Interpolating and forecasting lake characteristics using long-term monitoring data

It is virtually impossible to quantify the limnological characteristics of every aquatic ecosystem all the time. The goal of this study was to assess the capacity of lake-monitoring data to predict annually resolved characteristics in systems where measurements are not always made. To address this, we provide an analysis of interpolation (i.e., predicting a current lake characteristic based on current characteristics of other lakes) and forecasting (i.e., predicting a current lake characteristic based on historical trends and characteristics of a set of study lakes) in seven lakes over a 28yr time frame. The most effective interpolations are generated using 12–15 yr of training data. Interpolation models are 29% more effective, on average, when historical trends (forecasting) are also incorporated into the models. Forecasting models that predict lake characteristics using long-term trends in the focal lake were improved by including historical observations from other lakes. Direct comparisons of different prediction models further demonstrated that it is sometimes more effective to generate predictions based on a set of previously measured conditions (forecasts) rather than a set of known regional conditions that have been recently quantified (interpolations). Basic monitoring data have the potential to be upscaled to generate predictions of lake characteristics, but the effectiveness of predictions depend on the training data characteristics and prediction approaches employed. If one cannot directly measure a characteristic of an aquatic ecosystem, how can one best estimate it? A goal of many aquatic studies is to determine ecosystem characteristics without having to measure them everywhere and all the time (Fee and Hecky 1992; Downing et al. 2001; Pace 2001). As with many disciplines, there is a long history of predicting ecosystem characteristics in the aquatic sciences (Peters 1986; Likens 1989; Cole et al. 1991). Predictions in lakes, for example, have been generated using models that range in complexity from simple relationships between phosphorus and chlorophyll (Dillon and Rigler 1974) to complex efforts that couple terrestrial and aquatic process models, hydrologic and landscape models, and climate (Cardille et al. 2007). Lake prediction models are often driven by information about the system’s watershed (Soranno et al. 1996; Fraterrigo and Downing 2008), attributes of the lake (Vollenweider 1969), and/or processes occurring within the system (Ahlgren et al. 1988) that are often not readily available for every lake of interest (Evans et al. 2010). A clear need exists to develop novel predictive approaches that help increase scientific understanding and management of aquatic ecosystems (Pace 2001). Complex models are not necessarily synonymous with the best predictions, and simple models can be effective for generating predictions in a diverse range of situations (Downing et al. 2001; Debra et al. 2004). Research and management programs often collect baseline-monitoring data in aquatic systems, and upscaling this monitoring data to regional spatial scales has the potential to be a simple, effective approach for generating predictions through space and time. Two basic approaches are interpolation and forecasting prediction models. Interpolation models generate predictions based on a known set of known current conditions, while forecasting models generate predictions using past or historical conditions without knowledge of any current states. When lake dynamics are strongly correlated to regional scale drivers, suites of lakes often respond in a similar manner due to shared drivers among the systems (Baines et al. 2000; Magnuson et al. 2006c; Vogt et al. 2011). Consequently, information from monitored lakes can be used to interpolate the state of systems where measurements cannot be made (i.e., predict the current state of a focal system using observations of the current state in other systems; Evans et al. 2010). While interpolated predictions such as these can be generated with very little training data (Evans et al. 2010), synchrony among systems may not always be evident without many years of data (Magnuson et al. 2004). Thus, interpolation accuracy may vary depending on the extent of training data, and it is unclear how much training data is needed to maximize the effectiveness of simple interpolation models. Answers to these and related questions could improve methods for upscaling baseline-monitoring data to the wider landscape. The upscaling of baseline-monitoring data to the wider landscape using simple interpolation models has some potential limitations that may need to be considered as well. Interpolation models based on observations of current conditions in monitored systems lack any historical context (Magnuson 1990) in both the monitored systems and the focal systems where predictions are being generated. The lack of historical context emerges on two fronts. First, aquatic ecosystems often have memory (i.e., they are influenced by past events) and that memory can have important effects on current and future dynamics within the focal system (Montgomery and Reckhow 1984). Omission of memory or historical effects in interpolation models could therefore limit prediction capacity in these models. Historical states of the lakes used to generate interpolations may be important as well. Time lags are common in ecological systems (Magnuson 1990) and if * Corresponding author: [email protected] Limnol. Oceanogr., 57(4), 2012, 1113–1125 E 2012, by the Association for the Sciences of Limnology and Oceanography, Inc. doi:10.4319/lo.2012.57.4.1113