Skilful seasonal prediction of winter gas demand

A dataset of the daily total gas demand of Great Britain (GB) covering the period April 1996–March 2018, in giga (10⁹) Watt hours (GWh), was provided by National Grid. The gas demand value represents the total demand from residential and large industrial premises (non daily-metered and daily-metered demand respectively) and includes shrinkage (gas leaks and theft). It does not include gas consumers directly connected to the national transmission network, such as gas-fired power stations and large industrial units [19]. The variation in daily demand over the 22 year period is shown in black in the upper panel of figure 1, where a clear annual cycle is evident, with higher demand during the colder winter months and lower demand during the warmer summer months.

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The variation in winter mean demand is shown in figure 2 (dotted black line) and highlights a general reduction over the 22 year period. The demand variability is only weakly anti-correlated with winter mean temperature variability (r = −0.39), much lower than might be anticipated given the known drivers of gas demand. Thornton et al [2] demonstrated that low-frequency variability in both electricity and gas demand over a similar period was not driven by temperature, but was rather thought to relate to socio-economic changes over the period. Possible reasons for the reduction in gas demand over the period include more efficient gas boilers, better home insulation with more double glazing, increasing gas prices and a continued shift away from heavy industry [20].

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To accurately assess the weather-driven component of gas demand and its predictability, much of the demand variability that is not driven by the weather needs firstly to be removed. Thornton et al [2] developed a methodology to remove demand variability on timescales greater than 5 years (referred to as low-frequency variability), whilst retaining demand variability on a daily, seasonal and inter-annual timescale. This approach is used here and the first step involves identifying the slowly evolving background demand. This is achieved by fitting a smoothly evolving second order Fourier expansion to the daily demand data and is shown in red in figure 1. A gradual reduction in both the annual mean gas demand and magnitude of the annual gas demand cycle is seen over the data period. This background demand is then removed from the daily demand timeseries and replaced with a climatological-mean annual demand cycle. The resultant demand timeseries, where low-frequency variability has been removed, is used in the subsequent analysis and is shown in black in the lower panel of figure 1. The highest daily demand over the data period can be seen to shift from the winter of 2003–2018 (compare upper and lower panels). Full details of the methodology to remove low-frequency demand variability are given in Thornton et al [2].

Following the removal of low-frequency demand variability, the strength of the correlation between winter mean temperature and demand increases from −0.39 to −0.87, better reflecting the known relationship [2] (see figure 2). The low-frequency variability in observed winter temperature over the 22 year period is small. Consequently, when the 5 year running mean temperature trend is removed, its correlation with demand barely changes (r = −0.85).

The predictability of two characteristics of the winter gas demand are investigated, the winter mean gas demand and the number of high demand days per winter.

The Met Office's global environment model (HadGEM3-GC2 [21]) consists of global models of the atmosphere, the land surface [22], the ocean [23] and sea-ice [24]. Both the operational seasonal forecast system, GloSea5 [25], and the decadal prediction system, DePreSys3 [9], are built around this same model. The atmosphere component has a resolution of 0.83° longitude and 0.55° latitude (about 60 km at mid-latitudes), with 85 vertical levels and an upper boundary at 85 km. The ocean model's resolution is 0.25° in both latitude and longitude, with 75 vertical levels.

In GloSea5 a set of retrospective forecasts, called a 'hindcast' set, is available for winters 1993–2016. Ten ensemble hindcast members are available from each calendar week. The three nearest weeks of hindcasts centred around the desired start time are collected together. For example, for a winter forecast of Dec–Jan–Feb with a one month lead time, we use the hindcast start dates of 25 October, 1 November and 9 November, giving a total of 30 ensemble members per winter. The DePreSys3 hindcast set is available for winters 1981–2018 and includes 40 ensemble members initialised on the 1 November. In both systems, ensemble member differences are created using a stochastic physics scheme [25].

Although small differences in initialisation exist between the GloSea5 and DePreSys3 hindcast sets, the two ensembles are considered to be directly comparable [5, 9], giving a combined ensemble set of 70 members for winters 1997–2016. This large size is beneficial as the prediction skill of a system typically improves with ensemble size, because the noise between ensemble members is reduced, leaving a clearer ensemble mean forecast signal [5, 26–28].

