Offshore wind power forecasting error and electricity market implications

Wind energy has been identified as key to the European Union’s 2050 low carbon economy. However, as wind is a variable resource and stochastic by nature, it is difficult to plan and schedule the power system under varying wind power generation. This paper investigates the impacts of offshore wind power forecast error on the operation and management of a pool-based electricity market in 2050. The impact of the magnitude and variance of the offshore wind power forecast error on system generation costs, emission costs, dispatch-down of wind, number of start-ups and system marginal price is analysed. The main findings of this research are that the magnitude of the offshore wind power forecast error has the largest impact on system generation costs and dispatch-down of wind, but the variance of the offshore wind power forecast error has the biggest impact on emissions costs and system marginal price. Overall offshore wind power forecast error variance results in a system marginal price increase of 9.6% in 2050.

Impact of offshore wind power forecast error in a carbon constraint electricity market

This paper investigates the impacts of offshore wind power forecast error on the operation and management of a pool-based electricity market in 2050. The impact from offshore wind power forecast errors of up to 2000 MW on system generation costs, emission costs, dispatch-down of wind, number of start-ups and system marginal price are analysed. The main findings of this research are an increase in system marginal prices of approximately 1% for every percentage point rise in the offshore wind power forecast error regardless of the average forecast error sign. If offshore wind power generates less than forecasted (−13%) generation costs and system marginal prices increases by 10%. However, if offshore wind power generates more than forecasted (4%) the generation costs decrease yet the system marginal prices increase by 3%. The dispatch down of large quantities of wind power highlights the need for flexible interconnector capacity. From a system operator's perspective it is more beneficial when scheduling wind ahead of the trading period to forecast less wind than will be generated.

Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

Systematic model forecast error in Rossby wave structure

Diabatic processes can alter Rossby wave structure; consequently errors arising from model processes propagate downstream. However, the chaotic spread of forecasts from initial condition uncertainty renders it difficult to trace back from root mean square forecast errors to model errors. Here diagnostics unaffected by phase errors are used, enabling investigation of systematic errors in Rossby waves in winter-season forecasts from three operational centers. Tropopause sharpness adjacent to ridges decreases with forecast lead time. It depends strongly on model resolution, even though models are examined on a common grid. Rossby wave amplitude reduces with lead time up to about five days, consistent with under-representation of diabatic modification and transport of air from the lower troposphere into upper-tropospheric ridges, and with too weak humidity gradients across the tropopause. However, amplitude also decreases when resolution is decreased. Further work is necessary to isolate the contribution from errors in the representation of diabatic processes.

Measuring public infrastructure construction impacts on economic growth

The results identify the long-run equilibrium relationships among economic variables in Australia. This study can provide policy makers with information on a one standard error shock to each variable and insights into what percentages of the forecast error variance of a variable are explained by the innovations of each variable.

The role of technology on the dynamics of coal consumption-economic growth: new evidence from China

Coal comprises 70% of primary energy sources and 80% of electricity generation in China. This paper investigates the coal consumption-economic growth nexus in an integrated demand-supply framework over the period from 1978 to 2010. We incorporate the role of coal technology to explain the growth process. Using the Autoregressive Distributed Lag bounds testing approach, we find improvement in the coal-to-electricity efficiency indicator, a proxy for coal technology, causing almost a 35% increase in real GDP in the long run. The Toda-Yamamoto causality test indicates unidirectional causality from coal consumption to economic growth, feedback effects both for coal-to-electricity efficiency indicator to economic growth and coal demand and openness to coal consumption. For a robustness check, we forecast the validity of the causal relationships beyond the sample horizon using the generalised forecast error variance decomposition method. Our analysis suggests that improving overall efficiency in coal sector will continue to play a significant role in maintaining sustainable growth in China in the long run.

An analysis of sectoral equity and CDS spreads

In this paper, we find that CDS return shocks are important in explaining the forecast error variance of sectoral equity returns for the USA. The CDS return shocks have different effects on equity returns and return volatility in the pre-crisis and crisis periods. It is the post-Lehman crisis period in which the effects of CDS return shocks are the most dominant. Finally, we construct a spillover index and find that it is time-varying and explains a larger share of total forecast error variance of sectoral equity and CDS returns for some sectors than for others.

Coal - the black gold of economic growth in China: empirical evidence and the role of cleaner coal technologies in recent time

Coal comprises 70 per cent of China’s primary energy source and 80 per cent of China's electricity generation. This study investigates the long-run relationship between coal consumption-economic growth nexus considering both supply and demand side models in a multivariate framework over the period of 1978 and 2010. Our innovation in this paper is to include a coal-to-electricity efficiency indicator into the economic growth model ; and trade exposure in coal demand. Using Autoregressive Distributed Lag bounds testing approach, we find improvement in coal-to-efficiency indicator causes almost 35 per cent increase in real GDP in the long-run. The Toda-Yamamoto approach of causality test indicates unidirectional causality from coal consumption to economic growth; feedback effect both for coal-to-electricity efficiency indicator to economic growth and openness to coal consumption. For robustness check, using the generalised forecast error variance decomposition method we forecast the validity of causal relationships beyond the sample horizon. The paper suggests the role of advanced coal technologies will play a significant role along with other environmental and energy policies in maintaining sustainable economic growth in China .

A note on the analysis error associated with 3D-FGAT

The analysis-error variance of a 3D-FGAT assimilation is examined analytically using a simple scalar equation. It is shown that the analysis-error variance may be greater than the error variances of the inputs. The results are illustrated numerically with a scalar example and a shallow-water model.

Analysing UK real estate market forecast disagreement

Given the significance of forecasting in real estate investment decisions, this paper investigates forecast uncertainty and disagreement in real estate market forecasts. Using the Investment Property Forum (IPF) quarterly survey amongst UK independent real estate forecasters, these real estate forecasts are compared with actual real estate performance to assess a number of real estate forecasting issues in the UK over 1999-2004, including real estate forecast error, bias and consensus. The results suggest that real estate forecasts are biased, less volatile compared to market returns and inefficient in that forecast errors tend to persist. The strongest finding is that real estate forecasters display the characteristics associated with a consensus indicating herding.

Conditioning and preconditioning of the variational data assimilation problem

Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors in the data are dependent on the condition number of the Hessian of the variational least-squares objective function. The traditional formulation of VAR is ill-conditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatially-distributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence demonstrate the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more ill-conditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.