### Abstract

A dynamical relaxation scheme for assimilating observation data into a three-dimensional Richards equation-based numerical model was presented in Paniconi et al. (2003. Advances in Water Resources 26: 161-178). The technique, known as Newtonian relaxation or nudging, relies on a forcing term to reduce the difference between computed and observed values of a state variable such as soil moisture content. The forcing term contains data quality and nudging influence factors, and, importantly, spatio-temporal weighting functions that determine the manner and extent of spreading of a state variable beyond its measurement points and times. In this paper, a series of numerical experiments is run for a small catchment in southern Belgium to investigate the performance of the nudging algorithm. In a first set of runs for a short (10-day) simulation period, the model's sensitivity to influence radii and forcing strength parameters is examined. Here, we find that prediction errors decrease and numerical cost increases for increasing values of the parameters, except for the vertical radius of influence, where intermediate values produced the lowest prediction errors. Based on a compromise between numerical and physical results for this 10-day experiment, 'optimal' values were selected for these parameters, and a second, much longer (8-month) set of simulations is used to explore the effect of the observation frequency on the quality of the assimilation. Here, it is found that prediction errors are lowest at an intermediate frequency, whereas serious numerical difficulties occur at a high frequency. As could be expected, computational costs are highest when frequent observations are assimilated. However, since CPU times increase only very slowly as more observation datasets are added, we can conclude that the nudging method is computationally efficient, albeit quiet sensitive in terms of numerical performance to its parameter settings, and thus requires further study to devise more robust formulations of the algorithm.

Original language | English (US) |
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Pages (from-to) | 549-563 |

Number of pages | 15 |

Journal | Hydrological Processes |

Volume | 20 |

Issue number | 3 |

DOIs | |

State | Published - Feb 28 2006 |

Externally published | Yes |

### Keywords

- Data assimilation
- Groundwater modelling
- Newtonian nudging
- Richards equation
- Subsurface flow
- Unsaturated zone

### ASJC Scopus subject areas

- Water Science and Technology

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## Cite this

*Hydrological Processes*,

*20*(3), 549-563. https://doi.org/10.1002/hyp.5921