Various climate indices are considered as possible predictors of winter gas demand based on atmospheric temperature or the large-scale pressure field. These climate indices are calculated for both observations and forecasts. As a proxy for observations, the gridded 6 hourly instantaneous data sets of the 'Interim' version of the ECMWF Reanalysis (ERAI [29]) are used. The data has a resolution of 0.75° longitude by 0.75° latitude and is available over the gas demand data period. Three variables are used, 2 m temperature, mean sea level pressure (MSLP) and the geopotential height of the 500 hPa pressure level (Z500). The 6 hourly data is firstly averaged to a daily mean value and then the following indices are calculated:

• Winter mean UK temperature: temperature is averaged over the region of 10°W–5°E and from 50°–60°N to give a UK mean temperature.
• Winter mean NAO: the MSLP is averaged over the regions of Iceland (63°–70°N, 25°–16°W) and the Azores (36°–40°N, 28°–20°W) [9]. For each region the winter pressure anomaly from the long term climatology is established and then the difference in these anomalies (Azores—Iceland) is determined. The same diagnostic of the geopotential height field on the 500 hPa pressure level is used to give a mid-troposphere NAO index (NAO_Z500).
• Winter mean UK North–South pressure difference (ΔP): Thornton et al [3] found that the winter variation in GB daily electricity demand was strongly influenced by the regional pressure field to the north and south of the UK. An index was defined as the difference in pressure between a northern box (27°W–21°E, 57°–70°N) and a southern box (same longitudes, 38°–51°N), for regions see figure 4 in Thornton et al [3]. This is effectively a measure of the average westerly winds over the UK. This more UK centred pressure difference index is used here and a mid-tropospheric version is again calculated using the difference in the geopotential height field of the 500 hPa pressure level (ΔZ).
• Number of high demand weather type days per winter (N_WT): Thornton et al [3] found that four large-scale high pressure weather patterns drive low temperatures and high electricity demand in the UK (see their figure 5). The weather types were identified by applying K-means clustering to the daily MSLP fields of the wider region. Here we explore whether predictions of the number of such days per winter is a good predictor of winter gas demand. A day is defined as a high demand weather type day if it is sufficiently similar to one of the previously identified cluster centroids. Days are included if, the sum of the absolute pressure difference across the region is smaller, and the pattern correlation is higher, than the most dissimilar day within that cluster to the cluster centroid.

The same climate indices are also calculated using the forecast data. An index is calculated for each ensemble member individually and then these are averaged to give an ensemble mean index. Due to the significant signal to noise issue when predicting the climate in the mid-latitudes [5, 26, 28], the ensemble mean climate index is used as the climate predictor, rather than the individual ensemble member values. From here onwards, 'climate index' refers to the combined ensemble mean of the climate index.

For a climate index to be a skilful predictor of gas demand, it must have both a strong observed relationship with gas demand and be well predicted by the climate forecast system itself. Both are assessed using correlation coefficients: the Pearson correlation (r_P) when the variables are continuous (e.g. winter mean gas demand, temperature) and the Spearman rank correlation (r_S) if either of the variables is discrete (e.g. the number of high demand days per winter).

Skill in predicting gas demand is established by assessing the relationship strength between the forecast climate index and the observed gas demand variable, following the approach of Bett et al [16]. The ability of the climate index to predict above median, above upper tercile or the correct tercile of winter demand is assessed using the Heidke skill score (HSS).

To assess probabilistic forecast skill, a linear regression model is made between observed winter mean demand and the forecast climate index. The skill of probabilistic forecasts for the demand categories above can then be assessed, using the Brier and rank probability skill scores (BSS and RPSS respectively), employing leave-one-out cross validation. A preliminary assessment of the reliability of the probabilistic forecasts is also given. For a comprehensive description of the different statistical measures see Wilks [30].

Figure 3 summarises the prediction skill of winter mean gas demand using temperature as the predictor. As discussed previously, observed winter mean temperature is strongly anti-correlated with GB winter mean gas demand (r_P = −0.87, see figure 3(a), this is a repeat of figure 2, and is included to allow comparison with the predictions). The skill in forecasting winter mean temperature across North-western Europe and the Atlantic is shown in figure 4. Temperatures are skilfully forecast over many areas of the North Atlantic and over Scandinavia. In contrast there is little skill over continental Europe. Much of the skill over the ocean is however related to the low-frequency warming trend, such that when the 5 year running-mean winter-mean temperature trend is removed the prediction skill is negligible over most of the North Atlantic (not shown). There is significant skill in predicting the average temperature over the UK region, but the correlation magnitude is still relatively small (r_P = 0.38, see table 1 and figure 3(b)). A similar skill level is found when a 5 year running-mean temperature trend is removed.

