#### 3.2. Interactions in Maules Creek Catchment

[32] Collected data from the Namoi River for an 8 month period is shown in Figure 3. During the monitoring period there were two major flow events, consisting of a dam release (approximately 1 m change in river level) in early December 2009, followed by a natural flood (over 6 m increase in river level) in early January 2010 (Figure 3a, black line). These fluctuating river levels were reflected in the aquifer level data, although in a dampened and lagged manner (Figure 3a, gray line). The recorded temperature data ranged from approximately 10°C (winter) to 30°C (summer; Figure 3b). During summer the upper temperature sensor recorded higher temperatures than the lower sensor, while this reversed during the winter. Also, in the summer months the daily fluctuations were larger as compared to the winter months.

[33] The interpreted data is shown in Figure 4. The river-aquifer hydraulic gradient data (Figure 4a), demonstrate that during low flows prior to the major flow events, there was potential for slightly gaining conditions. This reversed to losing conditions due to the increased river stage during the events. This was then followed by a period of gaining conditions which likely reflects a return of bank storage to the river.

[35] The values for effective thermal diffusivity estimated using equation (12) (Figure 4c), generally fall within the expected literature range, and are slightly higher than the literature average, although it should be noted that these literature values assume *β* is negligible in equation (3). The effective thermal diffusivity results computed are inclusive of the effect of thermal dispersivity which increases with velocity. The estimated thermal diffusivities during low flows were slightly different before and after the major flow events. This may indicate that scouring and sedimentation/colmation processes are occurring. This may be either through reworking of the riverbed or movement of suspended material into the pores, resulting in changes in grain size and effective porosity.

[36] During the major flow events, however, the values for effective thermal diffusivity changed rapidly, and increased to unrealistic values (vertical gray shaded zone in Figure 4c). This was due to the transient conditions during the major flow events with velocities changing significantly on a time scale smaller than that used for individual and calculations. This violates a fundamental assumption of the method, as the analytical solution to the convection-conduction equation (i.e.,equation (7)) requires that fluid flow is at steady state within a period of diel temperature fluctuations. As the major departures in effective thermal diffusivity occur during the major flow events, which is likely to be the period of greatest SW-GW interaction, this is an inherent limitation of the proposed method, and of the existing methods [e.g.,*Hatch et al.*, 2006; *Keery et al.*, 2007].

#### 3.3. Method Comparison

[37] The same data as that plotted in Figure 4b but reinterpreted using equations (9) and (10) (with (13) and (14)) are shown in Figure 5. For this reinterpretation, literature values for effective thermal diffusivity were used [e.g., *Shanafield et al.*, 2011]. As the value of effective thermal diffusivity used increases, the velocities vary more and tend toward gaining conditions.

[39] The previously published data by *Rau et al.* [2010] but here reinterpreted using equations (11) and (12) (with (13) and (14)) are shown in Figure 6. Previously, the Darcy velocity results for Horsearm Creek (HC) derived from the data differed from those derived from the data (Figure 6a, dashed lines). Similarly, the Darcy velocity results for Downstream Elfin Crossing (DEC) differed depending on the data used (Figure 6c, dashed lines). However, when both the and data were used in equation (11), a single velocity result was obtained (Figures 6a and 6c, solid lines). As there is uncertainty in the value of *γ*, bounds were added to the reinterpreted Darcy velocities. The two interpretations of the data are different and would lead to somewhat different conclusions about the system. For example, at HC the new interpretation suggests the systems is neutral to slightly losing, while the old interpretation suggested that perhaps the system was at times losing at rates of more than −0.5 m d^{−1}.

[40] The corresponding values of *D* (i.e., from equation (12)) to the derived values of *v* (i.e., from equation (11)) are shown in Figures 6b and 6d. The effective thermal diffusivity data agree well for both locations and appear to be increasing with time. This could be due to a reduction in porosity over the monitoring period; *Rau et al.* [2010] reported that colmation was taking place. Alternatively, it could illustrate that the assumptions behind equation (7) are being violated. Further testing of the proposed method for its reliability under different scenarios (e.g., lateral flow conditions) is required.

[41] Having proposed a method (i.e., Figure 2) for interpreting field data (i.e., Figures 3 and 4), and applied the existing methods to the data (i.e., Figure 5), as well as reinterpreting previously published data from another site (i.e., Figure 6), it is now possible to make the following observations.

