A dynamic factor modeling framework for analyzing multiple groundwater head series simultaneously

- Groundwater time series are decomposed into common and specific dynamic factors.
- Explanatory variables are included using predefined transfer functions.
- Predictions improve by including observations from surrounding monitoring locations using dynamic factor modeling.
- Dynamic factor models improve detection of potential measurement errors.

SummaryIn this paper we present an approach in which we combine a dynamic factor model (DFM) and predefined response functions to analyze a set of groundwater head series simultaneously. Each groundwater head series is decomposed into: (a) one or more deterministic components as a response to known driving forces, (b) one or more common dynamic factors, representing spatial patterns not related to any of the input series and (c) one specific dynamic factor for each groundwater head series, describing unique variation for that series. The approach reduces the degrees of freedom for each response function, enables the application to irregular observed data, and exploits the correlation between residual series of a set of groundwater head series. The common dynamic factors may be interpreted as spatial patterns due to e.g. limitations in the model specification or concept, spatially correlated errors in input variables, or driving forces which have not been included in the model. In the latter case the model can be applied in the context of an alarming system, e.g. to monitor regional trends. The specific dynamic factor depicts the variation of a particular groundwater head series that cannot be related to any other time series of the set nor to any input series. Therefore the specific dynamic factor is suitable for analyzing local variations and detecting incidental measurement errors, for example in a quality control procedure. The DFM framework is illustrated with a set of 8 groundwater head series and applied for filling gaps in time series, reconstructing high-frequency data, and detecting outliers.