This study develops a new error modelling method for ensemble short-term and real-time streamflow forecasting, called error reduction and representation in stages (ERRIS). The novelty of ERRIS is that it does not rely on a single complex error model but runs a sequence of simple error models through four stages. At each stage, an error model attempts to incrementally improve over the previous stage. Stage 1 establishes parameters of a hydrological model and parameters of a transformation function for data normalization, Stage 2 applies a bias correction, Stage 3 applies autoregressive (AR) updating, and Stage 4 applies a Gaussian mixture distribution to represent model residuals. In a case study, we apply ERRIS for one-step-ahead forecasting at a range of catchments. The forecasts at the end of Stage 4 are shown to be much more accurate than at Stage 1 and to be highly reliable in representing forecast uncertainty. Specifically, the forecasts become more accurate by applying the AR updating at Stage 3, and more reliable in uncertainty spread by using a mixture of two Gaussian distributions to represent the residuals at Stage 4. ERRIS can be applied to any existing calibrated hydrological models, including those calibrated to deterministic (e.g. least-squares) objectives.

For streamflow forecasting, rainfall–runoff models are often augmented with updating procedures that correct forecasts based on the latest available streamflow observations of streamflow. A popular approach for updating forecasts is autoregressive (AR) models, which exploit the "memory" in hydrological model simulation errors. AR models may be applied to raw errors directly or to normalised errors. In this study, we demonstrate that AR models applied in either way can sometimes cause over-correction of forecasts. In using an AR model applied to raw errors, the over-correction usually occurs when streamflow is rapidly receding. In applying an AR model to normalised errors, the over-correction usually occurs when streamflow is rapidly rising. In addition, when parameters of a hydrological model and an AR model are estimated jointly, the AR model applied to normalised errors sometimes degrades the stand-alone performance of the base hydrological model. This is not desirable for forecasting applications, as forecasts should rely as much as possible on the base hydrological model, with updating only used to correct minor errors. To overcome the adverse effects of the conventional AR models, a restricted AR model applied to normalised errors is introduced. We show that the new model reduces over-correction and improves the performance of the base hydrological model considerably.

[1] Streamflows often vary strongly with season, and this leads to seasonal dependence in hydrological model errors and prediction uncertainty. In this study, we introduce three error models to describe errors from a monthly rainfall-runoff model: a seasonally invariant model, a seasonally variant model, and a hierarchical error model. The seasonally variant model and the hierarchical error model use month-specific parameters to explicitly account for seasonal dependence, while the seasonally invariant model does not. A Bayesian prior is used in the hierarchical error model to account for potential variation and connection among model parameters of different months. The three error models are applied to predicting streamflows for five Australian catchments and are compared by various performance scores and diagnostic plots. The seasonally variant model and the hierarchical model both perform substantially better than the seasonally invariant model. From a cross-validation analysis, the hierarchical error model provides both the most accurate prediction mean and the most reliable prediction uncertainty distribution in most situations. The use of the prior to constrain the model parameters in the hierarchical model produces more robust parameter estimation than the other two models.

Water, energy, and food, as the basic material resources of human production and life, play a prominent role in social and economic development. As the imbalance between the supply and demand of water, energy, and food increases, a highly sensitive and fragile relationship gradually forms among water, energy, and food. In this paper, Inner Mongolia in China is selected as a research area. Firstly, synergy theory is applied to establish the framework of a water–energy–food system. Then, a multi-objective programming model is constructed, where the objective functions are defined to minimize the integrated deviation degree and pollutant emissions of the water–energy–food system. Meanwhile, maximization of the water benefit, energy production, and food production is also considered. In addition, the model takes economy, environment, water, energy, and food as constraints. Finally, a genetic algorithm is designed for accurately assessing the most promising results. The results show that the cooperation degree of the water–energy–food system in Inner Mongolia is getting better and better, and the pollutant emission from the water–energy–food system is decreasing. In 2020, the proportion of agricultural water consumption fell by 1%, while that of industrial water consumption rose by 0.48%. The production of coal, natural gas, and power are all showing an increasing trend. Among them, the increase of natural gas production is as high as 38,947,730 tons of standard coal. However, the proportions of coal, natural gas, and power change inconsistently, where the proportions of coal and natural gas increase while that of power decreases. Corn production accounts for more than 80% of the total, which is in the eldest brother position in the food industry structure. Besides, there are differences between the planned values and optimal values of decision variables. Finally, suggestions are put forward to improve the sustainable development of water–energy–food in Inner Mongolia.

Skilful and localised daily weather forecasts for upcoming seasons are desired by climate-sensitive sectors. Various General circulation models routinely provide such long lead time ensemble forecasts, also known as seasonal climate forecasts (SCF), but require downscaling techniques to enhance their skills from historical observations. Traditional downscaling techniques, like quantile mapping (QM), learn empirical relationships from pre-engineered predictors. Deep-learning-based downscaling techniques automatically generate and select predictors but almost all of them focus on simplified situations where low-resolution images match well with high-resolution ones, which is not the case in ensemble forecasts. To downscale ensemble rainfall forecasts, we take a two-step procedure. We first choose a suitable deep learning model, very deep super-resolution (VDSR), from several outstanding candidates, based on an ensemble forecast skill metric, continuous ranked probability score (CRPS). Secondly, via incorporating other climate variables as extra input, we develop and finalise a very deep statistical downscaling (VDSD) model based on CRPS. Both VDSR and VDSD are tested on downscaling 60 km rainfall forecasts from the Australian Community Climate and Earth-System Simulator Seasonal model version 1 (ACCESS-S1) to 12 km with lead times up to 217 days. Leave-one-year-out testing results illustrate that VDSD has normally higher forecast accuracy and skill, measured by mean absolute error and CRPS respectively, than VDSR and QM. VDSD substantially improves ACCESS-S1 raw forecasts but does not always outperform climatology, a benchmark for SCFs. Many more research efforts are required on downscaling and climate modelling for skilful SCFs.

Seasonal climate forecasts from raw climate models at coarse grids are often biased and statistically unreliable for credible crop prediction at the farm scale. We develop a copula-based postprocessing (CPP) method to overcome this mismatch problem. The CPP forecasts are ensemble based and are generated from the predictive distribution conditioned on raw climate forecasts. CPP performs univariate postprocessing procedures at each station, lead time, and variable separately and then applies the Schaake shuffle to reorder ensemble sequence for a more realistic spatial, temporal, and cross-variable dependence structure. The use of copulas makes CPP free of strong distributional assumptions and flexible enough to describe complex dependence structures. In a case study, we apply CPP to postprocess rainfall, minimum temperature, maximum temperature, and radiation forecasts at a monthly level from the Australian Community Climate and Earth-System Simulator Seasonal model (ACCESS-S) to three representative stations in Australia. We evaluate forecast skill at lead times of 0–5 months on a cross-validation theme in the context of both univariate and multivariate forecast verification. When compared with forecasts that use climatological values as the predictor, the CPP forecast has positive skills, although the skills diminish with increasing lead times and finally become comparable at long lead times. When compared with the bias-corrected forecasts and the quantile-mapped forecasts, the CPP forecast is the overall best, with the smallest bias and greatest univariate forecast skill. As a result of the skill gain from univariate forecasts and the effect of the Schaake shuffle, CPP leads to the most skillful multivariate forecast as well. Further results investigate whether using ensemble mean or additional predictors can enhance forecast skill for CPP.