1. Introduction
Despite substantial improvements in model formulation, data assimilation systems, and observing systems, forecasts are still prone to failures. This is particularly true for extended-range forecasts (beyond 10 days) of the extratropical flow, which have moderate skill at the best of times. Apart from being of scientific interest, understanding the origin of forecast error is a first step toward future forecasting system improvements. One important piece of information is the origin of forecast error. For example, if extended-range predictability in the extratropics is primarily limited by model error in the tropics then future model development should focus on exactly this region.
The aim of this study is to investigate how much of the extratropical forecast error in extended-range (11–30 days) integrations originates from parts of the climate system with (potentially) enhanced extended-range predictability (e.g., Baldwin et al. 2003; Shukla 1998): the lower boundary conditions, the tropical atmosphere, and the stratosphere. To this end a relaxation technique (also sometimes called nudging) is used in which prognostic fields are relaxed toward reanalysis data during the course of the integration. In this way it is possible to artificially suppress the development of forecast errors in certain regions of the globe (e.g., tropical atmosphere).
The relaxation technique is a well-established technique in the atmospheric sciences. It has been used, for example, in data assimilation (see Kalnay 2003, for an overview), for determining corrections to empirically reduce model deficiencies (Kaas et al. 1999), for dynamical downscaling (von Storch et al. 2000), for better understanding planetary wave–synoptic wave interactions in the atmosphere (Straus and Yi 1998), and for validation of a synoptic system in an atmospheric circulation model (Bauer et al. 2008). The approach employed in this study is very similar to the method used at the European Centre for Medium-Range Weather Forecasts (ECMWF) in the 1980s in order to understand the origin of medium-range forecast error in the Northern Hemisphere extratropics (Haseler 1982; Klinker 1990; Ferranti et al. 1990). It has been decided to revive the relaxation technique at ECMWF as a diagnostic tool for the following reasons:
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The relaxation technique could also be used to understand forecast error in the extended range, addressing the monthly and seasonal forecasting problem.
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The availability of larger computer resources allows significant increases in sample size and therefore robustness of the results compared to previous studies.
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The availability of more realistic analysis data, particularly in the tropics, makes the relaxation technique much more effective.
The paper is organized as follows: in the next section details about the monthly forecast experiments and about the model formulation will be given. Subsequently the results will be presented. The impact that relaxing various regions has on forecast skill will be described first for the tropics and then the extratropics. For the extratropics the focus is on the role of the tropics and stratosphere. For tropical relaxation experiments the role of the Madden–Julian oscillation will be considered separately. Finally, the results will be summarized and discussed.
2. Methodology
a. Monthly forecasts
To investigate the origin of extratropical forecast error during boreal winter a large set of 30-day control and relaxation experiments has been carried out using model cycle 32r1 (used operationally at ECMWF from 5 June–5 November 2007) at a resolution of TL159 (about 125 km) and with 60 vertical levels. For each of the experiments a total of eighty-eight 30-day forecasts were carried out. Forecasts were started on the 15th of the months November, December, January, and February, for each of the winters from 1980/81 to 2001/02. Initial conditions were taken from the 40-yr ECMWF Re-Analysis (ERA-40) data. If not stated otherwise, sea surface temperature (SST) and sea ice fields were persisted throughout the forecast (hereafter CNT-PER). An additional control integration with observed SST and sea ice fields from ERA-40 was also carried out (hereafter CNT-OBS) in order to quantify the influence that “knowledge” of the lower boundary conditions has on atmospheric forecast skill.
Forecast experiments with relaxation of the following regions have been carried out:
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whole tropical atmosphere (TROP),
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tropical stratosphere (TROP-S),
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tropical troposphere (TROP-T),
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whole Northern Hemisphere (NH),
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Northern Hemisphere stratosphere (NH-S), and
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Northern Hemisphere troposphere (NH-T).
b. Relaxation formulation
The model state vector is represented by x and the reference vector toward which the model should be drawn (here reanalysis data) by xref. The strength of the relaxation is determined by λ, which generally can be a function of the variable, region (both the horizontal and vertical) and spatial scale (e.g., planetary scales only) considered. The units of λ are in (time step)−1. For a time step of 1 h employed in this study a value of λ = 0.1, for example, indicates that at each time step the model is “corrected” using 10% of the departure of x from xref.
