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--> --> -->Recently, higher-lower latitude linkages have been investigated from a different perspective: by employing a relaxation method (Jung et al., 2014; Semmler et al., 2016). This approach was originally introduced to diagnose the origin of forecast errors (Jung et al., 2010a) and to investigate the causes of the anomalously cold European winters in 2005/06 and 2009/10 (Jung et al., 2010b, 2011). The idea is to run two experiments using a Numerical Weather Prediction (NWP) model: a control forecast experiment using a standard set-up for weather prediction, and another experiment in which the NWP model is relaxed towards reanalysis data in the Arctic. Thus, in the relaxation experiment, the observed state is prescribed in the relaxation area. Comparing the relaxation experiment to the standard simulation in which the atmosphere can freely develop everywhere, given a lower boundary forcing, one can diagnose the influence that the atmosphere in the relaxation area has on remote regions. To reduce sampling uncertainty, this must be done several times in an ensemble approach with different start dates taken from the reanalysis data as initial conditions.
Here, we use the relaxation approach of (Jung et al., 2010a) to identify the main atmospheric pathways along which the Arctic atmosphere influences midlatitude weather and climate. By employing an NWP approach this study will also provide some insight into the potential improvement of medium-range weather forecasting in the midlatitudes that could be obtained by enhancing prediction capabilities in the Arctic (e.g. through an enhanced Arctic observing system). This study is an extension of the work by (Jung et al., 2014), which focused on the winter season and used ERA-40 rather than ERA-Interim data (this study) for relaxation; the latter is much enhanced in terms of the data quality and covers more recent years. Compared to the previous relaxation experiments in which primarily the mid-troposphere large-scale circulation was investigated, in this study we also consider the impact of tropospheric relaxation on surface parameters, which are more socioeconomically relevant. Furthermore, we do not restrict our investigation to the winter season. Rather, we consider the seasonal cycle of Arctic-midlatitude linkages and explore the possible reasons. Another important difference is the use of a clearly smaller relaxation area, restricted to the central Arctic.
The outline of this paper is as follows: Details of the experimental setup are given in section 2, followed by a description of the results in section 3. Finally, the outcomes of the study are discussed and conclusions drawn in section 4.
2.1. Experimental set-up
Numerical experiments were carried out with model cycle 38r1 of the Integrated Forecast System, which has been run operationally at the European Centre for Medium-Range Weather Forecasting (ECMWF) from 19 June 2012 to 18 November 2013. A spatial resolution of T L255 was employed, which corresponds to about 0.7° in the horizontal direction. In the vertical direction, 60 levels were used. Two 14-day forecasts with a time step of 45 min were computed for each month between January 1979 and December 2012, the first (second) forecast being initialized on the 1st (15th) day of the month. SST and sea-ice fields from ERA-Interim were used as lower boundary conditions. ERA-Interim data were also used for initialization of the forecast and as a reference when computing forecast errors. Model results were archived every 6 h and remapped onto a 2.5° grid.2
2.2. Relaxation set-up
To investigate the remote impacts of the Arctic, the development of error during the forecast was artificially reduced by relaxing the model towards reanalysis data in the polar regions north of 75°N (also south of 75°S). This was realized by adding an extra term of the following form to the prognostic equations: \begin{equation} -\lambda(x-x_{\rm ref}), \ \ (1)\end{equation} where x is the prognostic variable, x ref is the reanalysis value towards which the model state is drawn, and Λ is the relaxation strength parameter. In our study, Λ assumes a maximum value of 0.1 per time step. This means that, every time step, the model's tendency is moved towards the reanalysis data by taking 10% of the difference between the model result and reanalysis data. To smooth the border of the relaxation area, a hyperbolic tangent over a 20°-wide zonal belt was applied. In this region, Λ increases smoothly from zero to its maximum value, with the nominal border of the relaxation area in the middle of the 20° belt [for more details see (Jung et al., 2010a)]. The relaxation was applied in the troposphere, up to 300 hPa, to the zonal and meridional wind components, temperature, and the logarithm of surface pressure.In this study, two sets of forecasts were produced: one control integration (CTL) without relaxation, and one in which the troposphere was relaxed towards ERA-Interim data north of 75°N and south of 75°S (R75). Note that the relaxation was only applied to the tropospheric prognostic variables described above and not to surface parameters such as sea ice and SST, which were prescribed in the same way in CTL and R75, or snow cover, which freely developed from the initialization state in both CTL and R75. The difference between CTL and R75 was evaluated in terms of forecast skill in the Arctic and in the northern midlatitudes; the influence of the relaxation over Antarctica is described in a companion paper (Semmler et al., 2016). For the time scales considered here, it can be assumed that the relaxation over the Southern Hemisphere has no influence on the Northern Hemisphere, and vice versa. This is a reasonable assumption given that a forecast length of 14 days is hardly long enough for possible signals to cross hemispheres.