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Table 1.  Column 1: Pearson correlation coefficient (r_P) between winter mean gas demand (D_obs) and observed winter mean climate index (C_obs). Column 2: the hindcast skill in predicting the climate index (correlation of observed and hindcast climate index). Column 3: the hindcast skill in predicting winter mean gas demand (magnitude of correlation between D_obs and C_hc). All data considers winters 1997–2016. Bold values indicate the correlation is significant at the 5% level using a 1-sided Fisher Z test.

Climate Index	Obs relationship	Climate index	Gas demand
(C)	rP (Dobs, Cobs)	skill, rP (Cobs, Chc)	skill, $| {r}_{P}|$ (Dobs, Chc)
Temperature	−0.87	0.38	0.24
NAO	−0.62	0.63	0.40
NAOZ500	−0.66	0.63	0.55
ΔP	0.70	0.60	0.49
ΔZ	0.71	0.58	0.57
NWT	0.66	0.56	0.57

A forecast of UK average winter mean temperature is not found to be a good predictor of winter mean gas demand. Although the Pearson correlation coefficient between the hindcast temperature and observed demand has the correct sign (negative), its low magnitude ($| {r}_{P}| =0.24$) means it is not statistically significant at the 5% level. A large spread in the relationship can be seen in figure 3(c), leading to little variation in the probabilistic prediction of winter mean demand from year to year (figure 3(d)). Although the deterministic HSSs are positive for above median and above upper tercile demand, the equivalent probabilistic skill scores are worse or similar to those of a climatological forecast (e.g. RPSS_ter = 0.03, see table 2). In summary, although temperature variability drives a significant proportion of demand variability, forecast temperature is not a good predictor of winter mean gas demand due to the limited skill in predicting UK temperatures.

All circulation-based indices (NAO, NAO_Z500, ΔP, ΔZ and N_WT) have a strong observed relationship with winter mean gas demand (r_P of ∼0.6–0.7, see table 1, column 1). However none of the circulation indices have as strong a relationship with demand as winter mean UK temperature.

The skill in predicting the winter MSLP across North-western Europe and the wider North Atlantic is shown in the left panel of figure 5. Skill is found at both high (60°–70°N) and low (30°–40°N) latitudes. In contrast, over the mid-latitudes (40°–60°N) including over the UK there is not significant prediction skill. A similar picture is seen for the Z500 field (figure 5, right). Nevertheless, skilful predictions of the winter mean circulation indices are possible (r_P ∼ 0.6, see table 1, column 2), as the indices measure the difference in pressure between the skilfully predicted low and high latitude regions. This skill is important because it is the gradient in pressure which drives surface weather conditions. The total number of high demand weather type days per winter is also skilfully predicted at the 5% level (r_P = 0.56). This weather type skill effectively demonstrates skill in predicting the frequency of days where high pressure influences the UK in winter and is consistent with previous studies [8].

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Winter mean gas demand is skilfully predicted when using any of the circulation indices as the predictor, with correlations between hindcast index and observed demand ranging from approximately 0.4–0.6 (see table 1, column 3). Predictions of winter mean demand greater than the median or upper tercile are skilful, showing improvements over using a random or climatological forecast (scores often exceeding 0.25, see table 2). For below lower tercile demand all predictors give positive HSSs (∼0.3–0.6), however only NAO_Z500, ΔP and ΔZ give skilful probabilistic forecasts (BSSs of 0.05–0.12). This suggests a possible asymmetry, with better forecast skill for higher demand winters than lower demand winters, which could be beneficial given their larger impact.

