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Water–Air Temperature Relationships in a Devon River System and the Role of flow

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Water–Air Temperature Relationships in a Devon River System and the Role of flow HYDROLOGICAL PROCESSES Hydrol. Process. 17, 3069–3084 (2003) Published online 21 August 2003 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.1280 Water–air temperature relationships in a Devon river system and the role of flow B. W. Webb,* P. D. Clack and D. E. Walling School of Geography and Archaeology, University of Exeter, Amory Building, Rennes Drive, Exeter EX4 4RJ, UK Abstract: The nature of the water–air temperature relationship, and its moderation by discharge, were investigated for catchments ranging in size from 2Ð1 to 601 km2 in the Exe basin, Devon, UK and for data relating to hourly, daily and weekly time bases. The sensitivity and explanatory power of simple water–air temperature regression models based on hourly data were improved by incorporation of a lag, which increased with catchment size, although relationships became more sensitive and less scattered as the time base of data increased from hourly to weekly mean values. Significant departures from linearity in water–air temperature relationships were evident for hourly, but not for daily mean or weekly mean, data. A clear tendency for relationships between water and air temperatures to be stronger and more sensitive for flows below median levels was apparent, and multiple regression analysis also revealed water temperature to be inversely related to discharge for all catchments and time-scales. However, discharge had a greater impact in accounting for water temperature variation at shorter time-scales and in larger catchments. Copyright 2003 John Wiley & Sons, Ltd. KEY WORDS water–air temperature relationships; discharge effects; catchment scale INTRODUCTION In investigating the thermal regimes of streams and rivers, which are of considerable significance to aquatic ecology, water quality and the utilization of water resources, attention often has been given to the nature of statistical relationships between water and air temperatures (e.g. Johnson, 1971; Kothandaraman, 1972; Smith, 1981; Crisp and Howson, 1982; Webb, 1987; Stefan and Preud’homme, 1993; Caissie et al., 1998; Mohseni et al., 1998). Air temperature is commonly used as the independent variable in regression analysis of stream and river temperatures because it can be viewed as a surrogate for the net changes in heat flux that affect the water surface, and also because it approximates the equilibrium temperature of a water course. The latter is the temperature of the water surface at which no net exchange of energy occurs with the atmosphere (Edinger et al., 1968; Dingman, 1972). Linear regression models between air and water temperature have been developed successfully for data relating to different time periods, including 2-h values (Stefan and Preud’homme, 1993), daily, weekly and monthly and annual means (e.g. Webb, 1987; Crisp, 1988; Webb and Walling, 1993; Erickson and Stefan, 1996, 2000; Webb and Nobilis, 1997), and daily maxima and minima (Smith, 1979). Water–air temperature regression models offer a simple means of predicting water temperatures, not least because data on air temperature are usually much more readily available than information on the wide range of hydrometeorological parameters that are required to apply more sophisticated physically based models based on river energy budgets and mass transport of heat calculations (e.g. Bartholow, 1989; Sinokrot and Stefan, 1993; Kim and Chapra, 1997; Younus et al., 2000). Furthermore, such regression models are * Correspondence to: B. W. Webb, School of Geography and Archaeology, University of Exeter, Amory Building, Rennes Drive, Exeter EX4 4RJ, UK. E-mail: [email protected] Received 16 July 2002 Copyright 2003 John Wiley & Sons, Ltd. Accepted 8 January 2003 3070 B. W. WEBB, P. D. CLACK AND D. E. WALLING frequently characterized by high levels of explained variance, even when the meteorological station recording air temperature is located at a distance of several tens of kilometres from the river temperature monitoring site (Crisp and Howson, 1982; Mohseni et al., 1998; Pilgrim et al., 1998). Some studies (Sullivan et al., 1990) have cautioned that estimating water temperature from air temperature data collected at a remote location may lead to inaccuracies, although such problems have been found to be most significant in regions where air temperature gradients are steep and display abrupt changes (Lewis et al., 2000). Water–air temperature regression analysis has also proved a useful tool in studies seeking to predict future stream and river temperatures that may result from global warming (Mackey and Berrie, 1991; Webb, 1996), especially where information is required for ecological purposes and for