Atmospheric conservation properties in ERA-Interim

Authors


Abstract

We study the global atmospheric budgets of mass, moisture, energy and angular momentum in the latest reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF), ERA-Interim, for the period 1989–2008 and compare with ERA-40. Most of the measures we use indicate that the ERA-Interim reanalysis is superior in quality to ERA-40. In ERA-Interim the standard deviation of the monthly mean global dry mass of 0.7 kg m−2 (0.007%) is slightly worse than in ERA-40, and long time-scale variations in dry mass originate predominately in the surface pressure field. The divergent winds are improved in ERA-Interim: the global standard deviation of the time-averaged dry mass budget residual is 10 kg m−2 day−1 and the quality of the cross-equatorial mass fluxes is improved. The temporal variations in the global evaporation minus precipitation (EP) are too large but the global moisture budget residual is 0.003 kg m−2 day−1 with a spatial standard deviation of 0.3 kg m−2 day−1. Both the EP over ocean and PE over land are about 15% larger than the 1.1 Tg s−1 transport of water from ocean to land. The top of atmosphere (TOA) net energy losses are improved, with a value of 1 W m−2, but the meridional gradient of the TOA net energy flux is smaller than that from the Clouds and the Earth's Radiant Energy System (CERES) data. At the surface the global energy losses are worse, with a value of 7 W m−2. Over land however, the energy loss is only 0.5 W m−2. The downwelling thermal radiation at the surface in ERA-Interim of 341 W m−2 is towards the higher end of previous estimates. The global mass-adjusted energy budget residual is 8 W m−2 with a spatial standard deviation of 11 W m−2, and the mass-adjusted atmospheric energy transport from low to high latitudes (the sum for the two hemispheres) is 9.5 PW. Copyright © 2011 Royal Meteorological Society

1. Introduction

Reanalysis is a process whereby past observations of the atmosphere, which have ideally undergone modern data quality checks and re-processing, are reanalysed using a state-of-the-art numerical weather prediction (NWP) analysis and forecast system. This procedure produces the best possible analyses at that time, with the best time consistency, from a given NWP centre. However, because the analysis and forecast system is continually changing, with a view to improving weather forecasts, the reanalysis procedure needs to be repeated every few years in order to benefit from the latest enhancements to the system.

The European Centre for Medium-Range Weather Forecasts (ECMWF) has produced two major reanalyses: ERA-15 (Gibson et al., 1997) and ERA-40 (Uppala et al., 2005). These reanalyses, and others, provide a means of viewing the global circulation of the atmosphere, e.g. Kållberg et al. (2005), and numerous studies have gained insight into the workings of that circulation by using reanalysis data. However, ERA-40 (and ERA-15 before it) did suffer from various deficiencies (Uppala et al., 2005). ERA-Interim (Simmons et al., 2007; Uppala et al., 2008; Dee et al., 2011) was instigated to address some of the problems seen in ERA-40, in the satellite years in particular, and runs from 1989 to the present. It will continue in near real time until a replacement can be produced. Simmons et al. (2007) and Dee et al. (2011) discuss the improvements made to the ERA-Interim system and observations. The major improvements over ERA-40 are the use of 4D variational assimilation (4D-Var), variational bias correction (VarBC) of satellite radiances (Dee and Uppala, 2009), higher horizontal resolution, a new humidity analysis and improved model physics and the homogenisation of radiosonde temperature observations (Haimberger, 2007).

Here, we examine the properties of atmospheric mass, moisture, energy and angular momentum, mostly for the global domain, which are variables that are governed by simple physical constraints. Neither the ERA forecast nor assimilation systems are designed to satisfy these physical constraints, so the degree to which the reanalyses conform to these constraints provides one measure of the quality of the data. Mainly, we compare with ERA-40 but some comparison is also made with the reanalysis of the Japan Meteorological Agency (JMA) and the Japanese Central Research Institute of the Electric Power Industry (Onogi et al., 2007) and its continuation into near real time, JRA-25, the NCEP/DOE AMIP-II reanalysis, NRA2, (Kistler et al., 2001), the Global Precipitation Climatology Project (GPCP) precipitation data (Adler et al., 2003) and the Clouds and the Earth's Radiant Energy System (CERES) radiative fluxes.

This article is organised as follows. Section 2 below describes the data used in this study and then sections 3, 4 and 5 examine the properties of mass and moisture, energy and angular momentum respectively. Section 6 presents the summary and conclusions.

2. Data

This study mainly uses monthly averages for 1989–2008. ERA data are taken at full horizontal resolution from MARS (the ECMWF data archive) on all 60 model levels and at the surface. The horizontal model grids are N128 and N80 reduced Gaussian grids, giving grid lengths of approximately 80 and 125 km, for ERA-Interim and ERA-40 respectively. Where necessary, spectral data are transformed to the same grids. Vertical integration is performed on the model-level fields and the results for ERA-Interim and ERA-40 are archived in MARS. More information on the content of the ERA-Interim and ERA-40 archives can be found in Berrisford et al. (2009) and Kållberg et al. (2004). The data in most of the global maps shown here have been smoothed using a Hoskins-type spectral filter (Sardeshmukh and Hoskins, 1984) with an attenuation of 0.1 at wave number 106. Apart from removing the small-scale structure this enables the comparison of the spatial standard deviation between data of differing resolutions. Mass adjustment of the divergence of fluxes is carried out, where necessary, using the procedure given by Chiodo and Haimberger (2010). Note that this procedure introduces a non-zero global mean to the divergence. All linear trends shown here are computed from the anomalies from the mean annual cycle, because otherwise the trends might be contaminated with that cycle.

Some of the fields that we examine are analysed fields, which are constrained by observations, but others such as the surface and top of the atmosphere (TOA) radiative fluxes and surface turbulent fluxes can not be analysed so are estimated from short-range forecasts. The latter are model-produced and not directly constrained by observations and so are inherently less reliable than analysed fields. All ERA fluxes used here are from the twice-daily forecasts (at 0000 and 1200 UTC) and are accumulated from the first twelve hours of the forecast. All vertical fluxes from MARS are defined to be positive downwards. We confine this study to the first 20 years of ERA-Interim, from 1989 to 2008, including the overlapping 13-year period in ERA-40, from 1989 to 2001.

Monthly mean JRA-25 analyses and six-hour forecasts are taken on a regular N80 Gaussian grid, monthly mean NRA2 analyses and six-hour forecasts are taken on a 2.5° × 2.5° latitude/longitude or regular N47 Gaussian grid. Monthly mean fields are taken from GPCPv2.1 and CERES data on a 2.5° × 2.5° and 1° × 1° latitude/longitude grid respectively.

3. Mass and moisture

Mass is a very basic property of the atmosphere and as such warrants investigation when considering the quality of a reanalysis dataset. Here, we investigate the vertically integrated quantities of mass and water vapour and their difference, dry mass. The effects of water in other phases are small compared to those of water vapour and so are neglected (Trenberth and Smith, 2005).

For an atmospheric column, the mass, m, total column water vapour, TCWV, and dry mass, md, are computed from the pressure, p, and specific humidity, q, assuming a spherical Earth and uniform gravitational acceleration, g, so that

equation image(1)
equation image(2)
equation image(3)

where η is the hybrid coordinate (Simmons and Burridge, 1981) and the masses are measured in kg m−2. The real mass of the atmosphere is estimated to be 0.25% larger than that given by (1) due to the widening with height of air columns in the spherical geometry of the Earth (Bannon et al., 1997). The effects of the spatial variation of g and the non-spherical shape of the Earth were investigated by Trenberth and Guillemot (1994) and, to a good approximation, the total atmospheric mass of the Earth implied by (1) and expressed in kg should be increased by 0.43% (Trenberth and Smith, 2005).

The evolution of the masses is governed by the vertically integrated continuity equations for m, TCWV and md, which link the divergence of the mass fluxes with the atmospheric mass tendencies in the following way:

equation image(4)
equation image(5)
equation image(6)

where v is the horizontal vector wind, is the ‘horizontal’ gradient operator, E is evaporation and P is precipitation. Note that (4) and (5) have the same source term (EP, defined to be positive into the atmosphere), though this is not included in the ERA forecast model's continuity equation (4). For analyses, however, the assimilation of observations should introduce the effects of this source term.