In this study the relaxation is carried out in gridpoint space in order to allow for localization. Parameters being relaxed include the zonal and meridional wind components, temperature, and the logarithm of surface pressure; the same λ is used for each of these parameters. The reference fields used in this study are from the ERA-40 reanalysis (Uppala et al. 2005) at 6-hourly intervals (0000, 0600, 1200, and 1800 UTC). For all model time steps for which no direct analysis is available, neighboring analysis fields are linearly interpolated in time. Specific humidity has not been relaxed. This is because specific humidity from ERA-40 is known to be too high in the tropics. Furthermore, any possible impact of specific humidity on the atmospheric thermal structure and circulation is accounted for by relaxing temperature and the horizontal wind components.
When applying masks to spatially localize the relaxation, care has to be taken in order to reduce adverse effects close to the relaxation boundaries. Here the transition from relaxed to nonrelaxed regions is smoothed using the hyperbolic tangent. The smoothing in the horizontal is carried out over 20° belts, both in longitude and latitude. Boundaries stated in the text refer to the center of the respective 20° belt. The latitudinal dependence of λ in TROP/0.1 is illustrated in Fig. 1. In the following there will be also a discussion of experiments in which the relaxation is either limited to the stratosphere or troposphere. The transition in the vertical is smoothed over about eight model levels. For the tropospheric (stratospheric) relaxation experiment this corresponds to a pressure interval of about 200 hPa (50 hPa) in the 60-level version of the model used in this study (Fig. 2). In the stratospheric relaxation experiment λ starts to reduce below 50 hPa and is effectively 0 at about 100 hPa. This design has been chosen to test the influence of large-scale stratospheric circulation anomalies, which have been observed to first appear in the upper stratosphere and subsequently “propagate” downward into the lower stratosphere, where they are believed to affect tropospheric weather regimes (Baldwin and Dunkerton 2001) and, therefore, medium-range and extended-range tropospheric forecast skill.
3. Results
a. Tropical forecast error
Figure 3 shows mean absolute forecast error of 5-day-averaged zonal wind at the 250-hPa (tropical troposphere) and 50-hPa level (tropical stratosphere). The control integration (CNT-PER) shows increasing forecast error in the tropical troposphere throughout the 30-day forecast period suggesting that current forecasting systems possess some useful monthly forecast skill (see also Vitart 2004). In the tropical stratosphere there is no evidence for saturation of forecast error throughout the first 30 days suggesting a relatively high level of extended-range predictive skill.
Prescribing rather than persisting SST fields throughout the integration (CNT-OBS) reduces forecast error of the tropical troposphere slightly in the extended range; in the medium range better knowledge of SST has no impact on forecast skill (Fig. 3a). Not too surprisingly, the influence of the lower boundary conditions has a rather small effect, if any, on the tropical stratosphere.
The experiment with relaxation of the whole tropical atmosphere (TROP/0.1) shows that the relaxation is efficient in reducing forecast error in both the troposphere and the stratosphere. Throughout the 30-day forecasts, forecast error of zonal wind at 250 and 50 hPa are kept significantly below the level seen in the short range and early medium range (5-day average from D+1 to D+5).
The influence of the Northern Hemisphere (NH-S/0.1) and especially the tropical stratosphere (TROP-S/0.1) on tropical zonal winds at 250 hPa is relatively small (Fig. 3a). The largest “nonlocal” influence comes from the Northern Hemisphere extratropics, whose impact is felt throughout the whole forecast. This finding is consistent with the notion that extratropical forcing can influence tropical convection and equatorial waves (Kiladis and Weickmann 1992; Hoskins and Yang 2000).
