By Andy May

My new paper (May, 2025) emphasizes that while many of the underlying observations used to build weather reanalysis datasets, such as ERA5 (European Centre for Medium-Range Weather Forecasts or ECMWF Reanalysis v5) (Soci et al., 2024) or MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, Version 2) (Gelaro et al., 2017), are from radiosondes, weather reanalysis models are still models and have the same problems that other models have. Thus, they are not observations or measurements, like those in radiosonde data repositories such as IGRA2, and should not be treated as such. The reanalysis models assimilate surface measurements and satellite data in addition to radiosonde data and blend the measurements together into a global or regional grid using a general circulation atmospheric model. Weather reanalysis models produce reasonably consistent, physics-based periodic (usually every 6 to 12 hours) estimates of the global atmospheric state (Bloom et al., 1996), but they are not observations. Dr. Hans Hersbach of ECMWF (European Centre for Medium-Range Weather Forecasts) provides us with figure 1 below which is an illustration of the data assimilation process in ERA5.

Although like climate models in their structure, weather reanalysis models deal with shorter time periods, and they are constantly being updated with new data. This is good in that each new data item assimilated forces the model to be more realistic. However, data does not come into the model evenly, it arrives in uneven batches. There are several ways of dealing with this problem, but the most common is called incremental analysis updating or “IAU” (Bloom et al., 1996). IAU introduces new data to the model in a gradual manner.

There are numerous problems with adding new data to a model, one of the main problems is the new data will almost always differ from the computed model state at the time of the measurement to some degree. This causes “data shock” where the model must make a sudden, and non-physical, adjustment to accommodate the new data. Because the shock is unphysical and it doesn’t match the physics programmed into the model, the model can wander into an unstable state that takes time to recover from. MERRA-2 uses an IAU system to add new data (Gelaro et al., 2017).

ERA5 uses incremental “4D-Var” data assimilation (Lavers et al., 2024) to minimize new data shock. At each analysis point, usually every 12 hours, 4D-Var simulates both forward and backward in time to find the central 12-hour analysis state that minimizes total error. It inserts all the new data at once and at each data item’s precise measurement time and not gradually like the IAU process. It uses the model physics to choose the appropriate 12-hour analysis, thus the model physical state suffers less than it does with IAU, although it still has some spin-up data shock (Bernsen et al., 2008) to recover from after each 12-hour analysis just like all models do. In short, neither ERA5 nor MERRA-2 exactly honor all the measurements, but no model approximation can.

Conservation of Mass and Energy

Due primarily to the data assimilation processes, model approximations (or parameterizations), and finite resolution, reanalysis models do not perfectly conserve global or domain-wide energy and mass over long integrations. Model parameterizations are algorithms that estimate average critical climate quantities for the grid cells that cannot be modeled at the scale required, like cloud cover. ERA5 has a grid cell size of about 31 km and MERRA-2 about 50 km. The parameterized quantities, like cloud cover, require a much smaller scale (millimeters or less) to model using first principles.

As a result, over long periods of time these reanalysis climate models do not “close.” Closure refers to the degree to which the integrated budgets (sum of mass and energy fluxes, storage changes, and divergences) balance over time, ensuring the initial totals match the final totals after a long simulation run, after accounting for external forcings and inputs. Perfect closure is theoretically required to honor mass and energy conservation laws but never achieved in practice.

The error in atmospheric mass from the beginning of simulation runs to the end can be measured in terms of mm of water because the total dry mass of the atmosphere does not change with time, only the water content. Early models sometimes lost or gained dry atmospheric mass, but ERA5 and MERRA-2 are constrained so that dry mass is conserved (Gelaro et al., 2017), (Mayer et al., 2021), and (Wild & Bosilovich, 2024).

ERA5 generally exhibits tighter closure globally due to its higher resolution and advanced assimilation, while MERRA-2 shows improvements over its predecessor (MERRA) but larger residuals in some cases, particularly from cloud and aerosol effects.

Most modern studies of the troposphere rely mostly on weather reanalysis grids, thus any weaknesses in the weather reanalysis models carry over into these studies. Weather reanalysis models do not capture precipitation, radiation in and out of the climate system, cloud cover, wind speed, cyclones, extreme temperatures, or the double tropopause frequency very well, among other problems. For a summary of the problems with ERA5 and MERRA-2 compiled by Grok, download this report. Yet, even with all these problems, most published studies use weather reanalysis models because they are spatially and temporally continuous and they incorporate global quality-controlled radiosonde data (Xian & Homeyer, 2019).

ERA5 Imbalances

The ERA5 global TOA mean radiative energy imbalance from 2000-2020 is 0.68 ± 0.6 Wm^-2, versus the CERES EBAF satellite observations, after they have been corrected to match the ocean heat content changes, of 0.73 ± 0.7 Wm^-2 (Loeb et al., 2022). Positive values are a net input of energy into the climate system and negative values are net outgoing (cooling). The agreement between the two global numbers is better than the regional agreement, CERES and ERA5 differ substantially in the eastern Pacific off North America.

