Two‐zone transient storage modeling using temperature and solute data with multiobjective calibration: 1. Temperature

Abstract

[1] This paper presents the formulation and calibration of the temperature portion of a two-zone temperature and solute (TZTS) model which separates transient storage into surface (STS) and subsurface transient storage (HTS) zones. The inclusion of temperature required the TZTS model formulation to differ somewhat from past transient storage models in order to accommodate terms associated with heat transfer. These include surface heat fluxes in the main channel (MC) and STS, heat and mass exchange between the STS and MC, heat and mass exchange between the HTS and MC, and heat exchange due to bed and deeper ground conduction. To estimate the additional parameters associated with a two-zone model, a data collection effort was conducted to provide temperature time series within each zone. Both single-objective and multiobjective calibration algorithms were then linked to the TZTS model to assist in parameter estimation. Single-objective calibrations based on MC temperatures at two different locations along the study reach provided reasonable predictions in the MC and STS. The HTS temperatures, however, were typically poorly estimated. The two-objective calibration using MC temperatures simultaneously at two locations illustrated that the TZTS model accurately predicts temperatures observed in MC, STS, and HTS zones, including those not used in the calibration. These results suggest that multiple data sets representing different characteristics of the system should be used when calibrating complex in-stream models.

Increasing parameter certainty and data utility through multi-objective calibration of a spatially distributed temperature and solute model

“…It should also be noted that this calibration does not capture the peak of the tracer at Site 3, nor the tail of the tracer curve at Site 2, which is critical to understanding the transient storage within the study reach (Bencala and Walters, 1983). Similar to what Neilson et al (2010a) found, comparing Level 1 and 2 results (Table 3) illustrates the relative benefit of using two-objective optimization compared to single-objective optimizations. For Tests 5-10, Tests 6 and 10 did not meet the local criteria of E > 0.8 with tracer data used as a calibration objective, although Test 6 did meet the global criteria (Table 3).…”

“…The E values reported for the two-objective optimizations are based on the parameter set that represents the best trade-off solution or the pareto solution (Vrugt et al, 2003a,b;Boyle et al, 2000;Gupta et al, 1998Gupta et al, , 2003Neilson et al, 2010a). The best results are from Test 7 with values of 7 E MC2,Tr = 0.94, 7 E MC2,Temp = 0.91, and AE s = 0.81 (Table 3).…”

“…An 11.94 km study reach of the Virgin River ( Fig. 1) was divided into two main sections on the basis of bed slope (0.0039 between S1 and S2 and 0.0012 between S2 and S3) and stream substrate distribution identified from a previous mapping effort (Neilson et al, 2010a).…”

“…With B tot established, n was then set to result in appropriate average travel times. The longitudinal dispersion (D) coefficient was set based on the methods described in Neilson et al (2010a).…”

“…The TZTS model separates transient storage (Bencala and Walters, 1983) into two zones, (1) dead zones or the surface transient storage (STS) zone that represents the eddies, recirculating zones, and side pockets of water and (2) subsurface or hyporheic transient storage (HTS) zone, that represents the flow into or out of the stream substrate. As discussed in Neilson et al (2010a), sources and sinks of heat include fluxes across the air-water interface, bed conduction, conduction between the bed and deeper ground substrate, HTS exchange, and STS exchange. Solute mass is primarily influenced by HTS and STS exchange (Neilson et al, 2010b).…”