3.1. Global mass and moisture

For the case of global masses, the divergence terms are zero, so that (4) and (5) state that the global mass and water tendencies are governed by the global average of the same source term, EP, while (6) states that the global dry mass tendency has no source term. Hence, the variations in global mass and TCWV should be well correlated and the global mass of dry air, the difference between the two, should be conserved, making it a very basic property of the atmosphere. In reality, the dry mass changes for various reasons not taken account of in (6), the largest changes currently being due to the burning of fossil fuels. However, the effect of the latter is of order 0.1 kg m−2 (Trenberth and Smith, 2005) which is not detectable with current reanalyses, see below. It would be possible to maintain the global mass at a fixed value in the ERA forecast model. However, it is not possible to do so in the data assimilation system. Furthermore, we look to reanalyses to provide us with estimates of the global mass. So in ERA the mass is determined by the system and, as previously noted, the degree to which the system conserves the mass is one measure of the quality of the data.

First we look at the mean annual cycle in the global mass and TCWV, where both quantities reach their maximum in July or August and minimum in December or January (Table I). In ERA-Interim for the 20-year period 1989–2008 the range (maximum—minimum) of the annual cycle in TCWV of 3.1 kg m−2 is 15% larger than that in mass of 2.7 kg m−2. In ERA-40 for the 13-year period 1989–2001, the range in TCWV of 3.2 kg m−2 is 28% larger than that in mass, a similar result to that found by Trenberth and Smith (2005). Consequently, the range of the mean annual cycle in dry mass is smaller in ERA-Interim than in ERA-40, particularly for the period 1989–2001 when it is 0.4 kg m−2 for the former and 0.8 kg m−2 for the latter.

Table I. Mean annual cycle of global mass, TCWV and dry mass.
 MassMassMassTCWVTCWVTCWVDry massDry massDry mass
 EI 20EI 13E4 13EI 20EI 13E4 13EI 20EI 13E4 13
  1. For ERA-Interim (EI) and ERA-40 (E4) for the 20-year period 1989–2008 and 13-year period 1989–2001. The units are kg m−2 and 10000 kg m−2 has been subtracted to produce the values for mass and dry mass.

Jan48.348.248.023.123.023.925.225.224.1
Feb48.648.648.223.423.324.125.325.224.1
Mar48.948.948.523.723.724.625.325.223.9
Apr49.249.248.824.124.125.125.125.223.7
May49.449.649.224.524.625.724.825.023.5
Jun49.950.049.825.325.226.324.624.823.5
Jul50.850.950.526.126.127.124.724.823.4
Aug50.750.850.526.026.027.024.824.923.6
Sep49.849.849.724.924.825.724.925.023.9
Oct48.848.848.823.923.824.725.025.124.1
Nov48.348.348.323.223.224.125.125.124.2
Dec48.148.148.123.023.024.025.125.124.1
Ann49.249.349.024.324.225.225.025.023.8
Max-min 2.7 2.8 2.5 3.1 3.1 3.2 0.7 0.4 0.8

The monthly mean time series of analysed global mass, TCWV and dry mass (Figure 1) show that indeed, the variations in the analysed mass and TCWV are larger than those in dry mass, both for ERA-Interim and ERA-40, and this is measured by the standard deviations of the three quantities (Table II) from their annual climates (Table I). The standard deviation from the annual climate of global dry mass in ERA-Interim for the years 1989–2008 is 0.74 kg m−2 (0.073 hPa) or 0.0074% and in ERA-40 for 1989–2001 it is 0.58 kg m−2 (0.057 hPa) or 0.0058%. The free-running ERA-Interim model, in the absence of the assimilation of observations, is estimated to gain mass by about 0.3% per year (Agathe Untch, 2009, personal communication) and so the analyses conserve global dry mass much better than does the forecast model. This is due to the plentiful supply, and good treatment, of high-quality observations.

Figure 1.

Vertically integrated global monthly mean time series for 1989–2008 for ERA-Interim (solid) and ERA-40 (dashed) of (a) mass, (b) TCWV and (c) dry mass. The units are kg m−2 and 10000 kg m−2 has been subtracted to produce the values in (a) and (c).

Table II. Standard deviation of global mass, TCWV and dry mass.
 MassTCWVDry mass
  1. The values in parentheses are standard deviations from the mean annual cycle, otherwise they are from the annual climate. For ERA-Interim (EI) and ERA-40 (E4) for the 20-year period 1989–2008 and 13-year period 1989–2001. The units are kg m−2.

EI 201.12 (0.70)1.08 (0.30)0.74 (0.72)
EI 131.20 (0.75)1.11 (0.33)0.80 (0.78)
E4 131.07 (0.63)1.17 (0.38)0.58 (0.50)

Although as previously mentioned, the standard deviations of global dry mass are smaller than those for mass and TCWV, the values are at most only 50% smaller (Table II), indicating that the variations in dry mass are not negligible compared to those in mass and TCWV. The dry mass in ERA-Interim increases from a low point of 10023.7 kg m−2 in 1990 to a maximum of 10026.6 kg m−2 in 2000, then decreases to a low point of 10023.6 kg m−2 in 2007 (Figure 1). The behaviour in ERA-40 is different, with a minimum of 10022.6 kg m−2 in 1995, a maximum of 10025.4 kg m−2 in 1999 and returning to more usual values by 2001. The magnitudes of these variations are similar in ERA-Interim and ERA-40 (peak-to-peak values of 2.9 kg m−2 and 2.8 kg m−2 respectively) but the standard deviation in ERA-Interim is nearly 30% larger than that in ERA-40. This disparity occurs because although the dry mass in ERA-40 appears to suffer larger variations than ERA-Interim on month-to-month time-scales, e.g. in the latter half of 1998, that in ERA-Interim varies more on longer time-scales of years. There is no known physical reason why the dry mass in ERA-Interim should exhibit such long time-scale variations, or why it exhibits short time-scale variations in ERA-40, so it is likely that these variations are spurious.

The spurious variations in dry mass are due to problems either in the mass, TCWV or both. For TCWV, both the standard deviation from the mean annual cycle and the linear trends are considerably smaller than those for mass and dry mass and, for ERA-Interim in particular, those for dry mass are similar to those for mass (Figure 2 and Tables II and III). This indicates for ERA-Interim in particular, that the spurious variations in dry mass arise primarily from variations in the mass that are absent from the TCWV. Although after the eruption of Mount Pinatubo in 1991 in particular, the TCWV is larger in ERA-40 than in ERA-Interim (Figure 1(b)) (Uppala et al., 2005), there are only relatively small differences in the deviations from the mean annual cycle for TCWV in ERA-40 and ERA-Interim (Figure 2(b)). The TCWV anomaly in ERA-Interim is positive for the period 1989–1991, but then shifts by about 1 kg m−2 to negative values. Apart from the El Niño/Southern Oscillation (ENSO) period of 1997/1998 the negative values last until 2001, from when there is a gradual increase over time. The negative shift is associated with an increase in Special Sensor Microwave/Imager (SSM/I) satellite observations in 1992 which gradually decrease from 2006 onwards. In ERA-Interim, these observations were not treated correctly, leading to a decrease in TCWV and precipitation (Dee et al., 2011). For most of the period of this negative shift, the TCWV anomaly in ERA-40 is larger than in ERA-Interim, particularly during and after the ENSO event. This negative shift of TCWV in ERA-Interim must be a contributory factor to the spurious variations in dry mass, but the magnitude of the shift is not large enough to completely explain those variations.

Figure 2.

Vertically integrated global monthly mean time series anomalies for 1989–2008 for ERA-Interim (solid) and ERA-40 (dashed) of (a) mass, (b) TCWV and (c) dry mass. The units are kg m−2 and the reference period is 1989–2001.

Table III. Linear trend for global mass, TCWV and dry mass.
 MassTCWVDry mass
  1. For ERA-Interim (EI) and ERA-40 (E4) for the 20-year period 1989–2008 and 13-year period 1989–2001. The units are kg m−2decade−1.

