Seasonal Temperature Forecasts Research Articles

Fractional relaxation noises, motions and the fractional energy balance equation

Abstract. We consider the statistical properties of solutions of the stochastic fractional relaxation equation and its fractionally integrated extensions that are models for the Earth's energy balance. In these equations, the highest-order derivative term is fractional, and it models the energy storage processes that are scaling over a wide range. When driven stochastically, the system is a fractional Langevin equation (FLE) that has been considered in the context of random walks where it yields highly nonstationary behaviour. An important difference with the usual applications is that we instead consider the stationary solutions of the Weyl fractional relaxation equations whose domain is −∞ to t rather than 0 to t. An additional key difference is that, unlike the (usual) FLEs – where the highest-order term is of integer order and the fractional term represents a scaling damping – in the fractional relaxation equation, the fractional term is of the highest order. When its order is less than 1/2 (this is the main empirically relevant range), the solutions are noises (generalized functions) whose high-frequency limits are fractional Gaussian noises (fGn). In order to yield physical processes, they must be smoothed, and this is conveniently done by considering their integrals. Whereas the basic processes are (stationary) fractional relaxation noises (fRn), their integrals are (nonstationary) fractional relaxation motions (fRm) that generalize both fractional Brownian motion (fBm) as well as Ornstein–Uhlenbeck processes. Since these processes are Gaussian, their properties are determined by their second-order statistics; using Fourier and Laplace techniques, we analytically develop corresponding power series expansions for fRn and fRm and their fractionally integrated extensions needed to model energy storage processes. We show extensive analytic and numerical results on the autocorrelation functions, Haar fluctuations and spectra. We display sample realizations. Finally, we discuss the predictability of these processes which – due to long memories – is a past value problem, not an initial value problem (that is used for example in highly skillful monthly and seasonal temperature forecasts). We develop an analytic formula for the fRn forecast skills and compare it to fGn skill. The large-scale white noise and fGn limits are attained in a slow power law manner so that when the temporal resolution of the series is small compared to the relaxation time (of the order of a few years on the Earth), fRn and its extensions can mimic a long memory process with a range of exponents wider than possible with fGn or fBm. We discuss the implications for monthly, seasonal, and annual forecasts of the Earth's temperature as well as for projecting the temperature to 2050 and 2100.

Improved Trend-Aware Postprocessing of GCM Seasonal Precipitation Forecasts

Abstract Climate trends have been observed over the recent decades in many parts of the world, but current global climate models (GCMs) for seasonal climate forecasting often fail to capture these trends. As a result, model forecasts may be biased above or below the trendline. In our previous research, we developed a trend-aware forecast postprocessing method to overcome this problem. The method was demonstrated to be effective for embedding observed trends into seasonal temperature forecasts. In this study, we further develop the method for postprocessing GCM seasonal precipitation forecasts. We introduce new formulation and evaluation features to cater for special characteristics of precipitation amounts, such as having a zero lower bound and highly positive skewness. We apply the improved method to calibrate ECMWF SEAS5 forecasts of seasonal precipitation for Australia. Our evaluation shows that the calibrated forecasts reproduce observed trends over the hindcast period of 36 years. In some regions where observed trends are statistically significant, forecast skill is greatly improved by embedding trends into the forecasts. In most regions, the calibrated forecasts outperform the raw forecasts in terms of bias, skill, and reliability. Wider applications of the new trend-aware postprocessing method are expected to boost user confidence in seasonal precipitation forecasts.

The Role of Temperature Variability on Seasonal Electricity Demand in the Southern US

The reliable and affordable supply of energy through interconnected systems represent a critical infrastructure challenge. Seasonal and interannual variability in climate variables—primarily precipitation and temperature—can increase the vulnerability of such systems during climate extremes. The objective of this study is to understand and quantify the role of temperature variability on electricity consumption over representative areas of the Southern United States. We consider two states, Tennessee and Texas, which represent different climate regimes and have limited electricity trade with adjacent regions. Results from regression tests indicate that regional population growth explains most of the variability in electricity demand at decadal time scales, whereas temperature explains 44–67% of the electricity demand variability at seasonal time scales. Seasonal temperature forecasts from general circulation models are also used to develop season-ahead power demand forecasts. Results suggest that the use of climate forecasts can potentially help to project future residential electricity demand at the monthly time scale.Capsule Summary: Seasonal temperature forecasts from GCMs can potentially help in predicting season-ahead residential power demand forecasts for states in the Southern US.

