Transverse mixing and surface heat exchange in the Waikato River: A comparison of two models

Abstract

Two mathematical models of different complexity were used to study transverse dispersion and surface heat transfer in the lower Waikato River. A simple analytical streamtube model (HPLUME) gave adequate temperature predictions in a reach where the channel was fairly regular but performed poorly where there were extensive shallows. In the latter reach, a two‐dimensional numerical model (SYSTEM21) gave good temperature and flow predictions once properly calibrated. Model calibration proved to be difficult in the Waikato River because the natural river temperature varied significantly along the channel. A search method was developed to estimate both the transverse dispersion and surface heat exchange coefficients from measured plume temperature profiles based on the observation that transverse variations in natural temperature were small. This method was used to calibrate SYSTEM21 in two separate reaches. Coefficient estimates were sensitive to measurement errors and slight departures in homogeneity of natural temperature and it would be desirable to corroborate the estimates of E_z using dye tests. In the upper reach, the average transverse dispersion coefficient was E_z/hu∗ = 1 which is high but within the range of published values. A sharp bend and buoyant spreading contributed to the high E_z value. E_z increased with river flow because both h and u∗ increase with flow. In the lower reach, E_z/hu∗ = 0.1 which is lower than expected but islands may have affected the model calibration. The surface heat exchange coefficient averaged K = 84–167 W m⁻² s⁻¹ °C⁻¹ which falls within the range of published values. No significant relationship could be found between surface heat exchange coefficient and meteorological variables.

Keywords:

• water temperature
• excess temperature
• thermal pollution
• transverse dispersion
• surface heat exchange
• mathematical model