EI 200.290.010.28
EI 131.65−0.231.88
E4 131.090.440.65

For mass, there is generally good agreement between ERA-Interim and ERA-40 up until 1999 (Figure 1). However, there are some notable exceptions to this agreement. For example, the boreal summertime peak in ERA-Interim in 1997 is larger than that in ERA-40 while the opposite is true in 1992 and 1996. Both ERA-Interim and ERA-40 exhibit an increase in mass (and dry mass) during the mid 1990s (Figures 1(a) and 2(a)), culminating in the dramatic rise in mass and TCWV during 1997 associated with the El Niño event. During 2000, however, the mass (and dry mass) in ERA-40 decreases (Figure 1(a)) whereas that in ERA-Interim does not, and the anomaly remains positive until 2004 (Figure 2(a)).

It seems likely that the spurious long time-scale variations of dry mass seen in ERA-Interim in particular, are, for the most part, due to spurious variations in the mass (surface pressure) field, although there is a contribution from the TCWV. The rise in mass and dry mass during the mid 1990s is curious but occurs in ERA-40 too (and in JRA-25). The elevated levels of mass and dry mass from 2000 in ERA-Interim are in disagreement with ERA-40 and although the source of this problem is unknown, it could be related in part to the new surface pressure bias correction scheme in ERA-Interim (Simmons et al., 2007).

The global budgets also illustrate the degree to which the dry mass is conserved. The time series of the tendencies (calculated from the analysed values at the beginning of each month) of global mass and TCWV are reasonably well matched, having a standard deviation of 0.02–0.03 kg m−2 day−1 (Figure 3(a) and (b)). The standard deviation for the dry mass tendency is 0.015 and 0.023 kg m−2 day−1 for ERA-Interim and ERA-40 respectively (Figure 3(c)). While this tendency is not zero, as it would be if global dry mass were perfectly conserved, it is smaller than the tendencies of mass and TCWV. The tendencies of global mass and TCWV should be equal to the source, EP (Figure 3(d)). However, the standard deviation for the latter is 0.08 kg m−2 day−1 for ERA-Interim and the pattern is quite different to that for the tendencies. Also, there are long periods when EP is predominantly negative (1989–1996) and periods when it is positive (1998–2006). These shifts are related to changes in the observing system, such as the satellite measurements of TCWV from SSM/I (Dee et al., 2011). Clearly, the relationship between the budget terms depends crucially on the period considered. Although the agreement between the global tendencies of mass and TCWV and EP is not very good in ERA-Interim, it is still much better than for ERA-40 where EP is far too negative and has a standard deviation of 0.16 kg m−2 day−1, a problem which is related to the overactive hydrological cycle in ERA-40 (Uppala et al., 2005).

Figure 3.

Vertically integrated global monthly mean time series for 1989–2008 for ERA-Interim (solid) and ERA-40 (dashed) of (a) mass tendency, (b) TCWV tendency, (c) dry mass tendency and (d) EP (defined to be positive upwards into the atmosphere). The units are kg m−2 day−1.

3.2. Hemispheric dry mass budgets

It has long been known that one of the greatest sources of uncertainty in atmospheric analyses originates in the divergent wind (Boer and Sargent, 1985) and this problem has continued into more recent times (Graversen et al., 2007). Equations (4)–(6) link the tendencies of the mass fields with divergent mass fluxes. In forecasting models, erroneous divergent winds and mass fluxes lead to spurious surface pressure tendencies. In diagnostics, a further source of error is poor temporal sampling of the mass fluxes (Haimberger etal., 2001). Here, the mass fluxes are calculated from the four times daily analysed instantaneous values and so are not truly representative of the month as a whole—each instantaneous value of the vertically integrated mass flux divergence represents the column mass tendency at only one time step in the model.

Using reanalysis data we can use the tendencies of the mass fields, which are not so problematic to analyse as the divergent wind, to assess the quality of the divergent mass fluxes. For this problem we examine the dry mass budget, which is the simplest case because there is no source term in (6). Various previous studies have investigated hemispheric mass (e.g. Trenberth, 1981) and Zhao and Li (2006) found large discrepancies in the cross-equatorial mass flux from several reanalyses including ERA-40. Here, we concentrate almost exclusively on the hemispheric dry mass budget.

The tendency of the area-average dry mass, mda, is given by the average over an area A of (6) so that

equation image(7)

where v is the inward pointing wind normal to the line l around the area. This relation links the tendency of mda to the area-averaged convergence of vertically integrated dry mass fluxes, C, which is related by Gauss's Theorem to the line-averaged vertically integrated dry mass flux, V, into the area. In other words,

equation image(8)

where C is measured in kg m−2s−1 and V in kg m−1s−1. In the case of a hemisphere, the average cross-equatorial mass flux, V = Ca, where a is the radius of the Earth.

Figure 4(a) shows the monthly mean time series of dry mass for ERA-Interim in the two hemispheres to be highly anti-correlated. On average, the mass in the Southern Hemisphere (SH) is smallest in February with 10040.1 kg m−2 (Table IV) while in the Northern Hemisphere (NH) it is largest in February with 10010.5 kg m−2. The difference of 29.6 kg m−2, which is at a minimum, rises to a maximum value of 81.1 kg m−2 during July.

Figure 4.

Vertically integrated monthly mean time series for 1989–2008 of (a) NH (solid) and SH (grey) dry mass in ERA-Interim, (b) NH dry mass tendency, (c) NH convergence of dry mass fluxes and (d) NH dry mass budget residual (tendency—convergence). The curves in (b), (c) and (d) are for ERA-Interim (solid) and ERA-40 (dashed). The units in (a) are kg m−2—10000, and in (b), (c) and (d) they are kg m−2 day−1.

Table IV. Annual cycle of NH and SH dry mass and dry mass tendencies and the convergence of dry mass fluxes into the NH.
 SH dryNH drySH dry massNH dry massNH dry massERA-40 NH dry
 massmasstendencytendencyconvergencemass convergence
  1. For dry mass the units are kg m−2 and 10000 kg m−2 has been subtracted, otherwise they are kg m−2 day−1. All columns are for ERA-Interim (1989–2008) except the last column which is for ERA-40 (1989–2001).

Jan40.310.1−0.11+0.11−0.32+2.50
Feb40.110.5−0.02+0.02−0.45+2.33
Mar41.49.0+0.16−0.17−0.77+0.62
Apr45.64.5+0.07−0.08−0.92−0.86
May51.4 −1.8+0.32−0.34−1.49−3.80
Jun61.8 −12.5+0.25−0.25−1.75−5.92
Jul65.3 −15.8+0.02−0.01−1.87−6.28
Aug65.1 −15.6−0.05+0.06−1.97−5.63
Sep59.6 −9.8−0.32+0.32−1.52−3.70
Oct50.8 −0.8−0.22+0.23−1.37−2.75
Nov43.76.5−0.22+0.22−0.93−0.22
Dec41.58.6+0.09−0.10−0.71+1.88
Ann50.6 −0.60.000.00−1.18−1.84
max-min25.226.30.640.661.658.78

The tendencies of the NH area-average dry mass in ERA-Interim and ERA-40 are in good agreement (Figure 4(b)) and are an order of magnitude larger than the global tendencies (Figure 3(c)). This is an indication that the analysed global dry mass is well conserved in comparison with variations on the hemispheric scale.

For ERA-Interim, the hemispheric dry mass tendencies of the average annual cycle in both hemispheres show that dry mass flow into the Southern Hemisphere is maximised in May while flow into the NH is maximised in September, with peak magnitudes of about 0.3 kg m−2 day−1 (Table IV) or 1.91 Gg m−1 day−1.

The NH-averaged convergence of vertically integrated dry mass fluxes, C, in ERA-Interim does not agree well with the hemispheric tendencies on monthly time-scales (Figure 4) or for the mean annual cycle (Table IV). The convergence is so negatively biased (indicating that the flow is directed preferentially into the SH) that the mean annual cycle shows negative values for all months of the year with a large peak magnitude of 2.0 kg m−2 day−1, which is six times larger than that of the hemispheric mass tendencies. As discussed above, the mass is thought to be reasonably well analysed, so it would appear that it is the convergence that is poorly captured by the analysis. Interestingly, the NH convergence does appear to improve with time. The peak magnitude of nearly 4 kg m−2 day−1 occurs during 1989 but by 2002 this has decreased to less than 2 kg m−2 day−1. While the convergence in ERA-40 does indicate more northward flow, the magnitudes are an order of magnitude too large, with a peak value of −6.3 kg m−2 day−1 in the average annual cycle (Figure 4(b) and Table IV). Curiously, unlike in ERA-Interim, the convergence in ERA-40 does not appear to improve with time. The NH budget residual (tendency—convergence) is a measure of the degree to which the tendency of the analysed mass agrees with the analysed convergence of mass fluxes into the NH (Figure 4(d)). It is clear that the agreement is not good and the residual is dominated by the convergence term.