Embedding trend into seasonal temperature forecasts through statistical calibration of GCM outputs

AbstractAccurate and reliable seasonal climate forecasts are frequently sought by climate‐sensitive sectors to support decision‐making under climate variability and change. Temperature trend is discernible globally over the past decades, but seasonal forecasts produced by a global climate model (GCM) generally underestimate such trend. Current statistical methods used for calibrating seasonal climate forecasts mostly do not explicitly account for climate trends. Consequently, the calibrated forecasts also fail to capture the observed trend. Solving this problem can enhance user confidence in seasonal climate forecasts. In this study, we extend the capability of the Bayesian joint probability (BJP) modelling approach for statistical calibration of seasonal climate forecasts. A trend component is introduced into the BJP algorithm for embedding the observed trend into calibrated ensemble forecasts. We apply the new model (named BJP‐t) to three test stations in Australia. Seasonal forecasts of daily maximum temperatures from the SEAS5 model, operated by the European Centre for Medium‐Range Weather Forecasts (ECMWF), are calibrated and evaluated. The BJP‐t calibrated ensemble forecasts can reproduce the observed trend, when the raw ensemble forecasts and the BJP calibrated ensemble forecasts both fail to do so. The BJP‐t calibration leads to more skilful, more reliable and sharper forecasts than the BJP calibration.

Statistical Learning Methods as a Basis for Skillful Seasonal Temperature Forecasts in Europe

AbstractA statistical learning approach to produce seasonal temperature forecasts in western Europe and Scandinavia was implemented and tested. The leading principal components (PCs) of sea surface temperature (SST) and the geopotential at the 150-hPa level (GPT) were derived from reanalysis datasets and used at different lags (from one to five seasons) as predictors. Random sampling of both the fitting years and the potential predictors together with the Least Absolute Shrinkage and Selection Operator regression (LASSO) was used to create a large ensemble of statistical models. Applying the models to independent test years shows that the ensemble performs well over the target areas and that the ensemble mean is more accurate than the best individual ensemble member on average. Skillful results were especially found for summer and fall, with the anomaly correlation coefficient values ranging between 0.41 and 0.68 for these seasons. The correct simulation of decadal trends, using sufficiently long time series for fitting (70 years), and the use of lagged predictors increased the prediction skill. The decadal-scale variability of SST, most importantly the Atlantic multidecadal oscillation (AMO), and different PCs of GPT are the most important individual predictors among all predictors. Both SST and GPT bring equally much predictive power, although their importance is different in different seasons.

OBSERVATIONS-BASED COMPUTATIONAL ANALYTICS ON LOCAL CLIMATE DYNAMICS. PART 3: FORECASTING

Computational decision making is discussed in application to seasonal temperature forecasts taking into account inevitable nonlinear nature of local climate systems and deficiency of data on reliable observations. We focus on temperature extremes in terms of daily means and first involve the alternative conceptual model of local climate dynamics (the model of hysteresis regulation with double synchronization, so-called HDS-model) into such analytics. Recent years the HDS-model is describing successfully abnormal interannual temperature variability, on the basis of which it becomes potentially possible to extend forecasts of local daily means up to more than 1 year in future. In this connection the novel method of bifurcation traps is proposed, realized and tested. Results of processing the time series of temperature observations on daily mean surface air temperature illustrate peculiarities of this method in comparison with the traditional viewpoint on the forecasts. We believe that the discussion could be interesting in science and practice in order to increase the confidence of estimations on coming climate changes.

Mitigating the Impacts of Climate Nonstationarity on Seasonal Streamflow Predictability in the U.S. Southwest

AbstractSeasonal streamflow predictions provide a critical management tool for water managers in the American Southwest. In recent decades, persistent prediction errors for spring and summer runoff volumes have been observed in a number of watersheds in the American Southwest. While mostly driven by decadal precipitation trends, these errors also relate to the influence of increasing temperature on streamflow in these basins. Here we show that incorporating seasonal temperature forecasts from operational global climate prediction models into streamflow forecasting models adds prediction skill for watersheds in the headwaters of the Colorado and Rio Grande River basins. Current dynamical seasonal temperature forecasts now show sufficient skill to reduce streamflow forecast errors in snowmelt‐driven regions. Such predictions can increase the resilience of streamflow forecasting and water management systems in the face of continuing warming as well as decadal‐scale temperature variability and thus help to mitigate the impacts of climate nonstationarity on streamflow predictability.

