Forecast Distribution Research Articles

Polarisation of Russia’s spatial development: quo vadis?

Inequality is an inherent property of spatial development, but too high spatial inequality can have a number of serious consequences, from increased fiscal spending aimed at smoothing fiscal space to slowing national economic development and increasing separatist sentiment. The problem of heterogeneity in spatial development is therefore relevant, especially for countries with a large spatial extent, where such inequalities are naturally higher. In Russia the spatial inequality started to grow since the end of the 20th century and is still considered to be high. The aim of the work was to identify the features of the process of polarization of Russia’s spatial development by analyzing the dynamics of economic activity in Russian regions in the 21st century and obtaining extrapolation forecast of interregional distribution of economic activity.The study was carried out with the help of distribution dynamics analysis methods, using the theory of Markov process with discrete time and continuous state space. The above methods have allowed us to: assess the actual distribution of economic activity indicators of the regions and to conclude about its changes in the first two decades of the 21st century; to obtain extrapolation forecast of the distribution of regional economic activity indicators in the long-run, i.e. to forecast long-run spatial equilibrium; to identify and characterize groups of regions forming “convergence groups” in the long-run. The obtained results led to a conclusion about the increasing polarization of Russia’s regions by the level of economic activity both in the study period and in the long run, while maintaining the current trends, to substantiate the need to expand the practice of applying tools of place-based regional policy.

Distributionally Robust Joint Chance-Constrained Optimization for Networked Microgrids Considering Contingencies and Renewable Uncertainty

In light of a reliable and resilient power system under extreme weather and natural disasters, networked microgrids integrating local renewable resources have been adopted extensively to supply demands when the main utility experiences blackouts. However, the stochastic nature of renewables and unpredictable contingencies are difficult to address with the deterministic energy management framework. The paper proposes a comprehensive distributionally robust joint chance-constrained (DR-JCC) framework that incorporates microgrid island, power flow, distributed batteries and voltage control constraints. All chance constraints are solved <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">jointly</i> and each one is assigned to an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimized</i> violation rate. To highlight, the JCC problem with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimized</i> violation rates has been recognized as NP-hard and challenging to solve. This paper proposes a novel evolutionary algorithm that successfully solves this problem and reduces the solution conservativeness (i.e., operation cost) by around 50% compared with the baseline <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Bonferroni Approximation</i> . We construct three data-driven ambiguity sets to model uncertain solar forecast error distributions. The solution is thus robust for any distribution in sets with the shared moments and shape assumptions. The proposed method is validated by robustness tests based on these sets and firmly secures the solution robustness.

Effective uncertainty visualization for aftershock forecast maps

Abstract. Earthquake models can produce aftershock forecasts, which have recently been released to lay audiences. While visualization literature suggests that displaying forecast uncertainty can improve how forecast maps are used, research on uncertainty visualization is missing from earthquake science. We designed a pre-registered online experiment to test the effectiveness of three visualization techniques for displaying aftershock forecast maps and their uncertainty. These maps showed the forecasted number of aftershocks at each location for a week following a hypothetical mainshock, along with the uncertainty around each location's forecast. Three different uncertainty visualizations were produced: (1) forecast and uncertainty maps adjacent to one another; (2) the forecast map depicted in a color scheme, with the uncertainty shown by the transparency of the color; and (3) two maps that showed the lower and upper bounds of the forecast distribution at each location. We compared the three uncertainty visualizations using tasks that were specifically designed to address broadly applicable and user-generated communication goals. We compared task responses between participants using uncertainty visualizations and using the forecast map shown without its uncertainty (the current practice). Participants completed two map-reading tasks that targeted several dimensions of the readability of uncertainty visualizations. Participants then performed a Comparative Judgment task, which demonstrated whether a visualization was successful in reaching two key communication goals: indicating where many aftershocks and no aftershocks are likely (sure bets) and where the forecast is low but the uncertainty is high enough to imply potential risk (surprises). All visualizations performed equally well in the goal of communicating sure bet situations. But the visualization with lower and upper bounds was substantially better than the other designs at communicating surprises. These results have implications for the visual communication of forecast uncertainty both within and beyond earthquake science.