These results are for dry mass, so it could be possible that the cross-equatorial flux of TCWV is responsible for the poor and varying quality of this cross-equatorial dry mass flux. However, the cross-equatorial flux of TCWV has a relatively small magnitude and is stable, both in time and between ERA-Interim and ERA-40, so the same qualitative picture emerges from studying the cross-equatorial total mass flux (not shown), though in that case the EP must also be taken into account.

The dry mass budget residual for six regions of the globe is shown in Figure 5. They all have the common feature that the residual is much better in ERA-Interim than in ERA-40. The two regions where the residual is worst, i.e. largest, are the two polar caps, 90°N–60°N and 60°S–90°S. The two regions, 90°N–30°N and 30°S–90°S, are intriguing because in contrast to the hemispheric results, the ERA-Interim residuals are small during 1989–2002 and become larger thereafter.

Figure 5.

Vertically integrated monthly mean time series for 1989–2008 for ERA-Interim (solid) and ERA-40 (dashed) of dry mass budget residual (tendency—convergence) for (a) 90°N–60°N, (b) 90°N–30°N, (c) NH, (d) SH, (e) 30°S–90°S and (f) 60°S–90°S. The units are kg m−2 day−1.

3.3. Time-averaged mass and moisture budgets

Now we look at the time-averaged budgets of mass and moisture, where the tendency term is considered to be zero and the divergence term should balance the source term, if any.

In ERA-Interim for 1989–2008 the divergence of the moisture fluxes are well balanced locally by EP (Figure 6(a) and (b)). The residual (divergence—(EP)) (Figure 6(d)) is generally smaller than the individual terms. The global average of the residual (which is the global average of PE because the global average divergence is zero) is 0.003 kg m−2 day−1 and the global standard deviation is 0.3 kg m−2 day−1. Note that as previously discussed, the global mean does vary depending on the period considered, see Figure 3(d). In ERA-40 the balance is poorer, particularly over the tropical oceans where the residuals are larger than 2 kg m−2 day−1 over large areas, again reflecting the poor representation of the hydrological cycle. The global average of the residual (for 1989–2001) is 0.5 kg m−2 day−1 and the standard deviation is 1.1 kg m−2 day−1.

Figure 6.

Time-averaged vertically integrated mass and moisture budgets for ERA-Interim for 1989–2008 showing (a) divergence of moisture fluxes, (b) EP (defined to be positive upwards into the atmosphere), (c) divergence of dry mass fluxes and (d) moisture budget residual (divergence—(EP)). The units are kg m−2 day−1. All fields shown have been smoothed using a Hoskins spectral filter with an attenuation of 0.1 at wave number 106.

In the time average, the divergence of dry mass fluxes is equivalent to the budget residual because there is no source term in (6). The dry mass divergence is generally smaller in ERA-Interim than in ERA-40 (Figures 6(c) and 7(c)), where the global standard deviation is 10 and 25 kg m−2 day−1 for the two reanalyses respectively. However, these values are large compared with those for the moisture budget residuals, see above, and EP (Figures 6(b) and 7(b)), where the global standard deviations are 2.1 and 2.8 kg m−2 day−1 respectively. Although it is not necessary to mass-adjust the divergence of the moisture fluxes, the large values of dry mass divergence seen in this and the previous subsection indicate that in some cases it will be necessary to mass-adjust the divergence of fluxes, even in ERA-Interim, as done for example by Trenberth (1991) and Chiodo and Haimberger (2010).

Figure 7.

As Figure 6 but for ERA-40 for 1989–2001.

The net effect of the hydrological cycle in the atmosphere is to evaporate water from the oceans and transport it to land where it is rained out. We now use this idea to give us a simple physical measure of how well the moisture divergence and EP fields match in Figures 6(a) and (b) and 7(a) and (b). Each of these three processes should involve the same amount of water. So, the integral of EP over ocean should equal the atmospheric transport of TCWV from ocean to land (the integral of moisture divergence over ocean) which, in turn, should equal the integral of PE over land. In ERA-Interim for 1989–2008 the transport of 1.1 Tg s−1 is weaker than the oceanic EP and land PE of 1.2 Tg s−1, though the oceanic EP is smaller for the 1989–2001 period (Table V). The magnitudes for EP, PE and transport are larger for ERA-40 and the oceanic EP has the wrong sign due to the unrealistically large values of tropical precipitation (Uppala et al., 2005).

Table V. Hydrological cycle.
 Ocean EPTCWV TransportLand PE
  1. For ERA-Interim (EI) and ERA-40 (E4) for the 20-year period 1989–2008 and 13-year period 1989–2001. The units are Tg s−1.

  2. The columns are EP over ocean (defined to be positive into the atmosphere), the atmospheric transport of TCWV from the oceans to land and PE over land (defined to be positive out of the atmosphere).

EI 201.221.061.24
EI 131.051.001.21
E4 13−1.391.221.35

4. Energy

Global energy is another fundamental property of the atmosphere which has a particular significance today because of the need to monitor the planet for signs of global warming. Trenberth et al. (2009) (hereafter TFK09) examined the global energy flows in the atmosphere for the period March 2000 to May 2004 using a mixture of observations, reanalyses and theory. Here, we investigate the top of the atmosphere (TOA) incident solar radiation, the energy balances at the TOA and at the surface (Figure 8), and then investigate the budget of total atmospheric energy.

Figure 8.

Global atmospheric energy flows (W m−2) in ERA-Interim (red) for 1989–2008, ERA-40 (black) for 1989–2001 and TFK09 (blue) for March 2000–May 2004. The ERA-40 values in parentheses are estimated. Image adapted from Trenberth et al. (2009). © American Meteorological Society. Reprinted with permission.

4.1. Top-of-atmosphere incident solar radiation

The TOA incident solar radiation (TSRD) from various reanalyses is shown in Table VI. Note that the values for ERA-40 are not archived, so have been estimated. It is clear that the global values in ERA-Interim and ERA-40 are larger than the more usual value of 341.3 W m−2 by about 3 and 2 W m−2 respectively. The main reason for this error is that there is a bug in the solar radiation scheme of the ERA forecast system used to produce both sets of ERA products, which results in an increase of about 2 W m−2 in TSRD. This bug has since been corrected for operational and future use, but not for ERA-Interim. In the latter, there is a further increase of about 1 W m−2 in TSRD due to setting the solar constant at 1370 W m−2 instead of 1366 W m−2, as in ERA-40. In addition, TSRD in ERA-Interim has no specified 11-year solar cycle.

Table VI. Top of atmosphere (TOA) energy budget over the globe, oceans and land.
 DatasetGlobeOceansLand
  1. For ERA-Interim (1989–2008), ERA-40 (1989–2001), JRA-25 (1989–2008), NRA2 (1989–2008) and TFK09 (March 2000–May 2004). The units are W m−2 and fluxes are defined to be positive downwards. The ERA-40 values in parentheses are estimated values.

TOA solarERA-Interim344.2350.2329.2
RadiationERA-40(343)(349)(328)
downwardJRA-25341.3347.6326.0
(TSRD)NRA2341.3347.0327.0
 TFK09341.3345.4330.2
TOA net solarERA-Interim244.3254.7218.6
radiationERA-40237.2244.8218.6
(TSRN)JRA-25246.8256.6223.5
 NRA2236.2243.3218.3
 TFK09239.4247.7216.8
TOA netERA-Interim−245.5−248.2−239.0
ThermalERA-40−244.7−246.9−239.2
radiationJRA-25−254.6−256.9−249.1
(OLR)NRA2−243.3−245.7−237.2
 TFK09−238.5−240.8−232.4
TOA netERA-Interim−1.2+6.5−20.3
EnergyERA-40−7.5−2.1−20.6
(RT)JRA-25−7.8−0.3−25.6
 NRA2−7.1−2.4−18.9
 TFK09+0.9+6.9−15.6

4.2. Top-of-atmosphere energy balance

The agreement in the global TOA net thermal radiation (OLR) between ERA-Interim, with a magnitude of 246 W m−2, and ERA-40 is to within 1 W m−2 but this magnitude is 7 W m−2 larger than the estimate given by TFK09 (Table VI and Figure 8). The global TOA net solar radiation (TSRN) of 244 W m−2 in ERA-Interim is 7 W m−2 larger than in ERA-40, with the difference originating in the larger reflection of solar radiation over oceanic regions in ERA-40, and 5 W m−2 larger than in TFK09. The resulting TOA input of energy to the atmosphere, RT, for the globe is quite small in ERA-Interim, with a value of −1.2 W m−2 (a loss of energy), as compared to −7.5 W m−2 in ERA-40 and −7 W m−2 in both NRA2 and JRA-25. Unfortunately, the small energy loss at the top of the atmosphere in ERA-Interim is subject to spin-up and increases by about 25% during the subsequent 12 hours of the forecasts from 12 to 24 hours. The TOA energy losses in these reanalyses should be contrasted with the TOA energy gain of 0.9 W m−2 specified by TFK09 in order to account for the current warming of our planet.