The ERA5 model does a good job with the total global water vapor balance and loses almost none over the period (2001-2014). It does less well with precipitation, it overestimates total precipitation by 0.1 to 0.2 mm and most of the error is in the tropics (Lavers et al., 2024). Reanalysis models often have a precipitation “wet bias” that is most pronounced in the tropics. Lavers, et al. mention that the precipitation match has been improved in the latest versions of ERA5.

MERRA2 Imbalances

MERRA-2 is produced by NASA’s Global Modeling and Assimilation Office (GMAO). It is a global atmospheric reanalysis spanning 1980 to the present at ~50 km horizontal resolution with 72 vertical levels. MERRA-2 enforces a global dry atmospheric mass constraint, ensuring near-perfect dry mass conservation (~0.01% error per cycle), but its energy budget does not balance well.

MERRA-2’s all-sky reflected shortwave flux is ~7 Wm^-2 higher than CERES EBAF’s, resulting in a net TOA flux imbalance of -4 Wm^-2 for 2001-2015 (Hinkelman, 2019). This is a substantial bias, after all the entire human impact on climate from 1750-2019 is estimated to be only 2.72 Wm^-2 (IPCC, 2021, p. 959). While MERRA-2 performs better on trends and variability, this absolute difference should worry everyone.

At the surface, high clear-sky downward shortwave fluxes indicate that the MERRA-2 atmosphere is too transmissive. MERRA-2’s all-sky shortwave radiation down and longwave radiation up energy flux terms agree reasonably well with CERES EBAF, but its net flux agreement is poor (-4.7 Wm^-2) mainly because it overestimates cloud reflectivity. Analysis by region and surface type gives mixed outcomes. Clouds are overrepresented over the tropical oceans in MERRA-2, and somewhat underrepresented in marine stratocumulus areas. MERRA-2 also overestimates cloudiness in the Southern Ocean. The model also has problems in the polar regions, where the effects of snow and ice cover are important (Hinkelman, 2019).

Discussion

In general, ERA5 is a better weather reanalysis model than MERRA-2, but both have problems. Generally, ERA5 has a better resolution and a better methodology of integrating new data, but neither model has the resolution required to model clouds properly and, as a result, they do not estimate either cloudiness or precipitation well in key areas, like the tropics. Both models are poor at modeling tropical cyclones due to their large grid sizes, but ERA5 is a bit better at this than MERRA-2. Temperature prediction is very poor in the Arctic and Antarctic regions.

Weather reanalysis model products are very useful, but they cannot be considered data or observations, or used as such, as they often are, for example in AR6 figure TS.2 (IPCC, 2021, p. 50). There are places in AR6 that concede weather reanalysis model products are not observations, but some parts of the report treat them as observations. There is poor agreement between various models of radiosonde data in tropospheric temperature trends as shown in figure 2, from AR6 figure 2.12.

Figure 2 shows the tropospheric warming trend by altitude from radio occultation, using data from the infrared satellite instrument AIRS (Qian et al., 2025), and corrected and homogenized radiosonde data (RICH and RAOBCORE). All the measurements in figure 2 are from models, there are no direct measurements in the plot, although RICH and RAOBCORE (Haimberger et al., 2012) are the least removed from the actual radiosonde measurements (Haimberger et al., 2012). As figure 2 makes clear, the models match one another fairly well below about 10 km, but above 10 km there is little agreement and the match in the tropics from 10-17 km is poor.

Figure 3 compares the CMIP6 climate models to ERA5 and the RICH and RAOBCORE homogenized radiosonde results in the tropics (20°S to 20°N). The model results are in red, with the mean and the model spread indicated. Model runs with the actual sea surface temperature (SST) forced are in blue. The black and grey are the ERA5, RICH, and RAOBCORE model results.

Figure 3 demonstrates that not only is the match between ERA5 and the CMIP6 climate models poor, it is getting worse with time, since the post 1998 match is worse than the other time periods shown. The difference between forcing the SSTs (blue) and not forcing them (red) suggests that the models are not doing a very good job over the oceans, which cover 71% of Earth’s surface.

The greenhouse effect is strongest in the tropics due to the higher humidity in this region. Some researchers have suggested that the CMIP6 climate models have overestimated the climate sensitivity to CO₂ and greenhouses in general, and this is the cause of the mismatch in figure 3 in the tropical middle and upper troposphere (Mauritsen & Stevens, 2015), (McKitrick & Christy, 2020), and (Po-Chedley et al., 2022). McKitrick and Christy present evidence that the most straightforward way to reduce the mismatch in tropospheric warming rates in figure 3 is to lower the climate sensitivity to CO₂ in the climate models.

We would also suggest that a necessary validation step would be to select the best radiosonde data and check the nearest climate model grid cells against the actual radiosonde data, rather than the RICH, RAOBCORE, and ERA5 models. Just as the best way to compare the present to that past is to compare modern data to well selected proxies, the best way to compare radiosonde measurements to climate models is to find the best radiosonde data and compare the models to it, at the location of the radiosonde data.

Works Cited

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