Statistical Forecasting

Wilks, Daniel S.

doi:10.1016/b978-0-12-815823-4.00007-9

Cited by 230 publications

(314 citation statements)

References 120 publications

Supporting

Mentioning

295

Contrasting

Unclassified

Order By: Relevance

“…In the second part, we use simple statistical forecasts (described in more detail in section 3.3) to investigate the predictive skill arising from the relationship between

φ_{P C 150}^{'}

and month‐ahead wind electricity generation in different countries of Europe. The forecasts are evaluated with the Ranked Probability Score (RPS) and the Ranked Probability Skill Score (RPSS), as described by Wilks (2011). The RPS for three‐categorical forecasts is given by

R P S = true \sum_{m = 1}^{3} {([], ((), true \sum_{j = 1}^{m} y_{j}) - ((), true \sum_{j = 1}^{m} o_{j}))}^{2},

where y j is the three‐component vector of forecast cumulative probabilities for each tercile and o j is the three‐component vector of observations.…”

Section: Methodssupporting

confidence: 81%

“…The RPS for three‐categorical forecasts is given by

R P S = true \sum_{m = 1}^{3} {([], ((), true \sum_{j = 1}^{m} y_{j}) - ((), true \sum_{j = 1}^{m} o_{j}))}^{2},

where y j is the three‐component vector of forecast cumulative probabilities for each tercile and o j is the three‐component vector of observations. As noted by Wilks (2011), the RPS is computed with cumulative probabilities in order to penalize forecast probabilities for outcomes far away from the observation more strongly than probabilities close to the observation. Hence if the forecast probabilities for the three terciles are 20%, 50% and 30%, then y 1 =0.2, y 2 =0.7 and y 3 =1.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Does the lower stratosphere provide predictability for month‐ahead wind electricity generation in Europe?

Beerli

Wernli

Grams

2017

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

Wind power is playing an increasingly important role in Europe's electricity generation. Accurate forecasts of wind‐power output on various spatial and temporal scales are therefore of high interest for the energy industry. However, predictability of near‐surface wind on subseasonal time‐scales has received relatively little attention. The stratosphere is an important source of subseasonal predictability in winter. Here, we study the implications of the lower stratospheric circulation for month‐ahead wind electricity generation in Europe in winter. Using ERA‐Interim reanalysis and the novel wind‐power dataset Renewables.ninja, we demonstrate a strong relationship between the lower stratospheric circulation and month‐ahead wind electricity generation in different parts of Europe in the period 1985–2014. This relationship exists due to episodes of troposphere–stratosphere coupling, which lead to prolonged periods of either the positive or negative phase of the North Atlantic Oscillation (NAO). Since these persistent NAO periods are associated with strong surface wind anomalies, they have an important impact on wind electricity generation, in particular in Northern Europe. The state of the lower stratospheric circulation also determines the exact latitudinal position of these prolonged NAO patterns, with contrasting implications for wind electricity generation in specific countries. Using simple statistical forecasts, we show that the observed relationship between the lower stratosphere and wind electricity generation can be used for skilful forecasts of month‐ahead wind electricity generation. Particularly high forecast skill is found when the circulation in the lower stratosphere differs strongly from its climatological mean. Anomalous states of the lower stratospheric circulation therefore provide windows of subseasonal‐range predictability for wind‐power output in many European countries.

show abstract

“…In the second part, we use simple statistical forecasts (described in more detail in section 3.3) to investigate the predictive skill arising from the relationship between

φ_{P C 150}^{'}

R P S = true \sum_{m = 1}^{3} {([], ((), true \sum_{j = 1}^{m} y_{j}) - ((), true \sum_{j = 1}^{m} o_{j}))}^{2},

where y j is the three‐component vector of forecast cumulative probabilities for each tercile and o j is the three‐component vector of observations.…”

Section: Methodssupporting

confidence: 81%

“…The RPS for three‐categorical forecasts is given by

R P S = true \sum_{m = 1}^{3} {([], ((), true \sum_{j = 1}^{m} y_{j}) - ((), true \sum_{j = 1}^{m} o_{j}))}^{2},

Section: Methodsmentioning

confidence: 99%

Does the lower stratosphere provide predictability for month‐ahead wind electricity generation in Europe?