Dynamical and statistical downscaling of seasonal temperature forecasts in Europe: Added value for user applications

This work describes the results of a comprehensive intercomparison experiment of dynamical and statistical downscaling methods performed in the framework of the SPECS (http://www.specs-fp7.eu) and EUPORIAS (http://www.euporias.eu) projects for seasonal forecasting over Europe, a region which exhibits low-to-moderate seasonal forecast skill. We considered a 15-member hindcast provided by the EC-EARTH global model (similar to ECMWF System 4, but using bias corrected SST) for the period 1991–2012. In particular, we focus on summer mean temperature and evaluate the added value of downscaling for representation of the local climatology (mean values and extremes), improvement of model skill and performance in particular heatwave episodes. Whereas the suitability of dynamical downscaling for reducing the orographic biases of the global model depends on the region and model considered, statistical downscaling can systematically reduce errors in different order moments, from the mean to the extremes (as represented by the 95th percentile here). However, both dynamical and statistical methods lead to similar skill patterns with about the same overall performance as the global model, which shows higher values in south-eastern Europe. Therefore, no relevant added value is found in terms of model skill improvement. Finally, when focusing on the heatwaves of 2003, 2006, 2010 and 2012, the limitations of the global model to detect these hot episodes are inherited by all dynamical and statistical downscaling methods so no added value is neither found in this aspect. This work provides, to our knowledge, the largest and most comprehensive intercomparison of statistical and dynamical downscaling for seasonal forecasting over Europe.

Detecting Improvements in Forecast Correlation Skill: Statistical Testing and Power Analysis

AbstractThe skill of weather and climate forecast systems is often assessed by calculating the correlation coefficient between past forecasts and their verifying observations. Improvements in forecast skill can thus be quantified by correlation differences. The uncertainty in the correlation difference needs to be assessed to judge whether the observed difference constitutes a genuine improvement, or is compatible with random sampling variations. A widely used statistical test for correlation difference is known to be unsuitable, because it assumes that the competing forecasting systems are independent. In this paper, appropriate statistical methods are reviewed to assess correlation differences when the competing forecasting systems are strongly correlated with one another. The methods are used to compare correlation skill between seasonal temperature forecasts that differ in initialization scheme and model resolution. A simple power analysis framework is proposed to estimate the probability of correctly detecting skill improvements, and to determine the minimum number of samples required to reliably detect improvements. The proposed statistical test has a higher power of detecting improvements than the traditional test. The main examples suggest that sample sizes of climate hindcasts should be increased to about 40 years to ensure sufficiently high power. It is found that seasonal temperature forecasts are significantly improved by using realistic land surface initial conditions.

Calibration, Bridging, and Merging to Improve GCM Seasonal Temperature Forecasts in Australia

AbstractThere are a number of challenges that must be overcome if GCM forecasts are to be widely adopted in climate-sensitive industries such as agriculture and water management. GCM outputs are frequently biased relative to observations and their ensembles are unreliable in conveying uncertainty through appropriate spread. The calibration, bridging, and merging (CBaM) method has been shown to be an effective tool for postprocessing GCM rainfall forecasts to improve ensemble forecast attributes. In this study, CBaM is modified and extended to postprocess seasonal minimum and maximum temperature forecasts from the POAMA GCM in Australia. Calibration is postprocessing GCM forecasts using a statistical model. Bridging is producing additional forecasts using statistical models that have other GCM output variables (e.g., SST) as predictors. It is demonstrated that merging calibration and bridging forecasts through CBaM effectively improves the skill of POAMA seasonal minimum and maximum temperature forecasts for Australia. It is demonstrated that CBaM produces bias-corrected forecasts that are reliable in ensemble spread and reduces forecasts to climatology when there is no evidence of forecasting skill. This work will help enable the adoption of GCM forecasts by climate-sensitive industries for quantitative modeling and decision-making.