Optimization of operating conditions on ultra-fine coal grinding through kinetic stirred milling and numerical modeling

This study investigated ultra-fine coal grinding performance of four low- to moderate-cost grinding media in a laboratory stirred mill. Kinetic grinding tests showed that silica beads generated the finest product size with a P80 of 5.9 μm from a feed size of 24.4 μm while having a specific energy (SE) input of 309 kWh/ton. Nonetheless, the least energy consumption of 109 kWh/ton was achieved by alumina beads; however, yielding a coarser product size of 15.5 μm. In addition, test results indicate that optimizing media sizes, solids concentration, and using viscosity modifiers enhance coal ultra-fine grinding performance. Under the optimized testing conditions, a P80 of 2.7 μm was produced with a corresponding SE input of 270 kWh/ton using silica beads ranging from 420 to 850 μm and a dispersant dosage of 14 kg/ton. Moreover, the mathematical models generated based on population balance modeling provided an accurate forecast of the particle-size distribution.

Are macroeconomic forecasters optimists or pessimists? A reassessment of survey based forecasts

We examine the issue of macroeconomic uncertainty in the Eurozone Area using forecasts from the European Central Bank’s Survey of Professional Forecasters from the inception of the Euro in 1999Q1 to 2020Q2. We provide new insights concerning the optimism or pessimism of the distribution of forecasts by examining the 25th and 75th quartiles of the forecast distribution for each three key macro economic variables, GDP growth, inflation and unemployment. In addition, we examine the over- or under-confidence of forecasters in the survey by deriving the term structure of ex-ante uncertainty for up to 2 years ahead and compare it to ex-post uncertainty, enabling us to make some comparisons with existing US studies. Our results suggest that GDP growth forecasts tend towards optimism, while those for inflation and unemployment tend towards pessimism. In addition, ex-ante uncertainty in forecasts for the Eurozone Area is less than ex-post uncertainty at both the short and longer-term forecasting horizons, for all three variables. This suggests a tendency towards over-confidence on the part of Eurozone forecasters.

Bias Correction of Mixed Distributions of Temperature with Strong Diurnal Signal

Abstract The performance of first-moment and full-distribution bias-correction methods of monthly temperature distributions for seasonal prediction is analyzed by comparing two approaches: the standard all-in-data procedure and the 6-hourly stratification of data. Five models are applied to remove the systematic errors of the CFSv2 forecasts of temperature for the rainy season in the Ethiopian Blue Nile River basin domain. Using deterministic evaluation measures, it is found that the stratification marginally increases the forecast skill especially in regions where the data distribution of temperature is prominently multimodal. The improvement may be attributed to a split of the mixed distribution into a set of unimodal distributions. A necessary condition for this splitting into unimodal distributions is that the amplitude of the diurnal cycle be larger than the interannual variability in the sample. The maximum improvement of stratification is achieved by the first-moment correction model. Significance Statement This paper evaluates bias-correction methods of monthly forecast distributions of temperature to improve seasonal forecast skill. It is found that marginal skill is gained when bias correction of the diurnal cycle is performed. This paper contributes to the discussion on the value of subdaily model output data.

Ensemble updating of categorical state vectors

An ensemble updating method for categorical state vectors is proposed. The method is based on a Bayesian view of the ensemble Kalman filter (EnKF). In the EnKF, Gaussian approximations to the forecast and filtering distributions are introduced, and the forecast ensemble is updated with a linear shift. Given that the Gaussian approximation to the forecast distribution is correct, the EnKF linear update corresponds to conditional simulation from a Gaussian distribution with mean and covariance such that the posterior samples marginally are distributed according to the Gaussian approximation to the filtering distribution. In the proposed approach for categorical vectors, the Gaussian approximations are replaced with a (possibly higher order) Markov chain model, and the linear update is replaced with simulation based on a class of decomposable graphical models. To make the update robust against errors in the assumed forecast and filtering distributions, an optimality criterion is formulated, for which the resulting optimal updating procedure can be found by solving a linear program. We explore the properties of the proposed updating procedure in a simulation example where each state variable can take three values.

