Water Resources Management

, Volume 30, Issue 6, pp 1973–1986 | Cite as

Statistical Modelling of Vertical Soil Moisture Profile: Coupling of Memory and Forcing

  • Manali Pal
  • Rajib Maity
  • Sayan Dey


Information of Soil Moisture Content (SMC) at different depths i.e. vertical Soil Moisture (SM) profile is important as it influences several hydrological processes. In the era of microwave remote sensing, spatial distribution of soil moisture information can be retrieved from satellite data for large basins. However, satellite data can provide only the surface (~0–10 cm) soil moisture information. In this study, a methodological framework is proposed to estimate the vertical SM profile knowing the information of SMC at surface layer. The approach is developed by coupling the memory component of SMC within a layer and the forcing component from soil layer lying above by an Auto-Regressive model with an exogenous input (ARX) where forcing component is the exogenous input. The study highlights the mutual reliance between SMC at different depths at a given location assuming the ground water table is much below the study domain. The methodology is demonstrated for three depths: 25, 50 and 80 cm using SMC values of 10 cm depth. Model performance is promising for all three depths. It is further observed that forcing is predominant than memory for near surface layers than deeper layers. With increase in depth, contribution of SM memory increases and forcing dissipates. Potential of the proposed methodology shows some promise to integrate satellite estimated surface soil moisture maps to prepare a fine resolution, 3-dimensional soil moisture profile for large areas, which is kept as future scope of this study.


Soil moisture (SM) Vertical Soil Moisture Profile Memory Forcing Auto-Regressive Model with Exogenous Input (ARX) 



Authors wish to acknowledge Dr. Shivam Tripathi, IIT Kanpur for providing the daily soil moisture data from the study area. This is a part of International Soil Moisture Network. For details:

Compliance with Ethical Standards


This study is partially supported by a research project sponsored by the Ministry of Earth Science (MoES), Government of India (Sanction order# MoES/PAMC/H&C/30/2013-PC-II).

Conflict of Interest

Corresponding author Dr. Rajib Maity has received research grants from the Ministry of Earth Science (MoES), Government of India (Sanction order# MoES/PAMC/H&C/30/2013-PC-II). The other authors declare that they have no conflict of interest.

Research Involving Human Participants and/or Animals

The authors declare that the research does not contain any studies with human participants or animals performed by any of the authors.

Informed Consent

The authors declare that the ‘Informed Consent’ is not applicable in the research since it does not contain any studies with human participants or animals performed by any of the authors.

Supplementary material

11269_2016_1263_MOESM1_ESM.docx (80 kb)
ESM 1 (DOCX 80.1 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.School of Water ResourcesIndian Institute of Technology KharagpurKharagpurIndia
  2. 2.Department of Civil EngineeringIndian Institute of Technology KharagpurKharagpurIndia

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