We now estimate the temporally averaged spatial errors of RT in ERA-Interim by comparing the latter (adjusted to have zero global mean) with adjusted CERES data, which are thought to be accurate to within a few W m−2 (Fasullo and Trenberth, 2008a). The CERES TOA 2001–2009 annual climatology of radiative fluxes were adjusted so that the global average of RT would be 0.9 W m−2. This was achieved by increasing the magnitude of OLR by 1.5 W m−2 everywhere and uniformly increasing the albedo from 0.284 to 0.290. This adjustment is similar to that done by Fasullo and Trenberth (2008a), which was used by TFK09. In general, the errors in RT for ERA-Interim are negative in the Tropics, where the deficit reaches more than 50 W m−2 over South America. Over the Southern Ocean, RT in ERA-Interim is more than 10 W m−2 too large over large areas (Figure 9) and it is also too large over much of the extratropical Northern Hemisphere. These errors indicate that the meridional gradient of RT is too small in ERA-Interim, with too little radiation being absorbed at low latitudes and not enough being lost at high latitudes. These errors are qualitatively similar to those found for JRA-25 by Trenberth and Fasullo (2010) and for ERA-40 by Trenberth and Smith (2009) and which were found to be due to clouds over the tropical oceans having too large an albedo, while there was too little cloud over low latitude land and over the higher latitudes, particularly over the Southern Ocean (Trenberth and Fasullo, 2010).

Figure 9.

TOA adjusted energy input (RT) for ERA-Interim minus CERES data for 2001–2009. The units are W m−2.

4.3. Surface energy balance

At the surface the global downwelling thermal radiation (STRD) in ERA-Interim is 341 W m−2, which is about 3 W m−2 less than in ERA-40 (Figure 8) but 8 W m−2 larger than in TFK09, with the bulk of this latter discrepancy originating over the oceans (Table VIIa). The values for JRA-25 are 15 W m−2 smaller than in ERA-Interim, being only 326 W m−2. The value of 398 W m−2 in ERA-Interim for the surface global upwelling thermal radiation (STRU) agrees to within 2 W m−2 with the values from ERA-40, TFK09, NRA2 and JRA-25. The downward solar radiation at the surface (SSRD) is 188 W m−2 in ERA-Interim, which is 10 and 4 W m−2 larger than those in ERA-40 and TFK09 respectively. The values for JRA-25 are 9 W m−2 larger than for ERA-Interim. The global values of the surface turbulent fluxes of sensible heat (SSHF) for ERA-Interim are 17 W m−2 and agree to within about 2 W m−2 with ERA-40 and TFK09 (Table VIIb). However, the SSHF for NRA2 is less than half that of the other estimates. The global value of the surface turbulent fluxes of latent heat (SLHF) for ERA-Interim is 84 W m−2 which agrees with ERA-40 to within 1 W m−2 but is 4 W m−2 greater than in TFK09, while the values from JRA-25 and NRA2 are 6 and 9 W m−2 more intense respectively.

Table VIIa. Upward and downward radiative fluxes for the surface energy budget over the globe, oceans and land.
 DatasetGlobeOceansLand
  1. For ERA-Interim (1989–2008), ERA-40 (1989–2001), JRA-25 (1989–2008), NRA2 (1989–2008) and TFK09 (March 2000–May 2004). The units are W m−2 and fluxes are defined to be positive downwards.

Sfc solarERA-Interim188.1188.4187.2
radiationERA-40177.7178.1176.6
downwardJRA-25196.8193.7204.3
(SSRD)NRA2187.3185.3192.5
 TFK09184.3184.4184.7
Sfc solarERA-Interim−23.8−14.2−47.5
radiationERA-40−22.3−13.8−43.4
upwardJRA-25−25.1−13.4−53.0
(SSRU)NRA2−26.9−17.9−49.5
 TFK09−23.1−16.6−39.6
Sfc thermalERA-Interim341.2356.2303.9
radiationERA-40344.2359.4306.3
downwardJRA-25326.1342.2287.5
(STRD)NRA2340.0356.7298.1
 TFK09333.0343.3303.6
Sfc thermalERA-Interim−397.7 −408.6 −370.6
radiationERA-40−397.7 −408.5 −371.0
upwardJRA-25−398.7 −409.7 −372.4
(STRU)NRA2−396.9 −407.9 −369.1
 TFK09−396.0 −400.7 −383.2
Table VIIb. Net fluxes for the surface energy budget over the globe, oceans and land.
 DatasetGlobeOceansLand
  1. For ERA-Interim (1989–2008), ERA-40 (1989–2001), JRA-25 (1989–2008), NRA2 (1989–2008) and TFK09 (March 2000–May 2004). The units are W m−2 and fluxes are defined to be positive downwards.

Sfc net solarERA-Interim164.3 174.2139.7
radiationERA-40155.4 164.3133.2
(SSRN)JRA-25171.8 180.3151.3
 NRA2160.5 167.4143.0
 TFK09161.2 167.8145.1
Sfc netERA-Interim−56.5 −52.4−66.7
thermalERA-40−53.5 −49.0−64.7
radiationJRA-25−72.6 −67.6−84.8
(STRN)NRA2−56.9 −51.2−71.1
 TFK09−63.0 −57.4−79.6
Sfc sensibleERA-Interim−17.4 −13.1−28.2
heat fluxERA-40−15.7 −11.5−26.0
(SSHF)JRA-25−19.3 −16.3−26.6
 NRA2−7.8−5.9−12.4
 TFK09−17.0 −12.0−27.0
Sfc latentERA-Interim−83.5 −99.3−44.3
heat fluxERA-40−82.4 −99.0−41.2
(SLHF)JRA-25−89.3−110.7−38.1
 NRA2−92.2−108.0−52.6
 TFK09−80.0 −97.1−38.5
Sfc netERA-Interim6.99.40.5
EnergyERA-403.84.71.3
(FS)JRA-25−9.5 −14.21.7
 NRA23.62.37.0
 TFK090.91.30.0

In ERA-Interim, compared with ERA-40, some of the excess of downward solar radiation over land is reflected away and the remaining terms in the surface energy budget appear to more than compensate for the increase in solar radiation to give a net land surface energy imbalance of only 0.5 W m−2, which is an improvement of 0.8 W m−2 over ERA-40. Over the oceans, however, the compensation is not so large and the net surface energy imbalance is larger in ERA-Interim than in ERA-40. The global net loss of energy to the surface, FS, is 6.9 and 3.8 W m−2 in ERA-Interim and ERA-40 respectively (Figure 8 and Table VIIb). The values of FS in JRA-25 and NRA2 are −9.5 (a gain of energy for the atmosphere) and 3.6 W m−2 while in TFK09 it is specified to be 0.9 W m−2, which is required to satisfy current estimates of ocean warming. These reanalysis surface energy losses are quite considerable and the loss of 6.9 W m−2, for example, would lead to a loss of about 4355 MJ m−2 over twenty years, which is greater than the total energy of the atmosphere (2623 MJ m−2). There is some improvement of FS in ERA-Interim due to spin-down, where the surface energy imbalance decreases on average by about 13% during the subsequent 12 hours of the forecast from 12 to 24 hours.