Climate Change Influence On Ontario Corn Farms\u2019 Income

Our study quantifies the impact of climate change on the income of corn farms in Ontario, at the 2068 horizon, under several warming scenarios. It is articulated around a discrete-time dynamic model of corn farm income with an annual time-step, corresponding to one agricultural cycle from planting to harvest. At each period, we compute the income of a farm given the corn yield, which is highly dependent on weather variables: temperature and rainfall. We also provide a reproducible forecast of the yearly distribution of corn yield for the regions around ten cities in Ontario, located where most of the corn growing activity takes place in the province. The price of corn futures at harvest time is taken into account and we fit our model by using 49 years of county-level historical climate and corn yield data. We then conduct out-of-sample Monte-Carlo simulations in order to obtain the farm income forecasts under a given climate change scenario, from 0^circC to + 4^circC.

Evaluating the discrimination ability of proper multi-variate scoring rules

Proper scoring rules are commonly applied to quantify the accuracy of distribution forecasts. Given an observation they assign a scalar score to each distribution forecast, with the lowest expected score attributed to the true distribution. The energy and variogram scores are two rules that have recently gained some popularity in multivariate settings because their computation does not require a forecast to have parametric density function and so they are broadly applicable. Here we conduct a simulation study to compare the discrimination ability between the energy score and three variogram scores. Compared with other studies, our simulation design is more realistic because it is supported by a historical data set containing commodity prices, currencies and interest rates, and our data generating processes include a diverse selection of models with different marginal distributions, dependence structure, and calibration windows. This facilitates a comprehensive comparison of the performance of proper scoring rules in different settings. To compare the scores we use three metrics: the mean relative score, error rate and a generalized discrimination heuristic. Overall, we find that the variogram score with parameter p=0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=0.5$$\\end{document} outperforms the energy score and the other two variogram scores.

A Comparison Between Machine Learning and Functional Geostatistics Approaches for Data-Driven Analyses of Sediment Transport in a Pre-Alpine Stream

The problem of providing data-driven models for sediment transport in a pre-Alpine stream in Italy is addressed. This study is based on a large set of measurements collected from real pebbles, traced along the stream through radio-frequency identification tags after precipitation events. Two classes of data-driven models based on machine learning and functional geostatistics approaches are proposed and evaluated to predict the probability of movement of single pebbles within the stream. The first class built upon gradient-boosting decision trees allows one to estimate the probability of movement of a pebble based on the pebbles’ geometrical features, river flow rate, location, and subdomain types. The second class is built upon functional kriging, a recent geostatistical technique that allows one to predict a functional profile—that is, the movement probability of a pebble, as a function of the pebbles’ geometrical features or the stream’s flow rate—at unsampled locations in the study area. Although grounded in different perspectives, both models aim to account for two main sources of uncertainty, namely, (1) the complexity of a river’s morphological structure and (2) the highly nonlinear dependence between probability of movement, pebble size and shape, and the stream’s flow rate. The performance of the two methods is extensively compared in terms of classification accuracy. The analyses show that despite the different perspectives, the overall performance is adequate and consistent, which suggests that both approaches can provide modeling frameworks for sediment transport. These data-driven approaches are also compared with physics-based ones that are classically used in the hydrological literature. Finally, the use of the developed models in a bottom-up strategy, which starts with the prediction/classification of a single pebble and then integrates the results into a forecast of the grain-size distribution of mobilized sediments, is discussed.