Tropical zonal winds at the 50-hPa level (Fig. 3b) are clearly influenced by a better representation of the tropical troposphere. This is expected given that gravity waves and equatorial planetary-scale (Kelvin and Rossby) waves tend to propagate from the troposphere into the stratosphere (e.g., Baldwin et al. 2001; Ern et al. 2007). The tropical stratosphere is not only influenced from below; both the extratropical troposphere and stratosphere have some impact on the tropical stratosphere.
b. Northern Hemisphere forecast error
Figure 4 shows mean absolute forecast error of 5-day-averaged extratropical Northern Hemisphere1 geopotential height fields at the 500-hPa level (hereafter Z500) for various experiments. The control integrations with persisted and observed SST–sea ice fields (CNT-PER and CNT-OBS) show that it takes about 30 days for forecast error to saturate and that knowledge of the lower boundary conditions increases the skill in the extended range slightly (Fig. 4a); in the short and medium ranges, on the other hand, using observed rather than persisted lower boundary conditions provides little, if any, benefit (see also Jung and Vitart 2006).
Relaxing the tropics (TROP/0.1) and the Northern Hemisphere stratosphere (NH-S/0.1) both lead to a noteworthy reduction in Z500 forecast error over the Northern Hemisphere (Fig. 4a). In relative terms the forecast error reduction is largest in the extended range (beyond D+10), where it amounts to about 10%–20% of the forecast error of the control integration for TROP/1.0 and NH-S/1.0. The “delayed” positive impact of the tropical and stratospheric relaxation can be explained by the fact that forecasts are still quite successful in the short and medium ranges (where the relaxation has little work to do). Furthermore, it can be expected to take a few days for the signal (i.e., forecast error reduction) to propagate from the tropics and the stratosphere, respectively, into the Northern Hemisphere troposphere (e.g., Hoskins and Ambrizzi 1993; Baldwin and Dunkerton 1999; Jung and Barkmeijer 2006).
The sensitivity of the results to the strength of the relaxation [i.e., the choice of λ in Eq. (1)] for TROP and NH-S can be inferred from Figs. 4b,c, respectively. For the relaxation time scales considered here (1, 10, and 50 h) tropical relaxation appears to be less sensitive to the choice of λ than stratospheric relaxation. One way to interpret this result is that the reduction of Northern Hemisphere Z500 error is due to relatively persistent and large-scale rather than fast and small-scale tropical features. For NH-S, the forecast error reduction for Z500 appears to be relatively more sensitive to λ. One possible way of explaining the fact that a relatively strong relaxation is required for the Northern Hemisphere stratosphere is that stratospheric motions are strongly governed by the underlying troposphere (see below for more details).
As shown above, relaxation of the tropical atmosphere leads to reduced forecast error over the Northern Hemisphere. How much of this improvement originates in the tropical troposphere and how much in the tropical stratosphere? To answer this question, additional relaxation experiments have been carried out with relaxation of the tropical troposphere (TROP-T/0.1) and tropical stratosphere (TROP-S/0.1) only. Results from these experiments clearly show that it is primarily the tropical troposphere that influences the tropospheric flow over the Northern Hemisphere (Fig. 4d).
How the relaxation toward ERA-40 in different regions influences the predictability of the stratospheric circulation (in terms of geopotential height at 50 hPa, hereafter Z50) over the Northern Hemisphere can be inferred from Fig. 5. The forecast error of the control integration saturates much later at 50 hPa than it does at 500 hPa. This highlights the relatively high level of extended-range predictability of the Northern Hemisphere stratosphere. The tropics have some influence on the stratospheric circulation, especially beyond D+15 or so. Not too surprisingly, relaxing the stratosphere toward ERA-40 reduces Z50 forecast error over the Northern Hemisphere substantially. Interestingly, however, relaxing the extratropical troposphere has a similar influence, at least for values of λ much smaller than 1.0. These results are a reminder of the strong tropospheric forcing of the Northern Hemisphere stratosphere during boreal winter.