Cointegration modelling for empirical South American seasonal temperature forecasts

ABSTRACTThis study investigates an alternative modelling approach for empirical seasonal temperature forecasts over South America. Seasonal average temperatures are found to be non‐stationary at most parts of South America over the 1949–2012 period. Simple persistence and lagged regression methods have considerable correlation skill in forecasting next season temperature using previous season temperature as predictor. However, the presence of trends in both predictor and predictand temperature variables can affect correlation skill. Models that can account for non‐stationarity in these variables may do better in modelling and forecasting seasonal temperatures known to have trends. A novel method (cointegration), introduced here for empirical seasonal climate forecasting, is found to perform better than the traditional persistence and regression forecasts for places where the predictor and predictand temperatures have stochastic trends. Potential skill pairwise comparisons between temperature forecasts produced with cointegration and those produced using persistence and lagged regression have shown that the alternative cointegration method performs significantly better than the other two. One of the main reasons for the better performance of cointegration method is that the modelling procedure accounts for the existing non‐stationarity in the process, and thus enables the estimated model to predict out of the range as efficiently as possible. Overall, this method appears to be ideal for modelling and predicting climate under the current global warming scenario. This is because most of the climatic variables including temperature in particular cannot be assumed to be stationary through time under such warming scenario.

On the Weighting of Multimodel Ensembles in Seasonal and Short-Range Weather Forecasting

Abstract The performance of multimodel ensemble forecasting depends on the weights given to the different models of the ensemble in the postprocessing of the direct model forecasts. This paper compares the following different weighting methods with or without taking into account the single-model performance: equal weighting of models (EW), simple skill-based weighting (SW), using a simple model performance indicator, and weighting by Bayesian model averaging (BMA). These methods are tested for both short-range weather and seasonal temperature forecasts. The prototype seasonal multimodel ensemble is the Development of a European Multimodel Ensemble System for Seasonal-to-Interannual Prediction (DEMETER) system, with four different models and nine forecasts per model. The short-range multimodel prototype system is the European Meteorological Services (EUMETNET) Poor-Man’s Ensemble Prediction System (PEPS), with 14 models and one forecast per model. It is shown that despite the different forecast ranges and spatial scales, the impact of weighting is comparable for both forecast systems and is related to the same ensemble characteristics. In both cases the added value of ensemble forecasting over single-model forecasting increases considerably with the decreasing correlation of the models’ forecast errors, with a relation depending only on the number of models. Also, in both cases a larger spread in model performance increases the added value of combining model forecasts using the performance-based SW or BMA weighting instead of EW. Finally, the more complex BMA weighting adds value over SW only if the best model performs better than the ensemble with EW weighting.

Relations between Temperature and Residential Natural Gas Consumption in the Central and Eastern United States

Abstract The increased U.S. natural gas price volatility since the mid-to-late-1980s deregulation generally is attributed to the deregulated market being more sensitive to temperature-related residential demand. This study therefore quantifies relations between winter (November–February; December–February) temperature and residential gas consumption for the United States east of the Rocky Mountains for 1989–2000, by region and on monthly and seasonal time scales. State-level monthly gas consumption data are aggregated for nine multistate subregions of three Petroleum Administration for Defense Districts of the U.S. Department of Energy. Two temperature indices [days below percentile (DBP) and heating degree-days (HDD)] are developed using the Richman–Lamb fine-resolution (∼1° latitude–longitude) set of daily maximum and minimum temperatures for 1949–2000. Temperature parameters/values that maximize DBP/HDD correlations with gas consumption are identified. Maximum DBP and HDD correlations with gas consumption consistently are largest in the Great Lakes–Ohio Valley region on both monthly (from +0.89 to +0.91) and seasonal (from +0.93 to +0.97) time scales, for which they are based on daily maximum temperature. Such correlations are markedly lower on both time scales (from +0.62 to +0.80) in New England, where gas is less important than heating oil, and on the monthly scale (from +0.55 to +0.75) across the South because of low January correlations. For the South, maximum correlations are for daily DBP and HDD indices based on mean or minimum temperature. The percentiles having the highest DBP index correlations with gas consumption are slightly higher for northern regions than across the South. This is because lower (higher) relative (absolute) temperature thresholds are reached in warmer regions before home heating occurs. However, these optimum percentiles for all regions are bordered broadly by surrounding percentiles for which the correlations are almost as high as the maximum. This consistency establishes the robustness of the temperature–gas consumption relations obtained. The reference temperatures giving the highest HDD correlations with gas consumption are lower for the colder northern regions than farther south where the temperature range is truncated. However, all HDD reference temperatures greater than +10°C (+15°C) yield similar such correlations for northern (southern) regions, further confirming the robustness of the findings. This robustness, coupled with the very high correlation magnitudes obtained, suggests that potentially strong gas consumption predictability would follow from accurate seasonal temperature forecasts.