A mechanism for the skew of ensemble forecasts

AbstractIt is often not appreciated that forecast ensembles are generally skewed. The skew can arise from the state dependence of the chaotic system dynamics responsible for the ensemble spread. Generation of skew by this mechanism can be demonstrated in even the simplest dynamical system with state‐dependent noise, and even when the initial and the asymptotic (i.e., the “climatological”) forecast distributions are both symmetric. Indeed, forecast distributions of systems with state‐dependent noise in the dynamical tendencies must in general be both skewed and heavy tailed, with implications for forecasting extreme anomaly risks. Ensemble forecast systems that misrepresent such state‐dependent noise have state‐dependent errors in their forecast probability distributions. Because such errors depend on both the initial condition and forecast lead time, they cannot be removed by simple a posteriori bias corrections of the forecast distributions. The ensemble standard deviation is often used as a simple metric of ensemble spread even when the forecast distribution is not Gaussian. In a similar spirit, the ensemble skew S may be used as a simple metric of the difference D between the ensemble‐mean and most likely forecast, as well as the risk ratio R of extreme positive and negative deviations from the ensemble‐mean forecast. This is motivated by the facts that (1) the probability distributions of many geophysical quantities are approximately stochastically generated skewed (SGS) distributions, for which simple analytical relationships exist between these quantities, and (2) Gaussian distributions are a sub‐class of SGS distributions. However, S may serve as a useful metric of R and D even when the distributions are not strictly SGS distributions.

Here be dragons: important spatial uncertainty driven by climate data in forecasted distribution of an endangered insular reptile

AbstractThe effect of future climate change is poorly studied in the tropics, especially in mountainous areas, yet species living in these environments are predicted to be strongly affected. Newly available high‐resolution environmental data and statistical methods enable the development of forecasting models, but the uncertainty related to climate models can be strong, which can lead to ineffective conservation actions. Predictive studies aimed at providing conservation guidelines often account for a range of future climate predictions (climate scenarios and global circulation models). However, very few studies consider potential differences related to the source of climate data and/or do not account for spatial information (overlap) in uncertainty assessments. We modelled the environmental suitability for Phelsuma borbonica, an endangered reptile native to Reunion Island. Using two metrics of species range change (difference in overall suitability and spatial overlap), we quantified the uncertainty related to the modelling technique (n = 10), sample bias correction, climate change scenario, global circulation models (GCM) and data source (CHELSA vs. Worldclim). Uncertainty was mainly driven by GCMs when considering overall suitability, while for spatial overlap, the uncertainty related to data source became more important than that of GCMs. The uncertainty driven by sample bias correction and variable selection was much higher when assessed based on the spatial overlap. The modelling technique was a strong driver of uncertainty in both cases. We provide a consensus ensemble prediction map of the environmental suitability of P. borbonica to identify the areas predicted to be the most suitable in the future with the highest certainty. Predictive studies aimed at identifying priority areas for conservation in the face of climate change need to account for a wide panel of modelling techniques, GCMs and data sources. We recommend the use of multiple approaches, including spatial overlap when assessing uncertainty in species distribution models.

Near-term forecasting of companion animal tick paralysis incidence: An iterative ensemble model.

Tick paralysis resulting from bites from Ixodes holocyclus and I. cornuatus is one of the leading causes of emergency veterinary admissions for companion animals in Australia, often resulting in death if left untreated. Availability of timely information on periods of increased risk can help modulate behaviors that reduce exposures to ticks and improve awareness of owners for the need of lifesaving preventative ectoparasite treatment. Improved awareness of clinicians and pet owners about temporal changes in tick paralysis risk can be assisted by ecological forecasting frameworks that integrate environmental information into statistical time series models. Using an 11-year time series of tick paralysis cases from veterinary clinics in one of Australia's hotspots for the paralysis tick Ixodes holocyclus, we asked whether an ensemble model could accurately forecast clinical caseloads over near-term horizons. We fit a series of statistical time series (ARIMA, GARCH) and generative models (Prophet, Generalised Additive Model) using environmental variables as predictors, and then combined forecasts into a weighted ensemble to minimise prediction interval error. Our results indicate that variables related to temperature anomalies, levels of vegetation moisture and the Southern Oscillation Index can be useful for predicting tick paralysis admissions. Our model forecasted tick paralysis cases with exceptional accuracy while preserving epidemiological interpretability, outperforming a field-leading benchmark Exponential Smoothing model by reducing both point and prediction interval errors. Using online particle filtering to assimilate new observations and adjust forecast distributions when new data became available, our model adapted to changing temporal conditions and provided further reduced forecast errors. We expect our model pipeline to act as a platform for developing early warning systems that can notify clinicians and pet owners about heightened risks of environmentally driven veterinary conditions.