Beerli

Wernli

Grams

2017

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

show abstract

“…For each region the correlation between P lin i and the observed precipitation is shown in Figure (a). To evaluate the derived precipitation against observed precipitation, the Spearman's rank correlation is used in preference to the Pearson's correlation, as this avoids making assumptions about linearity, and deals better with outliers (Wilks, ). Using the Pearson's correlation gives generally similar results.…”

Section: Downscaling Atmospheric Drivers To Estimate Uk Regional Precmentioning

confidence: 99%

Improved seasonal prediction of UK regional precipitation using atmospheric circulation

Baker

Shaffrey

Scaife

2017

Intl Journal of Climatology

View full text Add to dashboard Cite

The aim of this study is to further our understanding of whether skilful seasonal forecasts of the large‐scale atmospheric circulation can be downscaled to provide skilful seasonal forecasts of regional precipitation. A simple multiple linear regression model is developed to describe winter precipitation variability in nine UK regions. The model for each region is a linear combination of two mean sea‐level pressure (MSLP)‐based indices which are derived from the MSLP correlation patterns for precipitation in northwest Scotland and southeast England. The first index is a pressure dipole, similar to the North Atlantic Oscillation but shifted to the east; the second index is the MSLP anomaly centred over the UK. The multiple linear regression model describes up to 76% of the observed precipitation variability in each region and gives higher correlations with precipitation than using either of the two indices alone. The Met Office's seasonal forecast system (GloSea5) is found to have significant skill in forecasting the two MSLP indices for the winter season, in forecasts initialized around the start of November. Applying the multiple linear regression model to the GloSea5 hindcasts is shown to give improved skill over the precipitation forecast by the GloSea5, with the largest improvement in Scotland.

show abstract

“…We determine the true observation‐ and background‐error covariance matrix elements using

R_{i, j} = σ_{r}^{2} e^{false(- normalΔ y_{i, j} false/ L_{r} false)},

where Δ y i , j is the distance between observations y i and y j , and

B_{i, j} = σ_{b}^{2} e^{((), - normalΔ x_{i, j} false/ L_{b})},

where Δ x i , j is the distance between states x i and x j , respectively. Both B and R are taken from Markov distributions (Wilks, 1995). For the assimilation experiments we have a single true solution; from this truth, pseudo‐observations are created by adding errors drawn from

scriptN false(0, boldR false)

and the background is determined by adding errors drawn from

scriptN false(0, boldB false)

.…”

Section: Illustration Of Theoretical Resultsmentioning

confidence: 99%

On diagnosing observation‐error statistics with local ensemble data assimilation

Waller

Dance

Nichols

2017

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

Recent research has shown that the use of correlated observation errors in data assimilation can lead to improvements in analysis accuracy and forecast skill. As a result, there is increased interest in characterizing, understanding and making better use of correlated observation errors. A simple diagnostic for estimating observation-error statistics makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. This diagnostic is derived assuming that the analysis is calculated using a best linear unbiased estimator. In this work, we consider whether the diagnostic is still applicable when the analysis is calculated using ensemble assimilation schemes with domain localization. We show that the diagnostic equations no longer hold: the statistical averages of observation-minus-background and observation-minus-analysis residuals no longer result in an estimate of the observation-error covariance matrix. Nevertheless, we are able to show that, under certain circumstances, some elements of the observation-error covariance matrix can be recovered. Furthermore, we provide a method to determine which elements of the observation-error covariance matrix can be estimated correctly. In particular, the correct estimation of correlations is dependent on both the localization radius and the observation operator. We provide numerical examples that illustrate these mathematical results.

show abstract

Statistical Forecasting

Cited by 230 publications

References 120 publications

Does the lower stratosphere provide predictability for month‐ahead wind electricity generation in Europe?

Does the lower stratosphere provide predictability for month‐ahead wind electricity generation in Europe?

Improved seasonal prediction of UK regional precipitation using atmospheric circulation

On diagnosing observation‐error statistics with local ensemble data assimilation

Contact Info

Product

Resources

About