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2.3. Data analysis
To study the seasonality of the Arctic influence on midlatitude weather, the year was divided into four seasons: winter (December, January, February); spring (March, April, May); summer (June, July, August); and autumn (September, October, November). In total, 204 forecast members were produced for each season. To reduce the noise level, the data were averaged over a time window of 24 h.To quantify the Arctic impact, several midlatitude (40°-60°N) regions have been defined: Europe (EURO; 20°W-40°E); northern Asia (NAS; 60°-120°E); and northern North America (NNAM; 130°-70°W). These regions were selected because they are highly populated areas that show relatively strong reductions in forecast error due to Arctic relaxation.
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2.4. Composite analysis
To understand whether the Arctic influence is linked to specific atmospheric situations (i.e. flow-dependence), we performed composite analyses for each region, in which we considered 500-hPa geopotential height (z500) and mean sea level pressure. For each pair of simulations, we considered the difference in the root-mean-square error (RMSE) between R75 and CTL. We calculated the RMSE using ERA-Interim data. We selected forecasts that were improved due to relaxation, considering each time window of 24 h separately. A forecast was considered to be improved for a particular time window if the error reduction was higher than the limit defined as the mean error reduction of the ensemble plus one standard deviation. For the composite of improved forecast members, we extracted corresponding reanalysis fields and averaged them. We did the same for the remaining forecast members to form a composite of neutral forecasts. To examine anomalous flow conditions for improved forecasts, we calculated differences between the two composites.3.1. Arctic influence on midlatitude prediction skill
The RMSE growth of daily averaged z500 with and without Arctic relaxation, averaged over the entire northern midlatitudes, is shown in Fig. 1a. For both integrations (CTL and R75), the error increases strongly during the first 10 days, after which error growth starts to saturate. The same holds for sub-regions of the northern midlatitudes (Figs. 1b-d), although there are differences in the magnitude of these values, with the largest values found for Europe (around 180 m in winter) and the smallest ones over northern Asia (around 120 m in winter). Over northern North America the values are similar to the average over the entire northern midlatitudes. A feature prevailing over the entire northern midlatitudes is that summer RMSE values are clearly smaller than winter RMSE values, reflecting the fact that day-to-day variability is much larger for the latter. Spring and autumn RMSE values are only slightly lower than those for winter. Over Europe (Asia) seasonal differences are largest (smallest).
Figure1. RMSE of z500 (units: m) as a function of forecast lead time (in days) for different seasons and forecast experiments (solid line: CTL; dashed line: R75): (a) averaged over the whole northern midlatitudes between 40°N and 60°N (MLAT); (b) averaged over Europe (40°-60°N, 20°W-40°E; EURO); (c) averaged over northern Asia (40°-60°N, 60°-120°E; NAS); (d) averaged over northern North America (40°-60°N, 130°-70°W; NNAM).Error reductions depicted in Fig. 2 are generally small and amount to around 5% when averaged over the entire northern midlatitudes. However, over northern Asia values are much higher, amounting to about 15% in autumn. In the other seasons, error reductions around 10% are found.