4.4. Total energy of the atmosphere

Following, for example, Boer (1982) and Trenberth and Solomon (1994) the total energy in an atmospheric column, TE, is given by

equation image(9)

where L, Cp, T, ΦS and k are the latent heat of condensation of water, the specific heat capacity of air at constant pressure, which depends on q (Kållberg et al., 2004), temperature, surface geopotential and kinetic energy ((v · v)/2) respectively. The evolution of TE is determined from

equation image(10)

where h = Lq + CpT + Φ is the moist static energy (Φ is geopotential), and TEI = RTFS is the input of energy to the atmosphere by the net fluxes of energy at the TOA and surface, which were discussed above. The effects of frictional dissipation are small and have been neglected (Trenberth and Solomon, 1994).

The global integral of the convergence term on the r.h.s. of (10) is zero, so that the evolution of the TE of the global atmosphere is governed simply by TEI. The absence of any divergent flux in the global case means that we do not have to worry about spurious divergent mass fluxes.

The mean annual cycle for the analysed global TE, whose peak to peak range is about 1% of the annual climate value of 2623 MJ m−2, reaches a maximum in July and a minimum in either December or January (Table VIII). The agreement in TE between ERA-Interim and ERA-40 is good but the annual climate for the latter is 0.1% larger than for the former. The monthly mean anomalies of TE for the two ERA datasets also show a good correspondence (Figure 10(a)) and are quite stable with no large trends. The standard deviation of the anomalies and linear trends for TE in ERA-Interim for the period 1989–2008 are 3 MJ m−2 and 1 MJ m−2decade−1 while in ERA-40 for the period 1989–2001 they are 3 MJ m−2 and 3 MJ m−2decade−1 respectively. These values are small compared to the global TE of the atmosphere. The most notable event in this time series is the temporary increase in TE by about 9 MJ m−2 which lagged by several months the increase in the Niño3.4 SST (sea-surface temperature) index associated with the 1997–1998 El Niño. There are also shifts of about 3 MJ m−2, to lower values in 1992 and back to higher values from 2001, which are consistent with the shifts of 1 kg m−2 in TCWV discussed in section 3.1.

Figure 10.

Vertically integrated global monthly mean time series for 1989–2008 for ERA-Interim (solid) and ERA-40 (dashed) of (a) analysed total atmospheric energy (TE) anomaly, (b) total energy tendency, (c) energy input (TEI) and (d) energy budget residual (energy tendency—energy input). The units in (a) are MJ m−2 and in (b), (c) and (d) they are W m−2. The reference period in (a) is 1989–2001.

Table VIII. Mean annual cycle of total energy (TE).
 EI 20EI 13E4 13
  1. For ERA-Interim (EI) and ERA-40 (E4) for the 20-year period 1989–2008 and 13-year period 1989–2001. The units are MJ m−2.

Jan2613.62612.32614.9
Feb2615.62614.72616.8
Mar2617.62616.82618.9
Apr2621.22620.52623.1
May2626.42626.12629.0
Jun2633.22632.72635.5
Jul2638.02637.42640.1
Aug2636.42635.82638.8
Sep2628.32627.32630.0
Oct2619.82618.82621.2
Nov2614.22613.52616.0
Dec2613.12612.52615.3
Ann2623.22622.42625.0
max-min 24.9 25.1 25.2

A consequence of a stable TE with a small standard deviation and trend is that, on average, the energy tendencies are close to zero in ERA-Interim and ERA-40 (Figure 10(b)). However, the combined effect of RT and FS give rise to a net loss of energy that is far from zero (Figure 10(c)), with average values of 8 and 11 W m−2 in ERA-Interim and ERA-40 respectively. The energy budget residual (TE tendency—TEI), which is equal to the monthly average of the analysis increments for energy divided by the length of the forecast (12 hours), is not close to zero, though it is smaller in ERA-Interim than in ERA-40 (Figure 10(d)). The energy increments in ERA-Interim vary on long time-scales, as also found by Chiodo and Haimberger (2010), but the variation is not straightforward. The values decrease from 1989 to 1999, then increase to 2005 and then decrease again to 2008.

Now we look spatially at the time-averaged budgets of TE where the tendency term in (10) is considered to be zero and the divergence term should balance the energy input, TEI. In ERA-Interim for 1989–2008 the divergence of the mass-adjusted (following Chiodo and Haimberger, 2010) energy fluxes is reasonably well balanced locally by TEI (Figure 11(a) and (b)) and the residual (adjusted divergence—TEI) (Figure 11(d)) is generally smaller than the individual terms. The global average of the residual is 8 W m−2 and the global standard deviation is 11 W m−2. In ERA-40 for 1989–2001 the balance is much poorer over much of the globe (Figure 12), with the average of the residual being 11 W m−2 and the standard deviation 25 W m−2.

Figure 11.

Time-averaged vertically integrated total energy (TE) budget for ERA-Interim for 1989–2008 showing (a) mass-adjusted divergence of energy fluxes, (b) energy input (TEI), (c) unadjusted divergence of energy fluxes and (d) energy budget residual (adjusted divergence—energy input). The units are W m−2. All fields shown have been smoothed using a Hoskins spectral filter with an attenuation of 0.1 at wave number 106.

Figure 12.

As Figure 11 but for ERA-40 for 1989–2001.

In ERA-Interim the balance between the TE divergence and TEI is worse if the divergence of the energy fluxes is not mass-adjusted (compare Figure 11(c) with 11(a) and (b)) and for ERA-40 the balance is much worse (Figure 12). The global standard deviation of the residual using the unadjusted divergence is 38 and 95 W m−2 in ERA-Interim and ERA-40 respectively. Even though the problem is not as acute in ERA-Interim as in ERA-40, it is still necessary to mass-adjust energy fluxes and their divergence in both reanalyses.

The net effect of the energy cycle of the atmosphere is that energy is absorbed at the TOA at low latitudes, some of which is lost to the surface while the remainder is transported to high latitudes and then, augmented by energy from the surface, is lost to space. A schematic diagram of these processes is shown in Figure 13. We now use this idea to give us a simple physical measure of how well the TE divergence and TEI fields match in Figure 11(a) and (b) and Figure 12(a) and (b). The difference between the energy in at the TOA and out at the surface at low latitudes (the spatial integral of TEI) should match the energy transport from low to high latitudes (the integral of TE divergence over low latitudes) which, in turn, should match the difference between the energy out at the TOA and in at the surface at high latitudes (the spatial integral of −TEI). The low latitudes are defined as 40°N–40°S with the remainder of the globe defined as the high latitudes. The region 40°N–40°S was chosen because its boundaries approximately coincide with the latitudes of zero TEI and energy divergence and the largest poleward energy fluxes (Trenberth and Carron, 2001; Fasullo and Trenberth, 2008b).

Figure 13.

Atmospheric energy cycle. Energy is absorbed at the TOA at low latitudes, some of which is lost to the surface while the remainder is transported to high latitudes and then, augmented by energy from the surface, is lost to space. Each of these processes is depicted by an arrow with the adjusted values (units: PW) for ERA-Interim for 1989–2008 (red) and ERA-40 for 1989–2001 (black). The difference between the energy in at the TOA and out at the surface at low latitudes (left-hand middle box) should match the energy transport from low to high latitudes which, in turn, should match the difference between the energy out at the TOA and in at the surface at high latitudes (right-hand middle box). The low latitudes are defined as 40°N–40°S with the remainder of the globe defined as the high latitudes. The unadjusted values are shown in parentheses.

The mass-adjusted horizontal atmospheric energy transports of 9.5 and 9.3 PW (the unadjusted transports are 10.3 PW) for ERA-Interim and ERA-40 respectively (Table IX and Figure 13) are similar to the sum of the peak atmospheric energy transports from the two hemispheres (about 5 PW in each) given by Trenberth and Carron (2001) and Fasullo and Trenberth (2008b). However, the horizontal transports are weaker than the energy losses at high latitudes, which range from 10.9 PW for ERA-Interim in the period 1989–2001 to 11.5 PW for ERA-40 in the same period (Table IX). A large part of this mismatch at high latitudes originates in the SH. The energy inputs at low latitudes are much weaker than the transports, varying from 6.9 PW for ERA-Interim in the period 1989–2008 to 5.8 PW for ERA-40. The mismatches between the three processes can be reduced by making simple global adjustments to TEI. If the annual climate of RT is adjusted to have zero global mean and FS is set to zero over land and adjusted to have zero mean over ocean, then the energy inputs at low latitudes and the energy losses at high latitudes vary between 9.5 and 9.3 PW (Table IX and Figure 13), which differ from the horizontal transports by only a few per cent. The origin of the adjustments to TEI reflects the imbalances of energy at the surface and TOA discussed in previous subsections. In ERA-Interim, the adjustments are dominated by those at the surface whereas in ERA-40 the adjustments come from both the surface and TOA. It is interesting that some of the energy inputs and losses at the surface are negative (Figure 13), which is probably indicative of the problems with the surface energy balance, rather than indicating that the signs should be reversed in reality. Given the problems with the energy balances at the TOA and surface, the adjusted energy inputs and losses (Table IX and Figure 13) should not be considered too reliable.

