Sensitivity analysis of a one dimensional heat transport model in the Ngongotaha Stream, New Zealand

Abstract or Summary

To quantify springs discharge over a 1 km reach in the Ngongotaha Stream, Rotorua, New Zealand, a new approach was developed in this study in which a one dimensional transient heat transport model was fitted to fibre optic distributed temperature sensing measurements where the main calibration parameters of interest were the unknown spring discharges. The heat transport model requires a large number of input parameters that affect the accuracy of the temperature simulation and ultimately quantification of groundwater discharge. To understand the model input-output relationship, a global sensitivity analysis (GSA) techniques including the Morris method (Morris, 1991) using PEST++ software (Welter et al., 2015) was investigated. For comparison, a linear sensitivity analysis method (Doherty, 2015), was used to quickly explore alternative model representations. To measure stream temperature, the fibre optic cable was deployed at the streambed near the left and right banks as the groundwater fed springs discharge laterally at both banks. Thirteen springs were identified in the study reach. The left and right bank temperature profiles showed that full mixing of the spring and stream water does not occur between most of the springs due to their close spacing. Datasets of measured temperatures at the left and right bank were transformed to a new single dataset using a weighted average where the weights reflect the degree of mixing downstream of a spring. The primary objective function for the sensitivity analysis was to minimize the sum of squared residuals between the stream temperature model predictions and the weighted average of the left and right bank temperature. Streamflow gauging upstream and downstream of the study reach showed that the stream gains ~ 500 L/s from groundwater which was used as the second objective function. The most sensitive parameters using the method of Morris were the shadow factor, discharge of springs no.5, 4 and 1 and the view to sky coefficient. The most sensitive parameters using the composite parameter sensitivity method were the temperature of springs no.13, 12 and 3, discharge of springs no.13, solar radiation and shadow factor. The results showed that the two methods provided different parameter importance rankings. The standard deviation of elementary effects in the method of Morris identifies the extent of interaction between parameters and non-linear effect of each parameter (Saltelli et al., 2004). Two parameters with high standard deviation of the elementary effects were view to sky coefficient and shadow factor. It is believed that the method of Morris results for these two parameters are more reliable than the composite method as this method does not take into account the interaction between parameters and non-linearity.