An important question, arising from these results, is why there are such pronounced seasonal and regional differences. To shed light on this issue, it is worth considering the climatological mean flow and its variability. Figures 3a, c, e and g show the z500 climatologies from the ERA-Interim data used for the relaxation experiments for different seasons. The meridional gradient of z500 is reduced by about a third in summer compared to winter, while spring and autumn take somewhat intermediate values. Furthermore, when taking the standard deviation over all six-hourly ERA-Interim output intervals per season for each gridpoint, it turns out that there is less variability in summer than in winter (not shown). In addition, the deviation from the zonal mean——that is, the strength of the climatological, stationary planetary waves——is weaker in summer than in winter, while spring and autumn are in between (Figs. 3b, d, f and h).
Figure2. RMSE reduction (units: %) of z500 forecasts due to Arctic relaxation as a function of forecast lead time (in days) for different seasons and regions: (a) averaged over the whole northern midlatitudes between 40°N and 60°N (MLAT); (b) averaged over Europe (40°-60°N, 20°W-40°E; EURO); (c) averaged over northern Asia (40°-60°N, 60°-120°E; NAS); (d) averaged over northern North America (40°-60°N, 130°-70°W; NNAM).Also, the regional differences in forecast error and its reduction in Figs. 1 and 2 can be explained by the atmospheric circulation (mean and variability). The large RMSE over Europe compared to the other regions can be explained by the large standard deviation of z500 over this region. When considering the deviation from the zonal mean of z500 (Figs. 3b, d, f and h), it becomes obvious that northern Asia and northern North America are the areas with northerly components in the mean westerly flow conducive for a large Arctic influence on the midlatitude weather and climate. For northern Asia, this materialises in the largest RMSE reduction from the relaxation. Interestingly, the same is not true for northern North America. One possible explanation would be the Pacific influence, given the prevailing westerly flow, strong upstream impact from a region known for the importance of midlatitude dynamics (North Pacific), and the southerly component over the Pacific Ocean (Figs. 3a, c, e and g). This may especially influence the western part of the northern North America region, reaching out to 130°W according to our definition.
Figures 4 and 5 provide a more comprehensive picture of the geographical distribution of the error reduction for the different seasons, both in the mid-troposphere (z500) and close to the surface (2-m temperature: t2m). We consider two forecast ranges: averaging over forecast lead times of 4-7 days, when there is still an influence from the initial conditions and error growth has not yet saturated; and averaging from 8-14 days, when the initial conditions play a smaller role and error saturation is much more pronounced.
Figures 4 and 5 confirm that the RMSE reduction due to Arctic relaxation shows some strong regional dependency. Perhaps the most striking feature is the relatively strong Arctic influence over the continents, especially over Asia, compared to the oceans. As mentioned above, this can be explained by the climatological troughs over the east coasts of northern Asia and northern North America, leading to transport of Arctic air into northern Asia and Canada (Fig. 3). As argued by (Jung et al., 2014), a possible explanation for a smaller impact over the oceans lies in the fact that the North Atlantic and North Pacific regions are primarily determined by midlatitude dynamics, due to the relatively low-latitude location of the main storm formation regions over the Gulf Stream and Kuroshio regions. Furthermore, from Figs. 3b, d, f and h, it becomes obvious that, over the oceans, there is a southerly component in the mean westerly flow, leading to a stronger influence from lower latitudes over the oceans.
Figure3. z500 (units: m) from the ERA-Interim data used for the relaxation: (a) winter mean; (b) mean stationary wave field (deviation from zonal averages) for winter; (c, d) as in (a, b) but for spring; (e, f) for summer; (g, h) for autumn.
