An artefactually introduced monthly cycle in the ensemble fields constrained by HadISST2

By Xiangbo Feng

ECMWF has recently developed two major ensemble products for 20th century climate, i.e. ERA-20CM and CERA-20C, within ERA-CLIM and ERA-CLIM2 projects. ERA-20CM is in ECMWF’s public datasets now, and CERA-20C has been scheduled to disseminate in the near future. There is no doubt that these two exciting climate datasets will become hugely popular in the research fields and also in other relevant communities. It is worth being aware of some uncertainty in their data before implementing them.

The former is a 10 member ensemble of atmosphere model integrations, using observationally based reanalysis HadISST2 to describe SST and sea ice and using CMIP5 radiative forcing to force model. There is no data assimilation applied. CERA-20C is a 10 member ensemble of coupled ocean-atmosphere reanalysis, also using HadISST2 to constrain SST of model via heat relaxation scheme, with data assimilation applied in ocean and atmosphere individually. They both provide daily atmospheric and SST fields (and ocean in CERA-20C) at 3 hours resolution. For more details on these two products, read Hersbach etal. (2015) and Laloyaux etal. (2016) respectively. One key point within these two products is that SST is strongly constrained by HadISST2, a 10 member ensemble of realizations produced by UK Met Office within ERA-CLIM project. Thanks to the involvement in ERA-CLIM2 project, I have limited internal access to CERA-20C data.

Interestingly, we recently found an unexpected monthly cycle in ensemble spread of daily SST field in both ERA-20CM and CERA-20C. The shape of the cycle is similar in both products, but phase is slightly lagged in CERA-20C (suspected to be due to the relaxation scheme applied in the data assimilation schemes). For demonstration, the monthly cycle in January (2005-2007) seen in CERA-20C is shown in Figure 1. It can be characterised by following features:

  • A month cycle consistently exists in SST ensemble spread at all latitudes and all months in all years from 1900 to 2010! In January 2005-2007, global average of the amplitude is 0.015 deg.C (Figure 1 top left), which is about 15% of spread mean.
  • The amplitude is larger in summer hemisphere and smaller winter hemisphere. This follows the pattern of SST spread mean (not shown).
  • In regions with strong western boundary currents, such as the Gulf Stream and Kuroshio, where SST uncertainty is usually the largest, the monthly cycle is not more significant than other regions. This indicates this signal is more likely produced at large scales.
  • This cycle generally has the lowest and highest values around 5th and 20th in each month, but with noticeable seasonal variations (5-10 days) at mid-high latitudes (Figure 1 top right).
  • This signal also exists in forecasting fields (Figure 1 bottom). The amplitude gradually becomes smaller when forecasting time steps are longer. This means that this signal is presumably propagating into atmosphere through ocean-atmosphere coupling.

2016 07 08 Xiangbo Feng - Picture1

Figure 1. Amplitude (top left) and phase lag (top right) of monthly cycle statistically fitted in time series of ensemble spread (standard deviation) of daily SST analysis, in January 2005-2007, and time series of global average (60°N-60°S) of ensemble spread of daily SST at different forecast leadtimes (0-24 h) on each day of January 2005-2007 (bottom). Note that the monthly cycle shown in maps is significant at 95% confidence level. Data are obtained from CERA-20C.

It turns out this is being imposed from the SST reconstruction method as an artefact of the HadISST2 data processing, which is briefly reported in section 3.1.1 of Hersbach et al. (2015). HadISST2 is constructed as a 10 member ensemble of realizations with a monthly window, based on methods separately considering large-scale variability and small-scale perturbations. Daily fields were then obtained by temporal interpolation of monthly analysis fields from adjacent months with weights such that the average of all daily fields in one analysis window equals the monthly analysis again. However, because of locally strong small-scale perturbations dominating the area-averaged ensemble spread at monthly window, this interpolation method leads to interference between the small-scale perturbations. As a result, the ensemble spread appears smaller at start dates of each month and larger at middle of month. In other words, a monthly cycle, which is supposed not to exist, is artefactually introduced by the interpolation process.

So, the next question is to what extent could this monthly spread variability modulate an atmosphere response through air-sea interactions?  It is expected that any changes in SST uncertainty will be reflected in the lower atmospheric fields, depending of course on the time scales and regions considered. This is especially expected in the case of CERA-20C which uses fully coupled ocean-atmosphere models.

The answer is that, at large scales, unfortunately we have not found a clear indication of this artefactual signal in the air so far. It is not surprising as at daily time scales the atmosphere usually has higher-frequency variations and much larger ensemble uncertainty than SST does, and this increases the difficulty of statistically distinguishing a cycle that has a relatively small amplitude. For example, in CERA-20C the global mean of ensemble spread of daily 2 m temperature (T2m) in January 2005-2007 is about 0.3 degC, which is 3 times that of SST. This is true even for the case where the atmosphere is forcing SST, like the Western Tropical Pacific with strong deep convection.

However, in the dry and calm regions of ocean, where the sensible heat flux is thought to be more responsible for atmospheric heating, a monthly cycle in T2m was found, although the indication is much less significant than in SST. Figure 2 shows the regional average of ensemble spread of SST at different forecast leadtimes (0-24 h) in the south-east Pacific, with corresponding T2m ensemble spread (note that the ensemble spread in T2m is increasing with forecast leadtimes). Despite the strong high-frequency variations, T2m does show a hint of a monthly cycle which well matches the phase and amplitude observed in SST. In all, we believe that this monthly variability does have an impact on the atmosphere, but it might need better ways to extract it from a background with a lot noise.

2016 07 08 Xiangbo Feng - Picture2

Figure 2. Time series of regional average (the south-east Pacific, 10°S-40°S and 120°W-80°W) of ensemble spread of SST (top), and T2m (bottom) at different forecast leadtimes (0-24 h) on each day of January 2005-2007. Note that the time series of T2m spread is detrended. Data are obtained from CERA-20C.


  • Be aware of this monthly cycle that is artefactually introduced into the ensembles of daily SST field in both ERA-20CM and CERA-20C, and of its potential impact on the atmosphere. If the daily fields of these two datasets are used in your work, please keep the possibility in your mind that the ensemble uncertainty is systemically varying with dates. This adds more uncertainty than originally designed.
  • This problem only exists in data with daily scale, and is not expected to influence the assessments at long term.
  • This problem can only be solved by improving the daily data processing scheme in HadISST2.


Hersbach, H., Peubey, C., Simmons, A., Berrisford, P., Poli, P. and Dee, D., 2015. ERA-20CM: a twentieth-century atmospheric model ensemble. Q.J.R. Meteorol. Soc., 141: 2350–2375. doi: 10.1002/qj.2528

Laloyaux, P., Balmaseda, M., Dee, D., Mogensen, K. and Janssen, P., 2016. A coupled data assimilation system for climate reanalysis. Q.J.R. Meteorol. Soc., 142: 65–78. doi: 10.1002/qj.2629

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