Figure 6 demonstrates the skill in predicting winter mean gas demand using ΔZ as the climate predictor. The strong observed relationship between ΔZ and demand is shown in figure 6(a), and the prediction skill of ΔZ is shown in figure 6(b). A significant linear relationship exists between observed demand and hindcast ΔZ (r = 0.57, see figure 6(c)), leading to a variation in the forecast of gas demand from year to year (figure 6(d)). The probability of above median demand, above upper tercile demand, and the correct tercile category is skilfully forecast and better than using a climatological forecast (BSS_med = 0.28, BSS_upper = 0.30, RPSS_ter = 0.32). Use of the linear regression model between hindcast climate index and observed demand, means forecasts are automatically bias adjusted and probabilities are reliable, for example see figure 7. Due to the small number of winters available, the reliability is only assessed across 4 probability bins. An operational forecast could therefore present the risk of an event using 4 categories, e.g. the probability (P) of above tercile demand is 'low' (P < 0.25), 'below median' (0.25 ≤ P < 0.5), 'above median' (0.50 ≤ P < 0.75) or 'high' (P ≥ 0.75), rather than giving actual probabilities.

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To explore how many ensemble members are needed to ensure a skilful forecast of gas demand, figure 8 shows how the prediction skill varies with ensemble size. Increasing the ensemble size from 1–30 leads to a rapid increase in prediction skill (the correlation increases from ∼0.1–0.5). Increasing the ensemble size even more leads to further improvements in the prediction skill, but at a much slower rate. Nevertheless, higher skill would likely be possible with more members.

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In summary, skilful prediction of winter mean gas demand is possible using a forecast of the winter mean atmospheric circulation. The improvement over using a temperature forecast occurs because of the better prediction skill of the circulation indices. The circulation indices are calculated over a much larger area compared to the temperature index, which may explain their better skill.

A day is classed as a high demand day if its demand is equal to or greater than the 95th percentile of daily winter demand calculated over all winters. Between 1997–2016 the observed number of high gas demand days per winter ('NG') varies between 0–15 (see black line, figure 9(a)). As these events stress the energy supply system an obvious question is whether their likelihood is predictable ahead of the winter. There is a strong correlation between winter mean gas demand and NG (r_S = 0.70). Consequently, if mean demand is skilfully predicted, NG may also be predictable to some extent.

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Although observed winter mean temperature has a reasonable relationship with NG (r_S = −0.55), temperature is not a useful predictor of NG (r_S = −0.11 between NG and hindcast winter mean temperature, see table 3, column 2). All circulation indices do however give skilful predictions of NG, with Spearman rank correlation magnitudes of approximately 0.4–0.6 (same table).

Table 3.  Column 1: Spearman rank correlation coefficient (r_S) between observed NG (NG_obs) and observed winter mean climate index (C_obs). Column 2: hindcast skill in predicting NG (correlation magnitude between NG_obs and C_hc). All data considers winters 1997–2016. Bold values indicate the correlation is significant at the 5% level using a 1-sided Fisher Z test.

Climate Index	Obs relationship	NG skill
(C)	rS (NGobs, Cobs)	$| {r}_{S}|$ (NGobs, Chc)
Temperature	−0.55	0.11
NAO	−0.49	0.42
NAOZ500	−0.47	0.63
ΔP	0.54	0.54
ΔZ	0.53	0.64
NWT	0.55	0.57

A demonstration of the prediction skill of NG, using winter mean ΔZ as the predictor, is shown in figure 9. Given NG is discrete and limited to positive numbers, linear regression is not suitable for modelling its relationship with ΔZ. Due to the small sample size there is also considerable uncertainty in the form of the relationship between observed ΔZ and the NG. Consequently we do not try to model the relationship, rather we assess the prediction skill using a deterministic approach. Figure 9(b) shows the relationship between hindcast ΔZ and observed NG. As the predicted atmospheric flow over the UK becomes less westerly (i.e. ΔZ becomes less negative), NG increases. The contingency table for above median counts show that the hit rate is far higher than the false alarm rate (see table 4), leading to a HSS of 0.6 (statistically significant at the 5% level using a 1000 member bootstrap as per table 2). For above upper tercile counts, the HSS is positive (HSS = 0.34) but it is not statistically significant at either the 5% or 10% levels. Very similar results are found for the other atmospheric circulation predictors, whilst a temperature based prediction is no better than when using a random forecast (HSS ≤ 0).

In summary, given a forecast of the atmospheric circulation, we can give a skilful forecast of above median counts of the number of high gas demand days per winter. A longer timeseries is needed to assess the predictability of winters with a higher number of high demand days.