Data-Driven Prediction of Thresholded Time Series of Rainfall and SOC models

We study the occurrence of events, subject to threshold, in a representative SOC sandpile model and in high-resolution rainfall data. The predictability in both systems is analyzed by means of a decision variable sensitive to event clustering, and the quality of the predictions is evaluated by the receiver operating characteristics (ROC) method. In the case of the SOC sandpile model, the scaling of quiet-time distributions with increasing threshold leads to increased predictability of extreme events. A scaling theory allows us to understand all the details of the prediction procedure and to extrapolate the shape of the ROC curves for the most extreme events. For rainfall data, the quiet-time distributions do not scale for high thresholds, which means that the corresponding ROC curves cannot be straightforwardly related to those for lower thresholds.Comment: 19 pages, 10 figure

Probabilistic methods for seasonal forecasting in a changing climate: Cox-type regression models

For climate risk management, cumulative distribution functions (CDFs) are an important source of information. They are ideally suited to compare probabilistic forecasts of primary (e.g. rainfall) or secondary data (e.g. crop yields). Summarised as CDFs, such forecasts allow an easy quantitative assessment of possible, alternative actions. Although the degree of uncertainty associated with CDF estimation could influence decisions, such information is rarely provided. Hence, we propose Cox-type regression models (CRMs) as a statistical framework for making inferences on CDFs in climate science. CRMs were designed for modelling probability distributions rather than just mean or median values. This makes the approach appealing for risk assessments where probabilities of extremes are often more informative than central tendency measures. CRMs are semi-parametric approaches originally designed for modelling risks arising from time-to-event data. Here we extend this original concept to other positive variables of interest beyond the time domain. We also provide tools for estimating CDFs and surrounding uncertainty envelopes from empirical data. These statistical techniques intrinsically account for non-stationarities in time series that might be the result of climate change. This feature makes CRMs attractive candidates to investigate the feasibility of developing rigorous global circulation model (GCM)-CRM interfaces for provision of user-relevant forecasts. To demonstrate the applicability of CRMs, we present two examples for El Niño/Southern Oscillation (ENSO)-based forecasts: the onset date of the wet season (Cairns, Australia) and total wet season rainfall (Quixeramobim, Brazil). This study emphasises the methodological aspects of CRMs rather than discussing merits or limitations of the ENSO-based predictor

Quality, trade, and exchange rate pass-through

This paper investigates the heterogeneous response of exporters to real exchange rate fluctuations due to product quality. We model theoretically the effects of real exchange rate changes on the optimal price and quantity responses of firms that export multiple products with heterogeneous levels of quality. The model shows that the elasticity of demand perceived by exporters decreases with a real depreciation and with quality, leading to more pricing-to-market and to a smaller response of export volumes to a real depreciation for higher quality goods. We test empirically the predictions of the model by combining a unique data set of highly disaggregated Argentinean firm-level wine export values and volumes between 2002 and 2009 with experts wine ratings as a measure of quality. In response to a real depreciation, we find that firms significantly increase more their markups and less their export volumes for higher quality products, but only when exporting to high income destination countries. These findings remain robust to different measures of quality, samples, specifications, and to the potential endogeneity of quality

Predicting Rainfall in the Context of Rainfall Derivatives Using Genetic Programming

Rainfall is one of the most challenging variables to predict, as it exhibits very unique characteristics that do not exist in other time series data. Moreover, rainfall is a major component and is essential for applications that surround water resource planning. In particular, this paper is interested in the prediction of rainfall for rainfall derivatives. Currently in the rainfall derivatives literature, the process of predicting rainfall is dominated by statistical models, namely using a Markov-chain extended with rainfall prediction (MCRP). In this paper we outline a new methodology to be carried out by predicting rainfall with Genetic Programming (GP). This is the first time in the literature that GP is used within the context of rainfall derivatives. We have created a new tailored GP to this problem domain and we compare the performance of the GP and MCRP on 21 different data sets of cities across Europe and report the results. The goal is to see whether GP can outperform MCRP, which acts as a benchmark. Results indicate that in general GP significantly outperforms MCRP, which is the dominant approach in the literature

Predictive Inference for Spatio-temporal Precipitation Data and Its Extremes

Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and subject to substaintial skewness which often arise in measurements of many environmental processes, and we apply the method to precipitation data in south-west Western Australia. A generalised hyperbolic Bayesian hierarchical model is constructed for the intensity, frequency and duration of daily precipitation, including the extremes. Unlike models based on extreme value theory, which only model maxima of finite-sized blocks or exceedances above a large threshold, the proposed model uses all the data available efficiently, and hence not only fits the extremes but also models the entire rainfall distribution. It captures spatial and temporal clustering, as well as spatially and temporally varying volatility and skewness. The model assumes that the regional precipitation is driven by a latent process characterised by geographical and climatological covariates. Effects not fully described by the covariates are captured by spatial and temporal structure in the hierarchies. Inference is provided by MCMC using a Metropolis-Hastings algorithm and spatial interpolation method, which provide a natural approach for estimating uncertainty. Similarly both spatial and temporal predictions with uncertainty can be produced with the model.Comment: Under review at Journal of the American Statistical Association. 27 pages, 10 figure

Data-based mechanistic modelling, forecasting, and control.

This article briefly reviews the main aspects of the generic data based mechanistic (DBM) approach to modeling stochastic dynamic systems and shown how it is being applied to the analysis, forecasting, and control of environmental and agricultural systems. The advantages of this inductive approach to modeling lie in its wide range of applicability. It can be used to model linear, nonstationary, and nonlinear stochastic systems, and its exploitation of recursive estimation means that the modeling results are useful for both online and offline applications. To demonstrate the practical utility of the various methodological tools that underpin the DBM approach, the article also outlines several typical, practical examples in the area of environmental and agricultural systems analysis, where DBM models have formed the basis for simulation model reduction, control system design, and forecastin

Challenges in quantifying changes in the global water cycle

Human influences have likely already impacted the large-scale water cycle but natural variability and observational uncertainty are substantial. It is essential to maintain and improve observational capabilities to better characterize changes. Understanding observed changes to the global water cycle is key to predicting future climate changes and their impacts. While many datasets document crucial variables such as precipitation, ocean salinity, runoff, and humidity, most are uncertain for determining long-term changes. In situ networks provide long time-series over land but are sparse in many regions, particularly the tropics. Satellite and reanalysis datasets provide global coverage, but their long-term stability is lacking. However, comparisons of changes among related variables can give insights into the robustness of observed changes. For example, ocean salinity, interpreted with an understanding of ocean processes, can help cross-validate precipitation. Observational evidence for human influences on the water cycle is emerging, but uncertainties resulting from internal variability and observational errors are too large to determine whether the observed and simulated changes are consistent. Improvements to the in situ and satellite observing networks that monitor the changing water cycle are required, yet continued data coverage is threatened by funding reductions. Uncertainty both in the role of anthropogenic aerosols, and due to large climate variability presently limits confidence in attribution of observed changes