Multi-model ensemble hydrologic prediction using Bayesian model averaging

Multi-model ensemble strategy is a means to exploit the diversity of skillful predictions from different models. This paper studies the use of Bayesian model averaging (BMA) scheme to develop more skillful and reliable probabilistic hydrologic predictions from multiple competing predictions made by several hydrologic models. BMA is a statistical procedure that infers consensus predictions by weighing individual predictions based on their probabilistic likelihood measures, with the better performing predictions receiving higher weights than the worse performing ones. Furthermore, BMA provides a more reliable description of the total predictive uncertainty than the original ensemble, leading to a sharper and better calibrated probability density function (PDF) for the probabilistic predictions. In this study, a nine-member ensemble of hydrologic predictions was used to test and evaluate the BMA scheme. This ensemble was generated by calibrating three different hydrologic models using three distinct objective functions. These objective functions were chosen in a way that forces the models to capture certain aspects of the hydrograph well (e.g., peaks, mid-flows and low flows). Two sets of numerical experiments were carried out on three test basins in the US to explore the best way of using the BMA scheme. In the first set, a single set of BMA weights was computed to obtain BMA predictions, while the second set employed multiple sets of weights, with distinct sets corresponding to different flow intervals. In both sets, the streamflow values were transformed using Box-Cox transformation to ensure that the probability distribution of the prediction errors is approximately Gaussian. A split sample approach was used to obtain and validate the BMA predictions. The test results showed that BMA scheme has the advantage of generating more skillful and equally reliable probabilistic predictions than original ensemble. The performance of the expected BMA predictions in terms of daily root mean square error (DRMS) and daily absolute mean error (DABS) is generally superior to that of the best individual predictions. Furthermore, the BMA predictions employing multiple sets of weights are generally better than those using single set of weights. © 2006 Elsevier Ltd. All rights reserved

Integrated High-Resolution Modeling for Operational Hydrologic Forecasting

Current advances in Earth-sensing technologies, physically-based modeling, and computational processing, offer the promise of a major revolution in hydrologic forecasting—with profound implications for the management of water resources and protection from related disasters. However, access to the necessary capabilities for managing information from heterogeneous sources, and for its deployment in robust-enough modeling engines, remains the province of large governmental agencies. Moreover, even within this type of centralized operations, success is still challenged by the sheer computational complexity associated with overcoming uncertainty in the estimation of parameters and initial conditions in large-scale or high-resolution models. In this dissertation we seek to facilitate the access to hydrometeorological data products from various U.S. agencies and to advanced watershed modeling tools through the implementation of a lightweight GIS-based software package. Accessible data products currently include gauge, radar, and satellite precipitation; stream discharge; distributed soil moisture and snow cover; and multi-resolution weather forecasts. Additionally, we introduce a suite of open-source methods aimed at the efficient parameterization and initialization of complex geophysical models in contexts of high uncertainty, scarce information, and limited computational resources. The developed products in this suite include: 1) model calibration based on state of the art ensemble evolutionary Pareto optimization, 2) automatic parameter estimation boosted through the incorporation of expert criteria, 3) data assimilation that hybridizes particle smoothing and variational strategies, 4) model state compression by means of optimized clustering, 5) high-dimensional stochastic approximation of watershed conditions through a novel lightweight Gaussian graphical model, and 6) simultaneous estimation of model parameters and states for hydrologic forecasting applications. Each of these methods was tested using established distributed physically-based hydrologic modeling engines (VIC and the DHSVM) that were applied to watersheds in the U.S. of different sizes—from a small highly-instrumented catchment in Pennsylvania, to the basin of the Blue River in Oklahoma. A series of experiments was able to demonstrate statistically-significant improvements in the predictive accuracy of the proposed methods in contrast with traditional approaches. Taken together, these accessible and efficient tools can therefore be integrated within various model-based workflows for complex operational applications in water resources and beyond

Harnessing seasonal GCM forecasts for crop yield forecasting through multivariate forecast post-processing methods