1) Regional impacts of tropical and stratospheric relaxation
So far, the focus has been on Z500 forecast error for the extratropical Northern Hemisphere as a whole. It is likely, however, that the Z500 response over the Northern Hemisphere described above shows some interesting spatial structure. Regional influences of how prescribing rather than persisting the lower boundary conditions affects Northern Hemisphere Z500 forecast error can be inferred from Figs. 6d–f. “Perfect knowledge” of the observed SST–sea ice fields has a positive impact primarily in the extended range over the North Pacific and over North America. The impact over the North Atlantic and Europe, on the other hand, is rather small (and not significant) throughout the first 30 days of the forecast.
Not too surprisingly, the tropical relaxation experiment, TROP/0.1 (Figs. 6g–i), leads to substantial forecast error reduction in the Northern Hemisphere subtropics (i.e., close to the relaxation region). The fact that the forecast error reduction with tropical relaxation appears to be largely “confined” to the subtropics in certain regions such as Southeast Asia might be explained by the presence of strong subtropical waveguides (e.g., Branstator 2002), which convey the energy in a zonal rather than a meridional direction. There is also a clear positive impact of a correct representation of the tropics in certain regions of the Northern Hemisphere midlatitudes such as the eastern North Pacific, the North American continent and the eastern North Atlantic. This is true from the medium range well into the extended range. Notice, that the eastern North Atlantic is an area that is known for the frequent occurrence of persistent ridges (“blocking”) and troughs, which both tend to produce high-impact weather over western Europe (e.g., U.K. floods in autumn 2000). North America is the other populated area in the Northern Hemisphere midlatitudes that benefits from improved forecasts of the tropical atmosphere.
In the medium and extended ranges, the stratospheric relaxation experiment leads to the largest forecast error reduction in high latitudes (Figs. 6j–l). This is consistent with the tropospheric response found in the ECMWF model as a result of changes in the strength of the stratospheric polar vortex (Jung and Barkmeijer 2006). Interestingly, Europe and northern parts of North America are also key beneficiaries of a better representation of the stratospheric circulation, both in the medium and extended ranges.
It is worth mentioning that the spatial structure of the response is much less sensitive to the exact choice of λ than is the magnitude (not shown).
The same experiments described above were repeated for the independent period 1958–81 (not shown). In general the conclusions remain unchanged, except for a small reduction of the tropical and stratospheric impact on Z500 forecast error over North America. This may at least be partly explained by the slightly poorer quality of the ERA-40 reanalysis during the presatellite era (Uppala et al. 2005).
2) Further exploring the tropical influence
Having demonstrated the beneficial impact of reduced tropical forecast error for Z500 forecasts over western Europe and North America, it is interesting to understand from which part(s) of the tropics the forecast improvement originates. To this end, three additional relaxation experiments were carried out (see also Table 1). The three tropical regions considered are the following:
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0°–140°E: Africa, Indian Ocean, and Maritime Continent (MCIN);
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140°E–90°W: Tropical Pacific (TPAC); and
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90°W–0°: South America and Atlantic (SAAT).
An investigation of the forecast error for these experiments in the tropics suggests that the forecast “improvement” is largely confined to the relaxation regions (not shown). This suggests that it is possible to trace extratropical forecast error reduction back to different tropical regions.
Figure 7 shows the impact of the various tropical relaxation experiments (with λ = 0.1) on mean absolute Z500 forecast error over the Northern Hemisphere. Forecast improvement for MCIN is largely confined to the Asian subtropical jet stream and the North Pacific region throughout the 30-day forecast period (Fig. 7b). Although there appears to be some beneficial influence in the North Atlantic by D+26 to D+30, this influence is relatively small (and not statistically significant) compared to the experiment in which the whole tropical belt has been relaxed (Fig. 7c). Relaxing the tropical Pacific, TPAC, leads to forecast improvements over the eastern North Pacific and over North America; farther downstream over the eastern North Atlantic and over Europe some significant forecast error reduction is evident beyond D+20 or so. Not too surprisingly, SAAT leads to forecast error reduction primarily in the North Atlantic region; the reason for the forecast error reduction in the extended range over North America is less clear. One possibility explanation is that relaxation in the “SAAT region” reduces forecast error in the central and eastern tropical Pacific, which in turn leads to forecast error reduction over North America through well-known teleconnections.