Table IX. Atmospheric energy cycle.
 Low lat TEITE TransportHigh lat −TEI
  1. For ERA-Interim (EI) and ERA-40 (E4) for the 20-year period 1989–2008 and 13-year period 1989–2001. The low latitudes are defined to be 40°N–40°S while the remainder of the globe defines the high latitudes. The unadjusted values are shown in parentheses. The units are PW. The columns are the adjusted energy input to the atmosphere (TEI) over low latitudes, the mass-adjusted atmospheric transport of total energy (TE) from low to high latitudes and the adjusted energy loss from the atmosphere (−TEI) over the high latitudes.

EI 209.51 (6.92)9.51 (10.29)9.51 (11.05)
EI 139.33 (6.73)9.48 (10.32)9.33 (10.86)
E4 139.37 (5.79)9.25 (10.33)9.37 (11.51)

5. Angular momentum

The axial component of the angular momentum of the atmosphere, AM, is a fundamental physical property of the atmosphere because its evolution in time is governed simply by the action of the torques exerted by frictional drag, in the boundary layer and due to the effects of gravity waves, TF, and the mountain torque, TM, involving the interaction of mountains and surface pressure (Starr, 1948). Furthermore, it is an interesting quantity to study because its variations are anti-correlated with the length of day (Hide et al., 1980; Rosen and Salstein, 1983). We write

equation image(11)
equation image(12)
equation image(13)
equation image(14)

where φ, u, Ω, ps and τ are the latitude, zonal wind, angular rotation rate of the Earth, surface pressure and the zonal component of frictional stress. The integral over S represents horizontal integration over the whole globe. Note that the angular momentum is a function of the global distribution of zonal winds and surface pressure according to (11). Here, the frictional torque is calculated from the (12-hour accumulated) forecast stress whereas the mountain torque is calculated from the four times daily analysed instantaneous surface pressure. We also note that this poor temporal sampling of the mountain torque will introduce an error and it also means that the budget residual (AM tendency—the total torque) is not strictly proportional to the analysis increment, though a small residual should still be indicative of high-quality data.

The mean annual cycle for the analysed global AM, whose peak to peak range is about 0.5% of the annual climate value of 1031 × 1025 kg m2s−1, reaches a maximum in December and a minimum in July (Table X). The agreement between ERA-Interim and ERA-40 is good. The monthly mean anomalies of AM for the two ERA datasets also show a good correspondence (Figure 14(a)) and are quite stable with no large trends. The standard deviation of the anomalies and linear trends for AM in ERA-Interim for the period 1989–2008 are 1.1 × 1025 kg m2s−1 and −0.5 × 1025 kg m2s−1decade−1 while in ERA-40 for the period 1989–2001 they are 1.1 × 1025 kg m2s−1 and −1.0 × 1025 kg m2s−1decade−1 respectively, which are small compared to the global AM of the atmosphere. The annual climate value of AM has a contribution of 1016 × 1025 kg m2s−1 from the surface pressure term and 15 × 1025 kg m2s−1 from the zonal wind term. The standard deviations for the wind term, however, are at least three times greater than those for the surface pressure term. The most notable events in the AM anomaly time series are the temporary increase in AM by about 3 × 1025 kg m2s−1 concurrent with the increase in the Niño3.4 SST index associated with the 1997–1998 El Niño, and in the late 1990s there is also a shift to slightly lower values.

Figure 14.

Monthly mean time series for 1989–2008 for ERA-Interim (solid) and ERA-40 (dashed) of (a) analysed angular momentum (AM) anomaly, (b) angular momentum tendency, (c) torque and (d) angular momentum budget residual (tendency—torque). The units in (a) are 1025 kg m2s−1 otherwise they are Hadleys (1018 N m). The reference period in (a) is 1989–2001.

Table X. Mean annual cycle of angular momentum (AM).
 EI 20EI 13E4 13
  1. For ERA-Interim (EI) and ERA-40 (E4) for the 20-year period 1989–2008 and 13-year period 1989–2001. The units are 1025 kg m2s−1.

Jan1031.51031.51031.7
Feb1031.41031.41031.7
Mar1031.41031.71032.0
Apr1032.01032.21032.6
May1031.91032.01032.3
Jun1029.21029.51029.7
Jul1027.21027.21027.5
Aug1027.41027.61027.9
Sep1028.91029.01029.2
Oct1031.11031.31031.6
Nov1032.21032.51032.8
Dec1032.31032.51032.8
Ann1030.51030.71031.0
max-min 5.0 5.3 5.4

As a consequence of the small trends and standard deviation in AM, its tendency (Figure 14(b)), calculated from the analysed values of AM at the beginning of each month, is small on average. The average torque, on the other hand, is much larger in magnitude, with an average value of −6 and −14 Hadleys for ERA-Interim and ERA-40 respectively (Figure 14(c)). This implies a loss of angular momentum during the 12-hour forecasts. The angular momentum budget residual does not oscillate about zero as it should, though it is much smaller and less variable in ERA-Interim than in ERA-40 (Figure 14(d)), indicating an improvement in data quality in the former. Furthermore, the residuals also improve with time (decrease towards zero) in both reanalyses, so that by 2006 the values in ERA-Interim are generally below 5 Hadleys. Again, this increase in quality with time is assumed to be indicative of the effects of the improving observing system and is associated with an increase of the torque over time (Figure 14(c)) rather than a large change in the analysed angular momentum tendency (Figure 14(b)). In the period 2006 to 2008 compared with 1989 to 1998 the total torque is 58% larger, the mountain torque is 34% smaller, the boundary layer frictional torque is 60% larger and the gravity wave drag frictional torque is 12% larger.

So it would appear that the improvement in time of the angular momentum budget residual (which is approximately proportional to the analysis increment) is dominated by an increase in the torque due to the boundary-layer frictional drag. This could be effected either by a reduction in the drag on surface westerlies or an increase of the drag on surface easterlies. However, more subtle changes in the analysed angular momentum, mountain torque and torque due to gravity wave drag may still be important in improving the budget residual.

6. Summary and conclusions

In this work we have studied the atmospheric properties of mass, moisture, energy and angular momentum in ERA-Interim and compared them with those in ERA-40. These variables were chosen because they are governed by simple physical constraints. However, neither the ERA forecast model nor assimilation system are designed to satisfy these physical constraints so the degree to which the reanalyses do so provides one measure of the quality of the data. Most of the measures used here indicate that the ERA-Interim reanalysis is superior in quality to ERA-40.

For ERA-Interim during 1989–2008 the standard deviation of the monthly mean global dry mass from the annual climate is 0.7 kg m−2 (0.07 hPa) or 0.007% and in ERA-40 for 1989–2001 it is 0.6 kg m−2 (0.06 hPa) or 0.006%. Although this indicates that global mass conservation is good, there has been a deterioration compared with ERA-40, though conservation in the mean annual cycle is better. There are spurious long time-scale variations evident in dry mass, which are particularly pronounced in ERA-Interim and which originate predominately in the surface pressure field.