Research on Probability Distribution of Short-Term Photovoltaic Output Forecast Error Based on Numerical Characteristic Clustering.

The forecast error characteristic analysis of short-term photovoltaic power generation can provide a reliable reference for power system optimal dispatching. In this paper, the total in-day error level was stratified by fuzzy C-means algorithm. Then the historical PV output data based on the numerical characteristics of point prediction output were classified. A General Gauss Mixed Model was proposed to fit the forecast error distribution of various photovoltaic output forecast error distribution. The impact of meteorological factors together with numerical characteristics on the forecast error was taken into full consideration in this analysis method. The predicted point output with high volatility can be accurately captured, and the reliable confidence interval is given. The proposed method is independent of the point prediction algorithm and has strong applicability. The General Gauss Mixed Model can meet the peak diversity, bias, and multimodal properties of the error distribution, and the fitting effect is superior to the normal distribution, the Laplace distribution, and the t Location-Scale distribution model. The error model has a flexible shape, a concise expression, and high practical value for engineering.

Online Spatio-Temporal Crowd Flow Distribution Prediction for Complex Metro System

As a key mission of the modern traffic management, crowd flow prediction (CFP) benefits in many tasks of intelligent transportation services. However, most existing techniques focus solely on forecasting entrance and exit flows of metro stations that do not provide enough useful knowledge for traffic management. In practical applications, managers desperately want to solve the problem of getting the potential passenger distributions to help authorities improve transport services, termed as crowd flow distribution (CFD) forecasts. Therefore, to improve the quality of transportation services, we proposed three spatiotemporal models to effectively address the network-wide CFD prediction problem based on the online latent space (OLS) strategy. Our models take into account the various trending patterns and climate influences, as well as the inherent similarities among different stations that are able to predict both CFD and entrance and exit flows precisely. In our online systems, a sequence of CFD snapshots is used as the training data. The latent attribute evolutions of different metro stations can be learned from the previous trend and do the next prediction based on the transition patterns. All the empirical results demonstrate that the three developed models outperform all the other state-of-the-art approaches on three large-scale real-world datasets.

Runoff forecasting model based on CEEMD and combination model: a case study in the Manasi River, China

Abstract Accurate forecasting of runoff is necessary for water resources management. However, the runoff time series consists of complex nonlinear and non-stationary characteristics, which makes forecasting difficult. To contribute towards improved forecasting accuracy, a novel combination model based on complementary ensemble empirical mode decomposition (CEEMD) for runoff forecasting is proposed and applied in this paper. Firstly, the original runoff series is decomposed into a limited number of intrinsic mode functions (IMFs) and one residual based on CEEMD, which makes the runoff time series stationary. Then, approximate entropy is introduced to judge the complexity of each IMF and residual. According to the calculation results of approximate entropy, the high complexity components are predicted by Gaussian process regression (GPR), the medium complexity components are predicted by support vector machine (SVM), and the low complexity components are predicted by autoregressive integrated moving average model (ARIMA). The advantages of each forecasting model are used to forecast the appropriate components. In order to solve the problem that the forecasting performance of GPR and SVM is affected by their parameters, an improved fireworks algorithm (IFWA) is proposed to optimize the parameters of two models. Finally, the final forecasting result is obtained by adding the forecasted values of each component. The runoff data collected from the Manasi River, China is chosen as the research object. Compared with some state-of-the-art forecasting models, the comparison result curve between the forecasted value and actual value of runoff, the forecasting error, the histogram of the forecasting error distribution, the performance indicators and related statistical indicators show that the developed forecasting model has higher prediction accuracy and is able to reflect the change laws of runoff correctly.