large geographical areas (e.g. Eaton and Scheller, 1996; Mohseni et al., 1999). Although simple linear regression models linking water to air temperatures have often been developed and utilised, the subtleties and complexities of the water–air temperature relationship are being increasingly recognized. For example, a study of the Straight River, Minnesota, USA has demonstrated that the water–air temperature regression relationship becomes steeper and less scattered as the time interval of the data increases from 2-h, through daily averages to weekly means (Stefan and Preud’homme, 1993). Strong relationships are also usually encountered when monthly mean values are used in regression analysis, but weaker and less sensitive relationships are evident when annual mean values have been analysed for a 90-year period in the River Krems, Austria (Webb and Nobilis, 1997). The lack of well-defined water–air temperature regression relationships associated with annual data probably reflects the limited variability of annual means of water and air temperature (Pilgrim et al., 1998; Erickson and Stefan, 2000). Regression relationships between daily minimum water and air temperatures also tend to be more scattered than those for daily mean or maximum values. This has been attributed to the fact that the higher thermal capacity of water prevents development of the low nocturnal minima characteristic of air temperature (Smith, 1979). Water temperature variations also tend to lag behind fluctuations in air temperature (Jeppesen and Iversen, 1987). For larger rivers, with higher flow volumes and greater thermal capacities, this effect becomes more pronounced and should be taken into account in developing water–air temperature relationships. Grant (1977) suggested that the maximum water temperature on a given day in the Ngaruroro River, New Zealand should be predicted not only from the maximum air temperature on that day but also from the maximum air temperature on the preceding day. Stefan and Preud’homme (1993) have shown more generally that regression relationships based on daily mean values can be significantly improved by introducing a lag into the data. This lag was 0 days for catchments 300 km2 or less in size, but more than 8 days for basins in excess of 4 ð 105 km2. The assumption that the water–air temperature relationship is linear has also been questioned. Several studies have demonstrated departures from linearity as air temperature falls below 0 °C (e.g. Crisp and Howson, 1982; Webb and Nobilis, 1997) and this can be ascribed to the release of latent heat with ice formation, which prevents water temperatures falling much below 0 °C. More recently, it has been suggested that the water–air temperature relationship derived from weekly mean values also departs from linearity at high air temperatures (>ca.25°C). Increases in the moisture-holding capacity of the atmosphere, which promote greater evaporation from the water surface and, in turn, increase evaporative cooling of the water course, together with enhanced back radiation as water temperatures rise, are considered responsible for this effect (Mohseni et al., 1998, 1999, 2002). Testing of data from 584 rivers in the USA has demonstrated that a continuous S-shaped curve, based on a non-linear logistic regression function, successfully represented departures of the water–air temperature relationship at both high and low air temperatures. Mohseni and Stefan (1999) have offered a general physical interpretation of this S-shaped relationship in terms of equilibrium temperatures and natural upstream temperatures (groundwater, snowmelt and dew point) in rivers. The influence of other factors on the water–air temperature relationship in water courses also has been recognized. For example, in a study of Minnesota rivers, Stefan and Sinokrot (1993) showed that different regression models existed for river sites open to high solar radiation receipts and those heavily shaded from incoming solar radiation by riparian vegetation. More recently, Erickson and Stefan (2000) reviewed the impacts that impoundments and reservoirs, groundwater inflows, wastewater inputs and stream shading and Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 3069–3084 (2003) RIVER-WATER–AIR TEMPERATURE RELATIONSHIPS 3071 wind sheltering have on linear water–air temperature regression parameters. Changing sources and volumes of runoff are also known to affect water temperature behaviour (e.g. Shanley and Peters, 1988; Gu, 1998a,b; Kobayashi et al., 1999, Langan et al., 2001), but there have been relatively few studies that have investigated the impact of stream and river discharge on the water–air temperature relationship. For rivers affected by seasonal snow- and ice-melt runoff, hysteresis has been identified and represented by looped relationships (Webb and Nobilis, 1994; Mohseni et al., 1998, 1999).
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