[42] 1. When equations (9) and (10) are used, a value for the effective thermal diffusivity has to be chosen. *Shanafield et al.* [2011] have shown that uncertainties in the effective thermal diffusivity lead to uncertainties in estimated thermal front velocities. This issue is therefore highly significant. To overcome this problem, literature values of the relevant thermal parameters are frequently adopted [e.g., *Fanelli and Lautz*, 2008; *Rau et al.*, 2010; *Lautz*, 2010; *Jensen and Engesgaard*, 2011]. *Lapham* [1989]is commonly referenced to justify this approach. However, this research reported a range of thermal parameters for fine-grained and coarse-grained sediment. The method proposed here bypasses this issue, and removes the uncertainty in thermal front velocity normally associated with uncertainty in the effective thermal diffusivity.

[43] 2. When equations (9) and (10) are used the issue of what the value for thermal dispersivity should be is also raised. There is debate in the literature as to whether dispersivity should be included within the effective thermal diffusivity term, and if so, what the velocity relationship should be [e.g., *de Marsily*, 1986; *Anderson*, 2005]. *Keery et al.* [2007] suggested that the disagreements should promote research into the matter. This has since been undertaken by *Rau et al.* [2012]; see equation (3). Again, the proposed method bypasses this issue as it does not explicitly or implicitly set the dispersivity term to zero. Rather, the method computes the thermal front velocity using and data (i.e., equation (11)) where the effective thermal diffusivity (inclusive of dispersivity) is implicitly included in the computation.

[44] 3. It is not always clear when using equations (9) and (10) which of the two should be used, or why they often do not give the same results. *Hatch et al.* [2006] notes that the two equations have differing sensitivities to velocity as well as other parameters (e.g., sensor spacing). In practice, the velocity results derived from data often differ from those derived from data [e.g., *Rau et al.*, 2010; *Swanson and Cardenas*, 2010; *Munz et al.*, 2011]. Furthermore, a trend is developing in the literature which focuses on the data [e.g., *Fanelli and Lautz*, 2008; *Vogt et al.*, 2010; *Gordon et al.*, 2012; *Schmidt et al.*, 2011; *Briggs et al.*, 2012]. As outlined in section 2, when the assumptions behind equation (7) are valid, which was the original basis for applying equations (9) and (10) to field data, there should not be a discrepancy in the velocity results. Or in other words, a value of effective thermal diffusivity exists such that the velocity results will be equal. This effective thermal diffusivity value is estimated using equation (12).

[45] 4. Since it is reasonable to assume that the effective thermal diffusivity does not change rapidly or to values outside a reasonable range, the results can indicate periods where the method assumptions are being violated. This provides a quality check on the thermal front velocity results. While a rapid departure from value of effective thermal diffusivity indicates that the method is invalid, it should be noted, however, that steadiness of estimated thermal diffusivity does not necessarily per se indicate times where all the model assumptions are valid. The steadiness of calculated effective thermal diffusivity implies steadiness of thermal front propagation, it does not imply that fluid fluxes are 1-D or that the thermal properties of the porous medium are constant in space and time. Nevertheless, the proposed method provides a new metric for detection of violations. This is particularly helpful for data where transient conditions may exist.

[46] 5. Finally, when using equations (9) and (10), iterative routines are required to solve for thermal front velocity. This has recently been automated by *Swanson and Cardenas* [2011] and *Gordon et al.* [2012]. However, the interactive routines can be numerically intensive. In addition, in the case of equation (10), they are potentially unstable, although limits can be imposed to help with stability. The method outlined in this paper circumvents this issue by solving for thermal front velocity as an explicit function of and without iteration.

[47] In summary, the proposed method overcomes five major issues by estimating the thermal front velocity using both and data without the need to specify a value for effective thermal diffusivity or the need for iteration (i.e., equation (11)). In addition, the method allows for the estimation of the effective thermal diffusivity (i.e., equation (12)). It should be noted though, in common with all methods based on *Stallman* [1965], the proposed method has inherent limitations due to the assumptions behind the model, namely, (1) fluid flow is in the vertical direction only, (2) fluid flow is steady state, (3) fluid and solid properties are constant in both space and time, and (4) fluid and solid temperatures at any particular point in space are equal at all times.