Awareness of the global scale of water-related issues has led to the development of gridded databases and environmental models applicable over regional, continental, and global domains. Solomon et al. , for example, recognized that computer models that access gridded databases were effective tools for water resource planning at large scales (in their case, planning hydroelectric projects in Labrador and Newfoundland). Since then, the capability to apply gridded databases to water resources planning has advanced rapidly with the increasing sophistication of computer technology and data acquisition methods. Considerable effort has been given to the assessment of freshwater resources and their use at a global scale [Shiklomanov, 2000; World Resources Institute (WRI), 2000]. Development and application of simulation methods for assessing freshwater resources has focused primarily on macroscale hydrologic models [Alcamo et al., 2003]. Less attention has been given to developing methods for assessing water quality in spite of its importance for the health of global ecosystems. However, there is growing recognition of the need to expand the scope of ecosystems analyses to include large-scale environmental issues such as climate change [Kundzewicz et al., 2007]. Furthermore, because of the synergistic relationship between water quality and river discharge, it makes sense to develop methods that couple water quality models with gridded systems for simulating flows.
 This work focuses on water temperature because of its influence on the processes and functions of global ecosystems. Furthermore, potential increases in water temperature, whether the result of land cover change, water management, and/or climate change, threaten the biodiversity and integrity of aquatic ecosystems [Hester and Doyle, 2011]. Analysis of water temperature records show increasing trends in water temperature for many streams, rivers, and lakes in North American and Europe [Foreman et al., 2001; Kaushal et al., 2010; Morrison et al., 2002; Webb and Nobilis, 1995, 2007]. These studies attribute the increases in water temperature to a diversion of water from streams and rivers for irrigation and water supply, construction of impoundments, thermal discharge, and altered patterns of land use such as logging, farming, and urbanization. There is also concern that climate change will lead to further increases in water temperature [Meyer et al., 1999; Poff et al., 2002; van Vliet et al., 2010].
 The effects of increasing water temperature on aquatic ecosystems can be widespread and may be reflected in changes in the geographic range and productivity of aquatic species, and the resultant stress on sensitive freshwater species. These effects can be amplified when coupled with changes in hydrologic regimes [Mantua et al., 2010]. In the northwestern United States and southwestern Canada, for example, water temperature and streamflow are key factors in providing suitable habitat for important stocks of cold water fish [Elsner et al., 2010]. The Independent Scientific Group (ISG)  attributes much of the risk to threatened or endangered Pacific salmon in the Columbia River system of Idaho, Oregon, and Washington to changes in water temperature and river discharge. There may also be impacts on societal needs for drinking water, recreation, irrigation, and industrial uses [Kundzewicz et al., 2007; Poff et al., 2002; van Vliet et al., 2010]. As a result, it will be necessary to develop water quality plans to mitigate or remediate impacts on the thermal regimes of aquatic environments. While it will be important to develop water quality plans at scales on the order of 10–100 m with deterministic process models of water temperature [Boyd and Kasper, 2003; Chapra et al., 2008; Theurer et al., 1984], there is also a need for water quality planning at larger scales, and in developing countries where water quality planning is limited [Kundzewicz et al., 2007].
 The water temperature model, RBM, described in this study has been applied to water quality issues in the Pacific Northwest [Perry et al., 2011; Yearsley, 2003, 2009] at length and timescales similar to other applications of the thermal energy budget method [Chapra et al., 2008; Cole and Wells, 2002; Sinokrot and Stefan, 1993]. In this study, however, RBM is linked to grid-based representations of surface climate, land cover, topography, and the physiography of stream channel systems. The grid-based modeling system concept developed in this study differs in a number of ways from deterministic process models such as HEATSOURCE [Boyd and Kasper, 2003], CEQUAL-W2 [Cole and Wells, 2002], and SNTEMP [Theurer et al., 1984] that are used to simulate water temperature. These deterministic models conceptualize river systems as a network of line segments or control volumes. The resulting simulations are meant to estimate a state (water temperature) in specific, idealized, natural river segments. In the grid-based approach (Figure 1), the hydrologic and water temperature models simulate the state variables essentially at nodes that aggregate stream or river properties in each cell rather than the temperatures of specific stream segments. Nodes are connected by channels in a network derived from a digital elevation model (DEM). Developing the modeling system with a grid-based approach has the advantage of providing access to the extensive gridded databases for model-forcing functions. Access to the extensive gridded databases will increase the capability for simulating water temperature and, ultimately, other water quality constituents in large river systems.
 The water temperature model, RBM, described in earlier works [Yearsley et al., 2001; Yearsley, 2009] is formulated with state-space structure. It has been used in those and other studies [Perry et al., 2011] to obtain nominal solutions to the thermal energy budget equations, where the nominal solution is the solution for which model uncertainty is zero (deterministic model). This paper describes further development of RBM to allow for propagation of uncertainty of water temperature estimates within the grid-based system.
 The objective of this work is to describe an integrated grid-based hydrologic/water-temperature model system, where the water temperature model is formulated in a state-space structure. Although the ultimate goal is to develop methods for large-scale analyses of the type that have been done with hydrologic models alone, the concept is tested here on a relatively small, but data-rich, river basin (it is, however, intended for application to larger rivers). Performance standards of models derived from observations alone (statistical models) and from deterministic process models developed within the framework of the thermal energy budget are compared to the results from the test basin for purposes of evaluating model robustness.