Forecast of rainfall distribution based on fixed sliding window long short-term memory

Applying data mining techniques for rainfall modeling because of a lack of sufficient memory components may increase uncertainty in rainfall forecasting. To solve this issue, in this research, a deep-learning-based long short-term memory (LSTM) model is developed for the first time for forecasting monthly rainfall data, and its capability is compared with a random forest (RF) data-driven model. To this end, monthly rainfall data for a period of 41 years (1980–2020) from two meteorological stations in Turkey, namely Rize and Konya, with different climatic conditions, are used. The analysis is carried out using optimum window sizes for determining the optimum lag times of rainfall time series. The performance of the models is evaluated using five statistical measures, namely root mean square error (RMSE), RMSE-observations standard deviation ratio (RSR), Legate and McCabe’s index (LMI), correlation coefficient (R) and Nash–Sutcliffe efficiency (NSE), and also using two visual means, namely Taylor and violin diagrams. The results reveal that the LSTM model, as a more efficient tool, outperforms the RF model in forecasting rainfall at both stations, with improved RMSE of 12.2–14.9%, RSR of 12.3–14.8%, R of 9.4–13.5% and NSE of 32.9–33.2%. The LSTM-based approach proposed herein could be adopted over any global climatic conditions to forecast the monthly rainfall with reasonable accuracy.

A k‐nearest neighbor‐based averaging model for probabilistic PV generation forecasting

AbstractProbabilistic forecasting of PV generation is crucial in uncertainty management to reinforce PV‐integrated power systems for long‐term planning. In this context, developing a reliable probabilistic forecast model is challenging due to weather conditions' stochastic nature and varying daily PV production patterns at multiple time instants. Due to varying probability distribution patterns, a nonparametric approach, such as quantile regression, is challenging to approximate the forecast error distribution. A forecast combination concept that yields impressive probabilistic forecasting results has rarely been utilized for PV generation forecasting. The use of complementary and sensible point forecasters characterizing different aspects of intricate PV production patterns in a k‐nearest neighbor quantile regression averaging framework is the proposed probabilistic forecasting model. The proposed forecasting model's accuracy is assessed with real‐world PV generation data from the USA for multi‐time instants. The probabilistic forecast performance of the proposed quantile k‐nearest neighbors regression averaging model is evaluated against the traditional quantile regression averaging, quantile regression forests, quantile k‐nearest neighbors, basic quantile regression, and regression bootstrapping in terms of the forecast (quantiles and prediction intervals) accuracy, using relevant error measures and scores. The proposed model has superior performance compared to the other models, as indicated by the lowest forecast errors and scores.

GARCH-Based “Value” for Equity Index Options: Expected—Not Realized—Volatility and the Distribution of Forecasts

GARCH-Based “Value” for Equity Index Options: Expected—Not Realized—Volatility and the Distribution of Forecasts

Sensitivity analysis of the convective‐scale AROME model to physical and dynamical parameters

AbstractA global sensitivity analysis of the convective‐scale Application of Research to Operations at Mesoscale (AROME) model is performed in order to determine the most influential parameters on the forecast of different near‐surface variables. For that purpose, the Morris method is applied to 21 parameters from six different physical and dynamical parametrization schemes, over different seasons. Results highlight a set of eight parameters with a noticeable influence on most variables, in particular 10 m wind speed and precipitation forecasts. The sensitivity of parameter uncertainties is also examined on different spatio‐temporal scales. A clear diurnal cycle of parameters influence is observed in summer, in close connection with the convective activity. In addition, the spatial distribution of parameters influence is mostly consistent with the underlying distribution of weather forecasts. A Sobol' sensitivity analysis, based on surrogate models, mostly confirms Morris conclusions and highlights some interactions between parameters.