Any Cold Springs

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Use the link below to share a full-text version of this article with your friends and colleagues. Learn more. If groundwater flow velocities are sufficiently high, most of the subsurface heat transport can occur by advection. This is the case, for example, in the Cascades volcanic arc where much of the background geothermal heat is transported advectively and then discharged when the groundwater emerges at springs. The temperature of spring water can thus be used to infer the geothermal heat flux. If spring water temperature is many degrees warmer than the ambient temperature, as it is at hot springs, determining the heat discharged at springs is straightforward.

At large-volume cold springs, however, the geothermal warming of water is small because the added heat is diluted in a large volume of water. We show that in order to interpret the temperature of cold springs we must for three processes: 1 conversion of gravitational potential energy to heat through viscous dissipation, 2 conduction of heat to or from the Earth's surface, and 3 geothermal warming.

Using spring temperature data from the central Oregon Cascades and Mount Shasta, California, we show that the warming due to surface heat exchange and dissipation of gravitational potential energy can be comparable to that due to geothermal heating.

Unless these confounding sources of heating are taken into , estimates of geothermal heat flux derived from temperatures of cold springs can be incorrect by large factors. Temperature can therefore be used as a tracer of hydrologic processes and for testing conceptual hydrogeologic models [e.

Temperature offers several advantages as a tracer because it is easy, quick, and inexpensive to measure accurately in the field. The temperature of groundwater also provides insight into the subsurface geological processes that generate heat. These include analytical models to interpret seasonal temperature fluctuations [e. The general conclusion of these models is that the predicted temperature of spring water depends on the volume flux of water. For a given aquifer, as the groundwater velocity increases, the heat added by geothermal warming is diluted into larger volumes of water, and consequently, spring temperatures become colder.

In fact, spring temperatures can be colder than the mean annual surface temperature at the discharge elevation if the water is recharged at much higher elevations, as first noted by Alexander von Humboldt in [ Davis , ]. In contrast, for very low velocities typically a result of low permeabilities , the subsurface temperature gradient is nearly undisturbed by groundwater flow and the temperature of spring water will be close to the mean annual surface temperature at the discharge elevation.

The warmest spring temperatures occur for an intermediate range of velocities such that groundwater flow removes most of the geothermal heat flux advectively, but the added heat is not diluted by large volumes of water [ Forster and Smith , ]. In this latter case, the temperature of spring water can be used to infer the background geothermal heat flux provided the area from which heat is collected is known [e. We then apply this model to cold springs in the Oregon and California Cascades. For these springs we show that the change in elevation and discharge are sufficiently large that the dissipation of gravitational potential energy sometimes dominates the inferred warming of discharged spring water.

We argue that ignoring GPE can lead to ificant errors in the amount of geothermal warming of water discharged at cold springs. The water flows through the aquifer in the x direction, and we assume that at any given position x , the temperature of the aquifer is uniform across its thickness; that is, it is thermally well mixed [ Langseth and Herman , ].

The well-mixed aquifer model is a good approximation in situations where advective heat transfer is important [ Fisher and Becker , ; Rosenberg et al. Nevertheless, it is large enough to matter in situations where there are large volumes of flowing groundwater high recharge rates and large elevation changes of the order of 1 km. These are both conditions that characterize large-volume springs on volcanoes, for example. The dashed curve neglects GPE and geothermal warming. The solid curves include GPE warming. In Figure 2b , model parameters are typical of those for the springs in the Oregon and California Cascades.

The temperature at the recharge elevation is assumed to be 0. First, if the aquifers are close to the surface d less than a few meters , springs will discharge water at temperatures close to the mean annual surface temperature. This is because the timescale for water to flow through the aquifer is long compared with the thermal diffusion timescale, so that water in the aquifer is able to equilibrate with the surface temperature. A more general conclusion is that when spring temperatures are cold and discharge is high, all three processes considered here geothermal heating, GPE dissipation, and heat transfer to the surface may need to be considered to interpret spring temperatures.

The recharge area is an approximately km 2 region on the flanks of the Medicine Lake shield volcano. While recharge is distributed over a broad area, we will assume for simplicity that the model shown in Figure 1 is still a reasonable approximation. A highly simplified sketch of the geometry of the system is shown in Figure 3. In fact, if conductive heat transfer to and from the surface is negligible, the spring water is also discharging all the geothermal heat it acquires, and the spring temperature can be used to estimate the geothermal heat flux.

This background heat flux is similar to that elsewhere in the Cascades arc [e. The resulting rapid and voluminous groundwater flow causes an advective disturbance to the subsurface temperature gradient that makes the use of borehole temperature measurements to determine heat flow challenging and controversial [ Ingebritsen et al. In this region, studies have shown that advectively transported heat discharged by hot springs represents a substantial fraction of the heat budget of the volcanic arc [ Ingebritsen et al.

In this section we reexamine the temperature of cold springs. In our analysis we will assume that heat conduction to and from the surface is negligible because aquifer depths are typically greater than many tens of meters [e. Data for these two regions come from James [] and Nathenson et al.

The dashed line in Figure 5d and Figures 5e and 5f as well shows the relationship between the mean annual surface temperature and elevation inferred from climate stations near Mount Shasta [ Nathenson et al. The slope of the dashed line is 4.

The plus s in Figure 5a show mean annual surface temperature as a function of elevation at climate stations in the Oregon Cascades, and we expect that the mean annual surface temperature should lie somewhere between the two dashed lines. The scatter of climate station temperatures in Oregon probably reflects local climate variations that are influenced by the various mountain chains in this region. By contrast, the linear relation between temperature and elevation found at Mount Shasta [ Nathenson et al. Figures 5a and 5d show that most springs discharge water at temperatures similar to, or colder than, the mean annual surface temperature.

That is, if all the spring water has the same recharge elevation and recharge temperature, and there is no heat transfer with the surface or addition of geothermal heat, then spring temperature as a function of elevation should have the same slope as the solid line. The high elevation cold springs at Mount Shasta do in fact exhibit this slope. Figures 5b and 5e show that some of the springs discharge water that is several degrees warmer than the temperature at the recharge elevation.

The recharge elevation in Figure 5 is estimated by using the oxygen isotope composition of the spring water as a tracer of recharge elevation. In mountainous regions, precipitation becomes progressively more depleted in the heavier isotope of oxygen due to rainout as air masses change elevation. In the Oregon and California Cascades, the isotopic composition of precipitation decreases by about 0. For the springs in the Oregon Cascades, James et al. These isotopically inferred recharge elevations are also consistent with those obtained by Manga [] from mass-balance considerations.

In both regions the spring water compositions fall on local meteoric water lines, implying that the isotopic composition of the water and thus our inferred recharge elevation is not ificantly affected by evaporation. At Mount Shasta, the uncertainty in recharge elevation cannot be determined, but may be as large as m.

In the limit that we can neglect heat transfer to and from the surface again, a reasonable approximation in the Cascades because of high recharge, typically 0. At Mount Shasta Figure 5f , there is scant evidence of geothermal warming. Although this is only a small deviation from the common approximation that the recharge temperature is the same as the mean annual surface temperature [e. Here we have shown that the conversion of gravitational potential energy to heat can be an important source of warming for many large-volume cold springs and must be ed for when interpreting spring temperatures in mountainous regions.

Correcting for the effects of GPE warming yields ificantly lower estimates of the contribution of geothermal warming to spring temperatures in the Oregon and California Cascades. The authors thank the anonymous A. Gonnermann, M. Saar, and two anonymous reviewers for useful comments and suggestions. Volume 40 , Issue 5.

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Any Cold Springs

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