Seasonal climate forecasts may be coupled with crop models to provide quantitative forecasts of crop yield, assess sensitivity to farm management decisions and manage risk associated with seasonal climate variability. Today, seasonal climate forecasts are produced by computationally expensive, physically-based global climate models, which capture large-scale climate patterns well. However, their coarse spatial resolution (typically >50km) means they do not reliably depict daily weather at sub-grid locations, limiting their direct use in crop models. Consequently, operational crop forecasting systems in Australia typically use alternative meteorological forcings such as historical climate analogues based on El Niño - Southern Oscillation phases, which may be less skillful than global climate model forecasts. An emerging tactic for coupling global climate model forecasts and crop models is to apply quantile mapping (otherwise known as cumulative distribution function matching) to adjust forecast ensemble members according to the historical distribution of observations. However, quantile mapping assumes the global climate model forecasts are highly skilful and well-behaved (which they are often not). The overly simplistic formulation of quantile-mapping propagates an assortment of model errors. Additionally, quantile-mapping cannot be used for downscaling to multiple sub-grid locations owing to its deterministic nature. Accordingly, an increasing number of studies are reporting negative results arising from coupling global climate model forecasts and crop models using quantile mapping. Hence, the overarching objective of this thesis is to develop more robust, spatially and temporally relevant post-processing methods to harness global climate model forecasts for use in crop models. To this end, I develop a new multivariate forecast post-processing workflow that combines Bayesian parametric methods and non-parametric methods to calibrate and downscale global climate model forecasts for use in crop models. Forecast calibration means to (1) minimise systematic error such as forecast bias, (2) ensure forecast uncertainty is reliably conveyed by ensemble spread, and (3) ensure forecasts are at least as skilful as climatology. Downscaling means, depending on the context, either: (1) producing a revised forecast with the correct local weather variability at a spatial scale smaller than the GCM grid (2) producing a local forecast based on large-scale climate drivers (e.g. sea surface temperature patterns) (this approach is also referred to as bridging), or (3) spatial or temporal disaggregation of a forecast. Crop forecasting models require physically-coherent inputs of rainfall, temperature and solar radiation. Previous research has established the suitability of the Bayesian joint probability modelling approach for calibrating monthly and three-monthly rainfall forecasts from global climate models. The Bayesian joint probability modelling approach has not previously been applied to post-process temperature or solar radiation forecasts or to post-process multivariate forecasts. However, it is formed on the general assumption that the joint distribution of two or more variables can be modelled as a multivariate normal distribution in transformed space. It can theoretically be extended for multivariate forecast post-processing with a relevant transformation for each variable. Thus the first objective of this thesis is to develop and evaluate several strategies for calibrating multivariate global climate model forecasts using the Bayesian joint probability modelling approach. Three strategies are compared: (1) simultaneous calibration of multiple climate variables in a single statistical model, which explicitly models inter-variable dependence via the covariance matrix; (2) univariate calibration coupled with an empirical ensemble reordering method (the Schaake Shuffle) that injects inter-variable dependence from historical data; and (3) quantile-mapping, which borrows inter-variable dependence from the raw forecasts. Applied to Australian seasonal (three-month) forecasts from the European Centre for Medium-range Weather Forecasts System4 model, univariate calibration paired with the Schaake Shuffle performs best in terms of univariate and multivariate forecast verification metrics. Direct multivariate calibration is the second-best method, with its far superior performance in in-sample testing vanishing in cross-validation, likely because of insufficient data to reliably infer the sizeable covariance matrix. Bayesian joint probability post-processing is confirmed to outperform quantile-mapping. Hence the Bayesian joint probability modelling approach and the Schaake Shuffle should, therefore, be preferred to quantile-mapping as a basis for calibrating GCM forecasts for crop forecasting applications. Global climate model forecast skill is best captured by post-processing on seasonal time scales. However, crop models require daily forecast sequences. Also, it is observed that some operational crop forecasting systems run separate crop models for multiple locations within a region and then aggregate the results into a regional forecast. Therefore, spatial forecasts are also needed. Accordingly, the second objective of this thesis is to develop and evaluate downscaling and disaggregation methods for post-processing global climate model forecasts to higher spatial and temporal resolutions. To this end, I develop an empirical multivariate downscaling method that imparts observed spatial, temporal and inter-variable relationships into disaggregated forecasts whilst completely preserving the joint distribution of forecasts post-processed at coarser spatial and/or temporal scales. Specifically, a Euclidean distance metric is devised to identify a nearest-neighbour in historical observations for each forecast ensemble member. The method of fragments is subsequently applied to simultaneously disaggregate the forecast spatial and temporally. The new method is demonstrated to perform well for downscaling skilful forecasts of rainfall, temperature and solar radiation for six locations in northeast Australia. The climatological distributions of the downscaled forecasts mirror observations and the observed frequency of wet days is also reproduced in forecasts. The new downscaling method is a step towards full integration of calibrated seasonal climate forecasts into crop models and has a significant advantage over quantile-mapping in that it can be applied for multiple sub-grid locations. The final objective of this thesis is to feed global climate model forecasts, post-processed using the new methods, to a crop decision support system to demonstrate an end-to-end solution for linking global climate model forecasts with a crop model to produce yield forecasts. The first crop forecasting application of the new methods is for sugarcane yield forecasting in Tully. The region is selected because it is a non-irrigated region, and it is thus suitable for assessing the value of climate forecasts. Two sets of post-processed forecasts are produced for the Tully Mill weather station in North-east Queensland. The first set is obtained by applying the Bayesian joint probability modelling approach to calibrate monthly rainfall, temperature and solar radiation forecasts for the grid cell containing Tully. The second set is obtained by using global climate model forecasts of the Niño 3.4 climate index (commonly associated with the El Niño Southern Oscillation), also using the Bayesian joint probability modelling approach, to produce local forecasts of monthly rainfall, temperature and solar radiation. In both cases, the monthly forecasts are subjected to the Schaake Shuffle and subsequently downscaled to daily sequences using identical methods. The calibration and bridging forecasts are used to drive a sugarcane crop model to generate long-lead forecasts of biomass in north-eastern Australia from 1982-2016. A rigorous probabilistic assessment of forecast attributes suggests that the calibration forecasts provide the most skilful forecasts overall although the bridging forecasts give more skilful yield forecasts at certain times. The biomass forecasts are unbiased and reliable for short to long lead times, suggesting that the new downscaling methods are effective. My end-to-end solution for linking global climate model forecasts and crop models enables quantitative modelling and risk management at the farm level. It has the potential to improve farm productivity and profitability through better decisions. Future research should investigate the value of the post-processing methods for a wide range of crops