3) The role of the Madden–Julian oscillation
Previous studies have highlighted the importance of the Madden–Julian oscillation (MJO; Madden and Julian 1972) in generating extratropical teleconnections, especially in the North Pacific region (Matthews et al. 2004). Given that the representation of the MJO in most atmospheric models is rather poor (e.g., Moncrieff et al. 2007) it seems plausible that improved prediction of the MJO will lead to improved extended-range forecasts of the extratropical circulation (Ferranti et al. 1990; Jones et al. 2004)—a notion that also features prominently in the The Observing System Research and Predictability Experiment (THORPEX) International Science Plan (Shapiro and Thorpe 2004). In the light of the earlier study by Ferranti et al. (1990), it is tempting to explain the beneficial impact of tropical relaxing on extended-range extratropical forecast skill, illustrated in previous sections, by more skilful treatments of the MJO.
To better understand the role of the MJO in the tropical relaxation experiments, diagnosis of the experiments was carried out separately for active and nonactive MJO episodes. Here, the classification into active and nonactive MJO episodes was carried out subjectively2 by inspecting individual Hovmöller diagrams of bandpass-filtered (30–60 days) tropical velocity potential anomalies at the 200-hPa level using ERA-40 reanalysis data. A summary of the forecast start dates for active and nonactive MJO periods is given in Table 2. Notice, for example, that the two strong MJO events during the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE) intensive observing period (Yanai et al. 2000) are captured by the active MJO subset.
If extratropical forecast error in the control integration is considered separately for periods with active and nonactive MJO then it turns out that Z500 forecast error over the Northern Hemisphere is smaller during active compared to nonactive MJO episodes (solid lines in Figs. 8a,b). These results, which are consistent with the study of Jones et al. (2004), suggest that extended-range forecasts of the Northern Hemisphere circulation with present-day versions of the ECMWF draw some of their skill from successful prediction of the MJO.
If improvements in the “prediction” of the MJO were the main contributor to the reduction of extratropical forecast errors in the tropical relaxation experiments, then we would expect the tropical relaxation to yield improvements primarily during active MJO periods. Comparing the differences in mean absolute errors between the tropical relaxation (TROP/0.1), control experiment for nonactive MJO (Fig. 8a), and active MJO (Fig. 8b) shows that this is not the case. In fact, if anything, then the reduction of Z500 forecast error over the Northern Hemisphere is larger during the nonactive compared to the active MJO episodes.
This conclusion is in stark contrast to the results by Ferranti et al. (1990). How can this discrepancy be explained? First, it should be mentioned that the analysis toward which the model is drawn in this study is of much higher quality compared to that used by Ferranti et al. (1990). This can be inferred from Fig. 9, which shows how the squared coherency spectrum3 between operational analyses and ERA-40 (re)analyses of equatorial velocity potential anomalies at the 200-hPa level depends on zonal wavenumber for two different periods. For the 1985–88 period, which represents approximately the period investigated by Ferranti et al. (1990), correspondence between the two analyses is confined to very low wavenumbers. This suggests that in the late 1980s only the largest spatial scales—including the MJO—were realistically represented by the then-operational analysis (i.e., constrained by the observations). For the 1998–2001 period, however, the agreement between the then-operational analysis and ERA-40 reanalysis is much better for all zonal wavenumbers. Second, differences in the predictive skill of the MJO in the 1980s compared to today may explain discrepancies regarding the role of the MJO in this study compared to that of Ferranti et al. (1990). Figure 10 shows that today’s forecasts of MJO-type atmospheric variability at D+10 show the same skill as D+3 forecasts used to show in the late 1980s. In fact, Boer (1995) finds “a comparatively rapid decrease of skill in the tropical region” for ECMWF forecasts during the period 1986–91. Vitart et al. (2007), on the other hand, point out that in a recent version of the ECMWF model there is useful skill in predicting the MJO up to D+15 to D+20 in advance.
