6):1384–1399

    CAS  Google Scholar 

  • Brandhorst N, Erdalb D, Neuweilera I (2017) Soil moisture prediction with the ensemble Kalman filter: handling uncertainty of soil hydraulic parameters. Adv Water Resour 110:360–370

    Google Scholar 

  • Carpenter SR, Caraco NF, Correll DL, Howarth RW, Sharpley AN, Smith VH (1998) Nonpoint pollution of surface waters with phosphorus and nitrogen. Ecol Appl 8(3):559–568

    Google Scholar 

  • Chaplot VAM, Le Bissonnais Y (2003) Runoff features for interrill erosion at different rainfall intensities, slope lengths, and gradients in an agricultural loessial hillslope. Soil Sci Soc Am J 67(3):844–851

    CAS  Google Scholar 

  • Chen Y, Zhang DX (2006) Data assimilation for transient flow in geologic formations via ensemble Kalman filter. Adv Water Resour 29(8):1107–1122

    Google Scholar 

  • Delesantro JM, Duncan JM, Riveros-Iregui D, Blaszczak JR, Bernhardt ES, Urban DL, Band LE (2022) The nonpoint sources and transport of baseflow nitrogen loading across a developed rural-urban gradient. Water Resour Res 58(7):e2021WR031533

    CAS  Google Scholar 

  • Emmerich WE, Woolhiser DA, Shirley ED (1989) Comparison of lumped and distributed models for chemical transport by surface runoff. J Environ Qual 18(1):120–126

    CAS  Google Scholar 

  • 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(C5):10143–10162

    Google Scholar 

  • Evensen G (2006) Data assimilation: the ensemble kalman filter. Springer, New York

    Google Scholar 

  • Gao B, Walter MT, Steenhuis TS (2004) Rainfall induced chemical transport from soil to runoff: theory and experiments. J Hydrol 295(1/4):291–304

    CAS  Google Scholar 

  • Gibert O, Abenza M, Reig M, Vecino X, Sánchez D, Arnaldos M, Cortina JL (2022) Removal of nitrate from groundwater by nano-scale zero-valent iron injection pulses in continuous-flow packed soil columns. Sci Total Environ 810:152300

    CAS  Google Scholar 

  • Harris SJ, Cendón DI, Hankin SI, Peterson MA, Xiao S, Kelly BF (2022) Isotopic evidence for nitrate sources and controls on denitrification in groundwater beneath an irrigated agricultural district. Sci Total Environ 817:152606

    CAS  Google Scholar 

  • Havis RN, Smith RE, Adrian DD (1992) Partitioning solute transport between infiltration and overland flow under rainfall. Water Resour Res 28(10):2569–2580

    CAS  Google Scholar 

  • He S, Gong Y, Zheng Z, Luo Z, Tan B, Zhang Y (2022) Effects of rainfall intensities and slope gradients on nitrogen loss at the seedling stage of maize (Zea mays L.) in the purple soil regions of China. Int J Agric Biol Eng 15(2):142–148

    Google Scholar 

  • Heathman GC, Ahuja LR, Baker JL (1986) Test of non-uniform mixing model for transfer of herbicides to surface runoff. Trans ASAE 29(450–455):461

    Google Scholar 

  • Hopson TM (2014) Assessing the ensemble spread–error relationship. Mon Weather Rev 142(3):1125–1142

    Google Scholar 

  • Houtekamer PL, Mitchell HL (2001) A sequential ensemble Kalman filter for atmospheric data assimilation. Mon Weather Rev 129(1):123–137

    Google Scholar 

  • Huang CL, Hu BX, Li XY, Ye M (2009) Using data assimilation method to calibrate a heterogeneous conductivity field and improve solute transport prediction with an unknown contamination source. Stoch Environ Res Risk Assess 23(8):1155–1167

    Google Scholar 

  • Huang C, Tong JX, Ye M (2020) Global sensitivity analysis for a prediction model of soil solute transfer into surface runoff. J Hydrol 599:126342

    Google Scholar 

  • Jamal A, Linker R (2020) Inflation method based on confidence intervals for data assimilation in soil hydrology using the ensemble Kalman filter. Vadose Zone J 19(1):e20000

    Google Scholar 

  • Jazwinski AH (2007) Stochastic processes and filtering theory. Courier Corporation, Chelmsford

    Google Scholar 

  • Jiang Z, Huang Q, Li G, Li G (2019) Parameters estimation and prediction of water movement and solute transport in layered, variably saturated soils using the ensemble Kalman filter. Water 11(7):1520

    Google Scholar 

  • Kivi MS, Blakely B, Masters M, Bernacchi CJ, Miguez E, Dokoohaki H (2022) Development of a data-assimilation system to forecast agricultural systems: A case study of constraining soil water and soil nitrogen dynamics in the APSIM model. Sci Total Environ 820:153192

    CAS  Google Scholar 

  • Li H, Kalnay E, Miyoshi T (2009) Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter. Quarterly J R Meteorol Soc A J Atmos Sci Appl Meteorol Phys Oceanogr 135(639):523–533

    Google Scholar 

  • Liu GS, Chen Y, Zhang XD (2008) Investigation of flow and transport processes at the MADE site using ensemble Kalman filter. Adv Water Resour 31(7):975–985

