Deterministic and Stochastic Generation of Evaporation Data for Long-Term Mine Pit Lake Water Balance Modelling

Abstract

Lakes commonly form in mine pits following the end of mining. A good understanding of the pit lake water balance over future decades to centuries is essential to understand and manage environmental risks from the lake. Evaporation is often the major or only outflow from the lake, thus being an important determinant of equilibrium lake level and environmental risks. A general lack of in situ measurements of pit lake evaporation has meant that estimates have usually been based on pan coefficients derived for other contexts or on alternative unvalidated evaporation models. Our research used data from an evaporation pan and weather station that were floated on a pit lake in semi-arid central Queensland, Australia. A deterministic aerodynamic evaporation model was developed from these data to infill missing values, and an adjusted aerodynamic model was used to reconstruct long-term historical daily evaporation data. With an average bias of 6.5% during the measurement period, this long-term model was found to be more accurate than alternative simple models (e.g., using the commonly used pan coefficient of 0.7 gave a bias of 45%). The reconstructed data were then used to fit and assess a stochastic model for the generation of future evaporation and rainfall realisations, assuming a stationary climate. Fitting stochastic models at a monthly time step was found to accurately represent the monthly evaporation statistics. For example, the cross-correlation between historical rainfall and evaporation was within the 25 and 75 percentiles of the modelled values in 11 of 12 months and always within the 2.5 and 97.5 percentiles. However, the stationary nature of the model presented limitations in capturing interannual anomalies, with continuous periods of up to 6 years, where the modelled annual rainfall was consistently lower and modelled annual evaporation consistently higher than the historical values. Fitting stochastic models at a daily time step had problems capturing a range of statistics of both rainfall and evaporation. For example, in 6 of the 12 months, the cross-correlation between historical rainfall and evaporation was outside the modelled 2.5 and 97.5 percentiles. This likely arises from the complex patterns in transitions from wet to dry days in the semi-arid climate of the case study. While the long-term model and monthly stochastic model are promising, further work is needed to understand the significance of the observed errors and refine the models.