To further elucidate the influence that changes in tropical forecast error have on extratropical predictive skill, a set of experiments has been carried out in which the model has been relaxed toward the initial conditions in the tropics only using λ = 0.1 h−1 (hereafter TROP-PER/0.1). In this way it is possible to artificially deteriorate forecasts of the tropical atmosphere (Ferranti et al. 1990). For nonactive MJO episodes it is found that increasing forecast error in the tropics leads to slightly larger extratropical forecast error in the medium range; in the extended range, however, deteriorating tropical forecasts has no impact compared to the control forecast (Fig. 8a). For nonactive MJO episodes this suggests that present-day extended-range forecasts of the extratropical atmosphere with the ECMWF model do not draw any predictive skill from the tropics. For active MJO episodes (Fig. 8b), on the other hand, the control forecast shows much lower forecast error compared to TROP-PER, suggesting that part of the present level of medium-range and extended-range extratropical forecast skill actually originates in the tropics and is associated with the MJO.
4. Discussion
The origin of extended-range forecast error has been studied with the ECMWF model by carrying out relaxation experiments. By spatially confining the relaxation it is possible to study the remote impact of forecast error reduction in certain regions. A schematic of the interactions considered along with estimates of their strength for extended-range forecasts is shown in Fig. 11.
The focus of this study has been on the influence that the tropics and the Northern Hemisphere stratosphere have on extended-range forecast skill of the Northern Hemisphere circulation. Emphasis has been put on the role of the tropics since it is widely believed that extended-range predictions of the extratopical atmosphere benefit from better forecasts of the MJO (e.g., Ferranti et al. 1990; Jones et al. 2004; Moncrieff et al. 2007); the influence of the Northern Hemisphere stratosphere has been studied in more detail in order to understand the role that anomalies in the strength of the stratospheric polar vortex and their “downward propagation” into the troposphere (Baldwin and Dunkerton 2001; Baldwin et al. 2003) have on extended-range forecast skill.
Our results show that a reduction of forecast error in the tropical troposphere has a beneficial impact on extended-range forecast skill over the Northern Hemisphere. In terms of populated areas this is especially true for North America and western Europe. Perhaps somewhat surprisingly, the results of this study suggest that the MJO plays a secondary role for explaining these results. Here, it is argued that this is due to a relatively high level of predictive skill in the current versions of the ECMWF forecasting system, both in the medium and extended range; leaving the relaxation relatively little work to do to suppress MJO-related forecast error. At the moment it is not clear which aspect(s) of the tropics we need to better simulate in order to realize the extratropical forecast error reduction implied by the tropical relaxation experiments. A more detailed analysis of this issue, including the role of systematic versus transient error in the tropics, will be part of a future study.
As mentioned in the introduction, the relaxation experiments were carried out in order to guide future forecasting system development. The tropical relaxation experiments, for example, provide some idea how much forecast skill, if any, could be gained by reducing forecast error in the tropics (e.g., by a better representation of physical processes). Our results suggest that reduced tropical forecast error is unlikely to increase extended-range skill in predicting the Northern Hemisphere tropospheric circulation beyond the current skill in the range from D+11 to D+15 (Fig. 4a). Notice, however, that there are large regional variations. These estimates have to be seen as rather optimistic given that in these experiments tropical forecast error is reduced to levels unlikely to be achieved in the future.