Figure4. RMSE reduction (units: %) of the z500 forecasts for the Northern Hemisphere north of 20°N due to Arctic relaxation and for different seasons: (a) winter averages over forecast lead times of 4 to 7 days; (b) winter averages over forecast lead times of 8 to 14 days; (c, d) as in (a, b) but for spring; (e, f) for summer; (g, h) for autumn. The dashed lines indicate the northern midlatitude region from 40°N to 60°N.The Arctic signal propagates southwards relatively quickly over Asia. During the second week, for example, RMSE reduction is evident as far south as 20°-40°N, although the picture becomes somewhat noisy as we go towards longer forecast lead time due to increased sampling variability. Over Europe and North America, and only in winter and spring, consistent improvements of between 5% and 10% are evident for days 4 to 7 and days 8 to 14. During the other seasons, the Arctic impact appears to be smaller and the results are less conclusive in terms of error reduction. The west coasts of North America and Europe, which are marked by maritime climate, show a rather small influence from the Arctic, consistent with the lesser influence over the oceans.
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3.2. Flow-dependence
Having established the existence of preferred pathways along which the Arctic influences midlatitude weather, it is worth asking whether the strength of this linkage is flow-dependent. Figure 6 shows the z500 anomalies over the Northern Hemisphere that go along with anomalously large improvements in forecast skill over Asia with Arctic relaxation. It turns out that the link is strongest when anomalous northerly flow from the Kara Sea brings air of Arctic origin towards the midlatitudes, as can be deduced from the positive z500 anomalies over northeastern Europe and negative z500 anomalies over parts of Asia——a feature that is especially true during boreal winter. The link is clearly reflected by a substantial cold anomaly close to the surface in winter (Fig. 7). The cold surface anomaly amounts to about 3 K and extends into the areas of Eastern and Central Europe, because the z500 anomalies lead to an anomalous easterly flow to the south of the positive z500 anomalies over northeastern Europe, and is accompanied by warm anomalies over the Barents Sea, Greenland, and northeastern North America. The colder European temperatures are consistent with a weaker zonality of the flow, which weakens the upstream influence from the North Atlantic. The circulation anomalies are similar to the positive phase of the Eurasia-1 pattern (Barnston and Livezey, 1987). In winter, the northerly flow anomaly from the Kara Sea into West Asia is accompanied by a southerly flow anomaly over East Asia, as can be deduced from the z500 anomalies in Fig. 6, indicating a weakening of the East Asian winter monsoon.
Figure5. As in Fig. 4, but for 2-m temperature forecasts (units: %).
Figure6. z500 difference (units: m) between mean composites for improved and neutral forecasts with Arctic relaxation for northern Asia (green box) and considering forecast lead times of 1 to 7 days. Stippled areas indicate statistically significant areas according to the Wilcoxon test.The character of the flow-dependence for Europe and North America——that is, anomalous northerly flow associated with cold-air outbreaks into the considered region increases the linkage——is comparable to that over Asia, at least during winter and spring (not shown). In winter and to some extent in spring, unusually skilful forecasts for Europe seem to be produced, especially in situations involving the negative phase of the East Atlantic pattern, as defined by (Barnston and Livezey, 1987). Similarly, like for northern Asia, the anomaly pattern reduces the zonality of the flow and weakens the North Atlantic influence. For northern North America, the anomalous flow pattern does not resemble any well-established teleconnection pattern. However, like in the other regions, it is associated with a change in the meridionality of the flow.
