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The behavior of environmental processes is difficult to predict with much certainty from the field observation data because the results of the time series models lack information on the physical knowledge of the process (Weijs, S.V., 2014). High levels of uncertainty in the field data due to space and time variability also make it difficult to use the data to reconstruct the spatial and temporal patterns (Drécourt and Rosbjerg, 2004). In order to obtain consistent spatial and temporal results, deterministic or stochastic physically based models have been used, but these models also come with their shortcomings because they cannot accurately reproduce the available measurement (Liu, Y., & Gupta, H. V., 2007). Since the model for an efficient reconstruction requires information from field data, and vice versa, this makes an analysis, and models complementary through an integration of the uncertain measurement and uncertain models through data fusion (Kistler et al., 2001; Compo et al., 2006). When predicting water quality problems with models, integration of observations is a critical issue for model quality (Errico, 1999; Errico et al., 2000). Also, water quality models used to predict the spatial hydrologic system variations are often weak due to model initialization, state errors and inadequate model physics and/or resolution (Walker and Houser, 2005). Also, satellite data retrievals of water quality are subject to errors and cannot provide complete space-time coverage. As the great statistician George Box noted: “All models are wrong, but some are useful.” From results obtained from the water quality simulation program (WASP) (Wool et al., 2006), there are so many assumptions and “parameterizations of our ignorance” that go into the models, we cannot use our results with confidence when making management decisions due to their degree of subjectivity. However, addressing George Box’s concern,, data fusion can be used to solve this problem.
Hydrologic modeling with data fusion methods is a quite recent developmetn; as such, there is an absence of existing general guidance on how to choose the best data fusion approach, which considers uncertainty correctly. This has been a limitation to extensive data fusion for hydrologic applications (Liu and Gupta, 2007). Data fusion started as a military project in the 60s, with the aim of controling the trajectory of missiles. Using a model alone would lead to erroneous trajectories because of the incomplete knowledge of atmospheric conditions, and it was impossible to collect data accurate enough to rely solely on them (Drécourt and Rosbjerg, 2004). This method was therefore designed to take the best of both worlds: where there is no observation, a physical model is used and relied upon. Where good data are available, they are used to represent the system, and, above all, the uncertainty of both the data and the model are taken into account (Drécourt and Rosbjerg, 2004). Such an approach is currently used in numerical weather prediction (NWP) and is a technique of merging observation data with prediction model data to more precisely predict the state of a system (Rabier, 2005). Its usage has also been successful in oceanography and hydrology. Monitoring networks for water quality modeling can be improved to reduce modeling uncertainty using data fusion (Yangxiao et al., 2006).