Stratospheric relaxation experiments show that reduced forecast error in the Northern Hemisphere stratosphere leads to reduced forecast error in the troposphere below. These results are consistent with previous modeling studies in which a relatively strong tropospheric response has been found to impose stratospheric perturbations (e.g., Boville 1984; Charlton et al. 2004; Jung and Barkmeijer 2006). However, here it is argued that the stratospheric relaxation experiments are very difficult to interpret in terms of the implied gain in tropospheric predictability. This is because tropospheric relaxation is as efficient in reducing stratospheric forecast error as is direct stratospheric relaxation, highlighting the strong influence of the troposphere on the Northern Hemisphere stratospheric during boreal winter (see also, e.g., Martius et al. 2009). A very illuminating discussion of difficulties in interpreting numerical experiments, in which a strongly forced component of the coupled system is artificially prescribed, is given by Bretherton and Battisti (2000) for the atmosphere–ocean system.4
Our conclusions are very similar to that from the study by Newman and Sardeshmukh (2008) in which a completely different approach is employed (diagnosis of linear inverse models fitted to observational data). They too find that tropical influences are generally larger than stratospheric influences in terms of the predictability of the extratropical troposphere during boreal winter.
One of the potential weaknesses of the tropical relaxation experiments is the presence of the transition zone around 20°N, where the relaxation coefficient changes in latitudinal direction (see Fig. 1). It could be argued, for example, that the presence of the transition zone leads to spurious reflection of extratropical Rossby waves. Furthermore, imbalances may occur within and close to the transition zones. While it cannot be excluded that spurious reflection and imbalances are detrimental, it is worth pointing out that the tropical relaxation is doing something realistic since, otherwise, extratropical forecast skill would not be reduced compared to the experiment without tropical relaxation. One way to reduce adverse effects is to relax divergence and vorticity rather than the horizontal wind components (Greatbatch et al. 2003). Another way would be to carry out experiments with the ECMWF four-dimensional variational data assimilation (4D-Var) data assimilation system in which all observations outside the tropics are blacklisted. Given the computational cost of 4D-Var data assimilation experiments it would only be possible to look at a limited number of cases. Preliminary results for a limited number of cases show that the two approaches yield very similar results thereby suggesting that the relaxation methods employed in this study is very effective (Jung and Rodwell 2010).
Summarizing, the relaxation technique appears to be a very powerful diagnostic technique in order to localize possible “remote” origins of forecast error. We applied the same technique (i) focusing more on medium-range rather than extended-range predictions, (ii) to study the origin of seasonal mean circulation anomalies such as the cold European winter of 2005/06 (Jung et al. 2010), and (iii) to understand to what degree extratropical systematic error has its origin in the tropics. Results of these studies will be reported in forthcoming papers.
Acknowledgments
The authors thank Soumia Serrar for useful discussions during the implementation of the relaxation code in the IFS. The authors further benefitted from discussions with Mark Rodwell and Anders Persson. Two anonymous reviewers provided useful suggestions that helped to improve the quality of the paper. Rob Hine improved the quality of the figures.
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Latitudinal dependence of λ in Eq. 1 (h−1) for the tropical relaxation experiment (TROP/0.1).
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Vertical dependence of λ in Eq. 1 (h−1) for tropospheric (solid) and stratospheric (dashed) relaxation experiments.
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Mean absolute error (m s−1) of 5-day-averaged forecasts of tropical zonal wind at (a) 250 and (b) 50 hPa. Results are shown for the control forecast with persisted (CNT-PER) and observed (CNT-OBS) SST/sea ice as well as for experiments with relaxation toward ERA-40 reanalysis data in the tropics (TROP/0.1), the tropical stratosphere (TROP-S/0.1), the Northern Hemisphere troposphere (NH-T/0.1), and the Northern Hemisphere stratosphere (NH-S/0.1).
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Mean absolute error (m) of 5-day-averaged forecasts of 500-hPa geopotential height fields over the Northern Hemisphere (north of 40°N): (a) control forecast with persisted and observed SST/sea ice as well as for experiments with relaxation of the tropics (TROP/0.1) and the Northern Hemisphere stratosphere (NH-S/0.1) toward ERA-40 reanalysis data. (b) As in (a), but for different tropical relaxation experiments (TROP/0.02, TROP/0.1, and TROP/1.0). (c) As in (a), but for different experiments with relaxation of the Northern Hemisphere stratosphere (NH-S/0.02, NH-S/0.1, and NH-S/1.0). (d) As in (a), but for relaxation of different parts of the tropical atmosphere (TROP/0.1, TROP-T/0.1, and TROP-S/0.1).