    CAS  Google Scholar 

  • Liu Z, Wang X, Jia S, Mao B (2023) Multi-methods to investigate spatiotemporal variations of nitrogen-nitrate and its risks to human health in China’s largest fresh water lake (Poyang Lake). Sci Total Environ 863:160975

    CAS  Google Scholar 

  • Melching CS, Yoon CG (1996) Key sources of uncertainty in QUAL2E model of Passaic river. ASCE J Water Resour Plann Manag 122(2):105–113

    Google Scholar 

  • Meng XB, Tong JX, Hu BX (2021) Using an ensemble Kalman filter method to calibrate parameters of a prediction model for chemical transport from soil to surface runoff. Environ Sci Pollut Res 28(4):4404–4416

    Google Scholar 

  • Shi J, Jin R, Zhu W (2022) Quantification of effects of natural geographical factors and landscape patterns on non-point source pollution in watershed based on geodetector: Burhatong River Basin, Northeast China as an example. Chin Geogra Sci 32(4):707–723

    Google Scholar 

  • Snyder JK, Woolhiser DA (1985) Effect of infiltration on chemical transport into overland flow. Trans Am Soc Agric Eng 28(5):1450–1457

    Google Scholar 

  • Tan CQ, Tong JX, Liu Y, Hu BX, Yang JZ, Zhou H (2016) Experimental and modeling study on Cr(VI) transfer from soil into surface runoff. Stoch Env Res Risk Assess 30(5):1347–1361. https://doi.org/10.1007/s00477-015-1161-y

    Article  Google Scholar 

  • Tong JX, Ye M (2020) A new soil mixing layer model for simulating conservative solute loss from initially saturated soil to surface runoff. J Hydrol 590:125514

    Google Scholar 

  • Tong JX, Hu BX, Yang JZ (2010a) Using data assimilation method to calibrate a heterogeneous conductivity field conditioning on transient flow test data. Stoch Env Res Risk Assess 24(8):1211–1223. https://doi.org/10.1007/s00477-010-0392-1

    Article  Google Scholar 

  • Tong JX, Yang JZ, Hu BX, Bao RC (2010b) Experimental study and mathematical modelling of soluble chemical transfer from unsaturated/saturated soil to surface runoff. Hydrol Process 24(21):3065–3073

    CAS  Google Scholar 

  • Tong JX, Hu BX, Yang JZ (2012) Using an ensemble Kalman filter method to calibrate parameters and update soluble chemical transfer from soil to surface runoff. Transp Porous Media 91(1):133–152. https://doi.org/10.1007/s11242-011-9837-3

    Article  CAS  Google Scholar 

  • Tong JX, Hu BX, Yang JZ, Zhu Y (2016) Using a hybrid model to predict solute transfer from initially saturated soil into surface runoff with controlled drainage water. Environ Sci Pollut Res 23(12):12444–12455

    CAS  Google Scholar 

  • Wallach R, van Genuchten MT (1990) A physically based model for predicting solute transfer from soil solution to rainfall-induced runoff water. Water Resour Res 26(9):2119–2126

    Google Scholar 

  • Wallach R, Jury WA, Spencer WF (1988) Transfer of chemicals from soil solution to surface runoff: a diffusion-based soil model. Soil Sci Soc Am J 52(3):612–618

    CAS  Google Scholar 

  • Wang X, Xu YJ, Zhang L (2022) Watershed scale spatiotemporal nitrogen transport and source tracing using dual isotopes among surface water, sediments and groundwater in the Yiluo River Watershed, Middle of China. Sci Total Environ 833:155180

    CAS  Google Scholar 

  • Wang L, Zheng F, Hu W, Zhang XJ, Shi H (2023) Interactive effects of rainfall intensity, kinetic energy and antecedent soil moisture regime on splash erosion in the Ultisol region of South China. CATENA 222:106863

    Google Scholar 

  • Wu G, Zheng X (2018) The error covariance matrix inflation in ensemble kalman filter. In: Kalman filters-theory for advanced applications

  • Zhang XC, Norton D, Nearing MA (1997) Chemical transfer from soil solution to surface runoff. Water Resour Res 33(4):809–815

    CAS  Google Scholar 

  • Zhang XC, Norton LD, Lei T, Nearing MA (1999) Coupling mixing zone concept with convection-diffusion equation to predict chemical transfer to surface runoff. Trans ASAE 42(4):987

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant 42072271).

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Key Laboratory of Groundwater Conservation of MWR, China University of Geosciences (Beijing), Beijing, 100083, People’s Republic of China

    Yang Gu & Juxiu Tong

  2. School of Water Resources and Environment, China University of Geosciences (Beijing), Beijing, 100083, People’s Republic of China

    Yang Gu & Juxiu Tong

Authors
  1. Yang Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juxiu Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

YG: Methodology, writing—original draft preparation, formal analysis, validation, and software. JT: Conceptualization, methodology, experiments, investigation, formal analysis, resources, data curation, and writing—reviewing and editing.

Corresponding author

Correspondence to Juxiu Tong.

Ethics declarations

Conflict of interest

The authors (Yang Gu and Juxiu Tong) declare no conflicts of interest exist.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gu, Y., Tong, J. Comparison of ensemble Kalman filter application to a prediction model of soil solute transfer into surface runoff by updating different parameters. Stoch Environ Res Risk Assess 37, 3261–3273 (2023). https://doi.org/10.1007/s00477-023-02448-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-023-02448-7

Keywords

Search

Navigation