Streamflow depletion is traditionally defined as the instantaneous change in the volumetric rate of aquifer–stream exchange after a finite period of continuous groundwater extraction. In the present study an alternative metric of streamflow depletion was considered: cumulative stream depletion (CSD), which described the total volumetric reduction in flow from an aquifer to a stream resulting from continuous groundwater extraction over a finite period. A novel analytical solution for the prediction of CSD was derived, based upon an existing solution that accounted for streambed conductance and partial stream penetration. Separately, a novel numerical solution for the prediction of CSD was derived, based on the derivation of an adjoint state solution. The accuracy of the two new solutions was demonstrated through benchmarking against existing analytical solutions and perturbation-based results, respectively. The derivation of the loading term used in the adjoint state solution identified three parameters of relevance to CSD prediction. First is streambed hydraulic conductivity and thickness, both of which contribute to a lumped parameterization of streambed conductance. Second is aquifer specific yield, which controls the rate at which hydraulic perturbations propagate through an aquifer. The computational advantage of the adjoint state approach was highlighted, in which a single numerical model run can be used to predict CSD resulting from any potential groundwater extraction location. The reduction in computation time achieved was proportional to the number of potential extraction well locations. Where the number of locations is large, reductions in computation times of nearly 100 % can be achieved.

While hydraulic fracturing is widely used to enhance the permeability of deep geothermal, gas and oil reservoirs, it remains challenging to infer the heterogeneous distribution of permeability in the fractured zone. Typically, a limited number of boreholes are available at which reservoir imaging and tracer testing can be conducted. The number of observations is often far fewer than the number of estimable permeabilities, making model inversion ill-posed. To overcome this problem, this study combined the autoencoder neural network (a deep learning approach) with Bayesian inversion algorithm (using Markov Chain Monte Carlo, MCMC sampling) to estimate permeability in the enhanced geothermal reservoir, based on a single-well-injection-withdrawal test (SWIW). The autoencoder neural network was used to reduce parameter dimensionality into low-dimension codes by four orders of magnitude, while MCMC sampling was used to update the low-dimension codes according to the SWIW observations. The spatial distribution of permeability was then reconstructed from these low-dimension codes using the original autoencoder neural network. Application of the approach to a synthetic enhanced geothermal system demonstrated that the methodology achieved rapid stabilization of the Bayesian inversion. When the root mean square error (RMSE) between modelled and observed borehole temperature and flow rate values was less than unity, estimated permeability values were comparable to the synthetic reference case, with a mean square error lower than 0.001 mD. The combination of the deep-learning based dimension reduction technique and Bayesian inversion algorithm allow the estimate of permeability distribution in deep artificial reservoirs based on limited number of boreholes.

The determination of flow state remains an important challenge in non-perennial river catchments. Previous studies interpreted stream channel temperature time series data using the moving standard deviation method to identify the timing and duration of flow. However, the performance of this technique requires the user to specify multiple subjective constraints. We implemented six variations of time-frequency analysis from three categories: (1) Fourier transform methods, (2) wavelet transform methods, and (3) Empirical Mode Decomposition methods. We evaluated and compared their ability to discern periods of flow from synthetic and field data of stream temperature time series data. Overall, all methods performed reasonably well, with performance of 63–99 % success in matching flow and no-flow periods. Greater variability in performance was observed when evaluating field data. Differences between methods include the ease of implementation and evaluation of results, computational needs, and ability to handle discontinuous data. We suggest five primary areas for future research to improve the general understanding of these time-frequency analysis techniques.

The traditional metric of streamflow depletion represents the instantaneous change in the volumetric rate of aquifer–stream exchange after a finite period of continuous groundwater extraction. In the present study an alternative metric of streamflow depletion was considered: cumulative stream depletion (CSD), which described the total volumetric reduction in flow from an aquifer to a stream resulting from continuous groundwater extraction over a finite period, at the final time of extraction. A novel analytical solution for the prediction of CSD was derived, based upon a forward solution that accounted for streambed conductance and partial stream penetration. Separately, a novel numerical solution for prediction of CSD was derived, based on the derivation and calculation of an adjoint state solution. The accuracy of these methods was demonstrated through benchmarking against existing analytical solutions and perturbation-based results, respectively. The derivation of the adjoint state solution identified three parameters of relevance to CSD prediction: streambed hydraulic conductivity and thickness, both of which contribute to the lumped parameterization of streambed conductance, as well as aquifer specific yield, which controls the rate at which hydraulic perturbations propagate through an aquifer. The computational advantage of the numerical adjoint solution was highlighted, where a single numerical model can be used to predict CSD resulting from any potential groundwater extraction location. The reduction in computational time required was proportional to the number of potential extraction well locations. If the number of potential locations is large then a reduction in model run time of nearly 100 % can be achieved.