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Mean absolute error (m) of 5-day-averaged forecasts of 50-hPa geopotential height fields over the Northern Hemisphere (north of 30°N) for control forecast with persisted SST/sea ice (CNT-PER) and experiments with the tropics (TROP/0.1), the Northern Hemisphere stratosphere (NH-S/0.1 and NH-S/1.0), and the Northern Hemisphere troposphere (NH-T/0.1 and NH-T/1.0) relaxed toward ERA-40 reanalysis data.
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
(a)–(c) Mean absolute forecast error of 500-hPa geopotential height field (m) for the control integration with persisted SST/sea ice (CNT-PER). (d)–(f) Difference in mean absolute forecast error for Z500 between the control integration with observed (CNT-OBS) and persisted (CNT-PER) SST/sea ice. (g)–(i) As in (d)–(f), but for the difference between TROP/0.1 and CNT-PER. (j)–(l) As in (d)–(f), but for the difference between NH-S/0.1 and CNT-PER. Results are shown for 5-day-averaged data: (left) D+6 to D+10, (middle) D+16 to D+20, and (right) D+26 to D+30. Differences significant at the 95% confidence level (two-sided t test) are hatched.
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Difference in mean absolute forecast error (m) compared to the control integration (CNT-PER) for relaxation (a)–(c) of the tropics (TROP/0.1), (d)–(f) the Indian Ocean–Maritime Continent (MCIN), (g)–(i) the central tropical Pacific (TPAC), and (j)–(l) the tropical South America/tropical Atlantic (SAAT). All relaxation experiments are based on λ = 0.1. Results are shown for 5-day-averaged data: (left) D+6 to D+10, (middle) D+16 to D+20, and (right) D+26 to D+30. Differences significant at the 95% confidence level (two-sided t test) are hatched.
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Mean absolute error (m) of 5-day-averaged 500-hPa geopotential height forecast error over the Northern Hemisphere (north of 40°N) for (a) nonactive and (b) active MJO episodes. Results are shown for the control integration CNT-PER (solid), TROP/0.1 (dashed), and TROP-PER/0.1 (dotted).
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Mean squared coherency of equatorial velocity potential anomalies at the 200-hPa level as a function of zonal wavenumber between operational analysis and ERA-40 reanalysis data: 1985–88 (solid) and 1998–2001 (dashed). The “chunk method” (see von Storch and Zwiers 1999 for details) has been used for smoothing.
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Predicted variance fraction of operational ECMWF forecasts of equatorial, large-scale (only zonal wavenumbers one has been retained) velocity potential at 200-hPa level for the periods 1986–89 (dash–dotted), 1998–2001 (dashed), and 2005–08 (solid) (see text and Boer 1994 for further details).
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Schematic of the estimated strength of the interactions for extended-range forecasts during boreal winter.
Citation: Monthly Weather Review 138, 6; 10.1175/2010MWR3255.1
Summary of 30-day forecast experiments. All experiments are based on model cycle 32R1 using a resolution of TL159 with 60 levels in the vertical. Lower boundary conditions were persisted for all relaxation experiments.
Forecast start dates used to compute active and nonactive MJO composites. Notice that all forecasts were started on the 15th of the respective month.
Here the Northern Hemisphere encompasses only the region north of 40°N in order to stay well clear of the relaxation zone used in experiment TROP/0.1.
Using an objective technique with various threshold did not change the conclusions.
The (squared) coherency is formally similar to the (squared) correlation coefficient and, therefore, gives a measure for the similarity of two fields as a function of zonal wavenumber (e.g., von Storch and Zwiers 1999).
The atmosphere and ocean in their study correspond to the troposphere and stratosphere, respectively, discussed here.