It has long been known that one of the greatest sources of uncertainty in atmospheric analyses originates in the divergent wind or mass flux (Boer and Sargent, 1985), and ERA-Interim analyses are no exception. In particular, the hemispheric dry mass divergence, or cross-equatorial mass flux, is not well analysed in ERA-Interim. This occurs because divergent winds and tropical winds, and in particular the meridional component of tropical winds (B.J. Hoskins, 2009, personal communication), are not well balanced and so are not constrained by the many satellite and synoptic observations of radiances, pressure and temperature. Graversen et al. (2007) speculated that the mass can be well analysed while the mass fluxes are not, because the forecast model moves the surface pressure towards the model's own climate by means of spurious mass fluxes which, unlike for surface pressure, are not corrected by the assimilation of observations. However, there has been a considerable improvement in the representation of the cross-equatorial dry mass flux, or hemispheric dry mass divergence, on going from ERA-40 to ERA-Interim. This is thought to be mainly due to the use in ERA-Interim of 4D-Var data assimilation which should contribute to better time consistency than the 3D-Var used in ERA-40, though the homogenised radiosonde data (Haimberger, 2007) and VarBC of satellite radiances (Dee and Uppala, 2009) used in ERA-Interim may also be important. Furthermore, there appears to be an improvement in these divergent winds with time in ERA-Interim (but apparently not in ERA-40), a fact which is presumably due to the improving observing system and the ability of the 4D-Var in ERA-Interim to take advantage of it. Another measure of the improvement of the divergent winds is that the global standard deviation of the time-mean divergence of dry mass flux, or budget residual, in ERA-Interim of 10 kg m−2 day−1 is less than half the value of 25 kg m−2 day−1 in ERA-40.

Although far better than in ERA-40, moisture is still problematic in ERA-Interim. The global EP in ERA-Interim has a temporal variation about 3 times larger than the TCWV tendencies and there are long periods of several years when EP is either predominantly positive or negative which is related to changes in the observing system, such as the satellite measurements of TCWV from SSM/I (Dee et al., 2011). It has not been found necessary to mass-adjust the moisture divergence in ERA-Interim where, for 1989–2008, the global time-averaged moisture budget residual and its standard deviation is 0.003 kg m−2 day−1 and 0.3 kg m−2 day−1. In ERA-40 for 1989–2001 the values of 0.5 kg m−2 day−1 and 1.1 kg m−2 day−1 are much larger.

The net effect of the hydrological cycle in the atmosphere is to evaporate water from the oceans and transport it to land where it is rained out. We have used this idea to give us a simple physical measure of how well the moisture divergence and EP fields match. Each of these three processes should involve the same amount of water. So, the integral of EP over ocean should equal the atmospheric transport of TCWV from ocean to land (the integral of moisture divergence over ocean) which in turn should equal the integral of PE over land. In ERA-Interim for 1989–2008 the transport of 1.1 Tg s−1 is weaker than the oceanic EP and land PE of 1.2 Tg s−1. The precipitation over land in ERA-Interim for 1989–2008 (2.25 kg m−2 day−1) is 5% larger than that from GPCP; see Simmons et al. (2010) for detailed comparisons with observations. Over oceans, however, the difference is greater (Dee et al., 2011), with ERA-Interim values (3.14 kg m−2 day−1) being 9% larger than those in GPCP. If these observations are reliable and the transport is considered to be realistic, then the ERA-Interim evaporation over the ocean (3.43 kg m−2 day−1) must be 9% too large. However, Trenberth et al. (2007) estimated the average transport of water from ocean to land to be 1.3 Tg s−1, in which case, assuming GPCP to be correct, the ERA-Interim evaporation over land (1.53 kg m−2 day−1) would be 9% too strong and over ocean it would be 8% too strong.

The TOA time-averaged global energy losses are much improved in ERA-Interim compared to ERA-40, with values of 1 and 8 W m−2 respectively. However, the opposite is true at the surface where the values are 7 and 4 W m−2. At the surface over land however, the energy loss of 0.5 W m−2 in ERA-Interim is 0.8 W m−2 smaller than that in ERA-40. The largest discrepancies in the global energy flows (Figure 8) between ERA-Interim and ERA-40 are in the solar radiation at the TOA and surface, which probably originates in changes to the clouds. Furthermore, Kållberg (2011) speculated that the spin-up of cloud in the ERA-Interim forecast model is responsible for the spin-down of the surface energy losses and spin-up of the TOA energy losses. We have also compared the TOA annual climate of radiative fluxes in ERA-Interim with those from adjusted CERES data and found similar deficiencies to those found by Trenberth and Fasullo (2010) for reanalyses including ERA-40 and JRA-25. They found that the problems originated in too bright clouds over tropical oceans, too little cloud over low-latitude land and too little cloud over higher latitudes, particularly over the Southern Ocean. So it would seem that ERA-Interim still suffers from various problems due to the misrepresentation of clouds.

TFK09 discussed the current uncertainty in the downwelling thermal radiation at the surface (STRD). They estimated this quantity to be 333 W m−2 while other estimates quote values of 340 W m−2 or higher. The value in ERA-Interim is towards the higher end of these estimates, being 341 W m−2. However, as already noted, deficiencies exist in ERA-Interim, particularly in the clouds, which have a large influence on STRD.

In ERA-Interim for 1989–2008 the global average of the time-averaged mass-adjusted energy budget residual is 8 W m−2 and the global standard deviation is 11 W m−2. In ERA-40 for 1989–2001 the balance is much poorer over much of the globe with the average of the residual being 11 W m−2 and the standard deviation 25 W m−2. The standard deviations of the residuals using the unadjusted divergence are larger, with values of 38 and 95 W m−2 in ERA-Interim and ERA-40 respectively. So even though the problem is not as acute in ERA-Interim as in ERA-40, it is still necessary to mass-adjust energy fluxes and their divergence in both reanalyses. Regardless of whether or not the energy divergences are mass adjusted, the energy budget residuals, which are proportional to the analysis increments for energy, are smaller in ERA-Interim than those in ERA-40. The energy increments in ERA-Interim vary on long time-scales, as also found by Chiodo and Haimberger (2010).

The net effect of the energy cycle of the atmosphere is that energy is absorbed at the TOA at low latitudes, some of which is lost to the surface while the remainder is transported to high latitudes and then, augmented by energy from the surface, is lost to space (Figure 13). We have used this idea to give us a simple physical measure of how well the energy divergence and TEI fields match. The difference between the energy in at the TOA and out at the surface at low latitudes should match the energy transport from low to high latitudes (the integral of divergence of energy fluxes over low latitudes) which, in turn, should match the difference between the energy out at the TOA and in at the surface at high latitudes.

The mass-adjusted horizontal atmospheric energy transports of 9.5 and 9.3 PW (the unadjusted transports are 10.3 PW) for ERA-Interim and ERA-40 respectively (Figure 13) are similar to the sum of the peak atmospheric energy transports from both hemispheres (about 5 PW in each) given by Trenberth and Carron (2001) and Fasullo and Trenberth (2008b). However, the horizontal transports are weaker than the energy losses at high latitudes and much larger than the energy inputs at low latitudes. The mismatches between the three processes can be reduced to just a few per cent by making simple global adjustments to TEI. However, given the problems with the energy balances at the TOA and surface, the adjusted energy inputs and losses should not be considered too reliable. We saw in section 4.2 that compared with CERES data, the meridional gradient of RT in ERA-Interim is too weak. If RT were to be made compatible with CERES data, then the low-latitude energy input would have to be increased by 17% and the energy loss from high latitudes would have to be increased by 12%. This either implies that the adjusted atmospheric energy transports are at least 10% too weak or that the globally adjusted FS is too weak.

The angular momentum budget residuals, which are approximately proportional to the analysis increments, in ERA-Interim are smaller than in ERA-40. Furthermore, these residuals decrease with time in both ERA-Interim and ERA-40, presumably because of the improving observing system.

We have seen that the analysis increments for both energy and angular momentum are smaller in ERA-Interim than in ERA-40. For the case where there are very few observations and/or very poor observations, small analysis increments (which indicate the change in the variable from the forecast to the analysis due to the assimilation of observations) would indicate that the forecast state is close to the analysed state because the observations are unable to change the analysis significantly. However, in ERA-Interim there is a good supply of high-quality observations, and ERA-Interim analyses and forecasts are known to be more consistent with observations than for ERA-40 (Simmons et al., 2007; Uppala et al., 2008; Dee et al., 2011). In this case, the smaller analysis increments are thought to indicate an improvement in both the analyses and associated forecasts.

Acknowledgements

We would like to thank many of the staff of the ECMWF for enabling this work to be carried out, but Jean-Jacques Morcrette and Agathe Untch deserve particular thanks, as do Rob Hine and Anabel Bowen for cleaning up the figures and creating Figure 13. We would also like to thank Kevin Trenberth and one anonymous reviewer for making helpful suggestions on improving this work. PB is funded by NCAS-Climate and HS is funded by JMA.

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