Analogue forecasting of New Zealand climate anomalies

AbstractAn analogue forecast scheme is described for multifield prediction of monthly and seasonal New Zealand climate anomalies on the basis of the methodology of Livezey and Barnston (1988) for US seasonal temperatures. The method is applied to predicting terciles of temperature and precipitation for six regions of New Zealand. Empirical orthogonal function analysis is used to reduce sea surface temperature and sea‐level pressure predictors down to a set of five independent indices, which incorporate variations due to El Niño‐Southern Oscillation, Indian Ocean sea temperatures and a wave 3 pattern in the Southern Hemisphere westerlies. A full bootstrap cross‐validation procedure is carried out, along with Monte Carlo tests, to assess the skill of the method on independent data and to determine the significance of the results. Significant skill is found for seasonal temperature forecasts for the summer and winter seasons; there is less success in predicting monthly temperatures or rainfall at either timescale. Considerable care is required to constrain the climate state vector, from which analogues are defined, and to constrain the search procedure itself, in order to produce results that are stable with respect to small parameter changes in the model. For the New Zealand region, 5 to 7 is found to be the optimum number of ‘closest analogues’, and the inclusion of anti‐analogues improves the predictions, at least in the seasonal case. Skill in predicting regional temperature and rainfall is shown to be related to a combination of skill in predicting sea‐level pressure patterns and to how strongly these patterns project onto temperature and rainfall anomalies. Copyright © 2005 Royal Meteorological Society.

Long-Lead Seasonal Temperature Prediction Using Optimal Climate Normals

This study is intended to determine the spatially varying optimal time periods for calculating seasonal climate normals over the entire United States based on temperature data at 344 United States climate divisions during the period of 1931–1993. This is done by verifying the seasonal climate normals as a forecast for the same season next year, The forecast skill is measured by the correlation between the predicted and observed anomalies relative to the 30-yr normal. The optimal time periods are chosen to produce the highest correlation between the forecasts and the observation. The results indicate that generally (all seasons and all locations) annually updated climate normals averaged over shorter than 30-yr periods are better than the WMO specified 30-yr normal (updated only every 10 years), in terms of the skill in predicting the upcoming year. The spatial pattern of the optimal averaging time periods changes with season. The skill of optimal normals comes from both the annual updating and the shorter averaging time periods of these normals. Using optimal climate normals turns out to be a reasonably successful forecast method. Utility is further enhanced by realizing that the lead time of this forecast is almost one year. Forecasts at leads beyond one year (skipping a year) are also reasonably skillful. The skill obtained from the dependent verification is lowered to take account of the degradation expected on independent data. In practice the optimal climate normals with a variable averaging period were found to be somewhat problematic. The problems had to do primarily with the temporal continuity and spatial consistency of the forecasts. For the time being, a constant time period of 10 years is used in the operational seasonal temperature forecasts for all seasons and locations.

Seasonal Temperature Forecasts as Products of Antecedent Linear and Spatial Temperature Arrays

Abstract Our objective is to evaluate the potential for extracting the maximum information contained in antecedent temperature patterns that operationally could be used in formulating winter seasonal forecasts in the United States. In particular, examination of the predictability of winter temperatures given autumn temperatures is made using derived contingency tables, discriminant equations of antecedent principal components, and canonical correlation analysis. Contingency tables were constructed based on tercile classifications of a seventy-five year dependent record (1895–1969). Testing of an independent data period (1970–78) using these tables produced winter forecasts with no appreciable skill in the aggregate (−0.04). Discriminant analysis deprived linear combinations of the five principal components of the antecedent seasonal (autumn) temperatures to distinguish between specific terciles of the predictand season (winter). Despite encouraging results for the dependent period, forecast skill for the ...