Figure7. The 2m temperature difference (units: K) between mean composites for improved and neutral forecasts (with respect to z500) with Arctic relaxation for northern Asia (green box) in winter and considering forecast lead times of 1 to 7 days. Stippled areas indicate statistical significance according to the Wilcoxon test.Our Arctic relaxation experiments bring an improvement to forecasts in the northern midlatitudes, which is largest over continental areas——especially during winter and in Asia. It is reassuring that results are consistent with (Jung et al., 2014), despite the clearly smaller relaxation area (north of 75°N instead of north of 70°N). Compared to (Jung et al., 2014), it is a new and important result that the Arctic influence is strongest in winter and weakest in summer. Over Asia, reductions in forecast error of up to 15%, both in z500 and in t2m, could be achieved if one has perfect knowledge of the Arctic atmosphere. Thus, our results suggest that improved weather predictions in the Arctic (e.g. through an improved observing system) have the potential to improve prediction skill in the continental midlatitudes——especially during periods with anomalously northerly flow. In summer, the impact of the Arctic over continental areas is generally weaker due to reduced amplitudes of stationary planetary waves associated with more zonally oriented flow.
Even though our relaxation approach is different from the methods used in most previous studies on the influence of the Arctic on the midlatitudes, and even if we are investigating the influence of the Arctic troposphere as opposed to Arctic surface conditions such as sea ice or snow cover, it is noteworthy that the main pathways identified along which the Arctic can influence the midlatitudes are consistent. Previous studies suggest that Siberia tends to be most strongly influenced in winter by changes in Arctic surface conditions, such as the sea-ice concentration and snow——especially over the Barents Sea/Kara Sea area and Eurasia, but also over the entire Arctic in the preceding summer/autumn (e.g. Honda et al., 2009; Francis et al., 2009; Cohen et al., 2012). In turn, Siberia has been identified to be a key region that influences the weather of Northern Europe and to some extent the whole northern midlatitudes (Cohen et al., 2001, 2012). Indeed, in cases of a strong pathway from the Kara Sea to West Asia due to northerly flow anomalies from the Kara Sea to West Asia, cold anomalies over West Asia extending into Eastern and Central Europe, and southerly flow anomalies over East Asia occur. The latter indicates a weakening of the East Asian winter monsoon. This has been associated with sea-ice loss in the Barents Sea/Kara Sea in the preceding autumn (Wu et al., 2015). However, in the present study, it is not sea-ice loss driving the stronger pathway from the Kara Sea to West Asia, as the following consideration indicates.
Given the pronounced loss of Arctic sea ice during recent decades (e.g. Parkinson and Comiso, 2013), it is worth asking the question as to whether associated large-scale circulation changes might alter the teleconnectivity and hence the impact that Arctic prediction has on lower latitudes. In this context, a trend towards enhanced meridionality, especially over the continents, could lead to an intensification of the influence of the Arctic atmosphere on the northern midlatitudes. Therefore, it could be expected that most of the strongest improved forecasts over West and Central Asia would occur towards the end of the considered time period from 1979 to 2012. However, such trend could not be identified in any of the seasons over the past 30 years. Therefore, it can be argued that the recent Arctic sea-ice loss has not prompted any change in the strength of the influence of the Arctic atmosphere on northern midlatitude weather and climate. This also means that we cannot confirm previous findings, such as those of (Francis and Vavrus, 2012) and (Tang et al., 2013), linking stronger meridionality in the flow and more extreme cold and hot events with shrinking Arctic sea ice in winter and summer, respectively. It remains to be seen if possible future circulation changes will be large enough to change the strength of the influence that the Arctic atmosphere exerts on the northern midlatitudes.
Oceanic areas such as the North Atlantic and North Pacific, as well as the west of North America and Western Europe, are less affected by the Arctic, at least on the time scales considered here. It might be argued that this is a result of the relatively southerly location of the jet stream along with a predominantly southwesterly flow, suggesting that midlatitude (and probably also tropical and subtropical) dynamics play a more important role instead.
Our experiments show that there is scope for improved weather forecasts, especially in northern Asia, but to some extent in northeastern Europe and northern North America too, if forecasts can be improved in the Arctic off the Siberian coast, and to some extent off the Canadian Arctic coast. In contrast, an improvement in Arctic weather forecasting capabilities does not seem likely to help with improving weather forecasts for the western coasts of Europe and North America.
