Interannual variations in the atmospheric heat budget

Kevin E. Trenberth, David P. Stepaniak and Julie M. Caron

National Center for Atmospheric Research
P. O. Box 3000
Boulder, CO 80307

(303) 497 1318; (303) 497 1333 (FAX)

18 December, 2000
J. Geophys. Res. Atmospheres


A new dataset of the computed vertically integrated energy transports in the atmosphere is exploited to examine relationships with other fields. A case study reveals very large monthly divergences of these transports regionally with El Niño-Southern Oscillation (ENSO), the associated changes with the Pacific-North American teleconnection pattern, and with the North Atlantic Oscillation. In the tropical Pacific during large El Niño events the divergence of the atmospheric energy transports exceeds 50 $W m^{-2}$ over broad regions for several months. Examination of the corresponding top-of-the-atmosphere net radiative fluxes shows that it is primarily the surface fluxes from the ocean to the atmosphere that feed the divergent atmospheric transports. A systematic investigation of the covariability of sea surface temperatures (SSTs) and the divergence of atmospheric energy transport, using singular value decomposition (SVD) analysis of the temporal covariance, reveals ENSO as dominant in the first two modes, explaining 62% and 12% of the covariance in the Pacific domain and 39.5 and 15.4% globally, respectively. The first mode is well represented by the time series for the SST index for Niño 3.4 region (170-120$^\circ$W, 5$^\circ$N to 5$^\circ$ S). Regression analysis allows a more complete view of how the SSTs, outgoing longwave radiation, precipitation, diabatic heating and the atmospheric circulation respond with ENSO. The second mode indicates aspects of the systematic evolution of ENSO with time, with strong lead and lag correlations. It primarily reflects differences in the evolution of ENSO across the tropical Pacific from about the dateline to coastal South America. High SSTs associated with warm ENSO events are damped through surface heat fluxes into the atmosphere which transports the energy into higher latitudes and throughout the tropics, contributing to loss of heat by the ocean, while the cold ENSO events correspond to a recharge phase as heat enters the ocean. Diabatic processes are clearly important within ENSO evolution.

1. Introduction

It is widely accepted that persistent climate anomalies arise primarily from interactions of the atmosphere with other components of the climate system because the heat capacity of the atmosphere is small and equivalent to that of only about 3.1 m of the ocean (factoring in the 70% or so ocean coverage of the planet). Accordingly, a key forcing of atmospheric climate variability on all time scales is through the surface fluxes of heat, moisture and momentum. Because conduction of heat is small, the masses of land and ice sheets involved in climate variability on interannual and decadal time scales are very small, and the main role of land is through variations in moisture storage and supply. Consequently, the main actively-varying heat sources and sinks for the atmosphere are the oceans and sea ice, where turbulent exchanges play key roles.

The sea surface temperature (SST) field is a key field in the two-way communication between the atmosphere and ocean. To the extent that SST anomalies persist they have to be supported by a substantial heat content anomaly of the ocean mixed layer, especially if they are to have an influence on the atmosphere. Such an influence typically means that the anomalous heat is being drained from the ocean and thus a negative feedback occurs, as seems to be the case generally in the tropics [ Barnett et al., 1991]. Aside from having a large reservoir to call upon in the ocean, an alternative way in which persistent climate anomalies can develop is if the atmosphere-ocean evolves as a coupled system, as occurs in El Niño-Southern Oscillation (ENSO).

In this paper we explore contemporary variations in the global atmospheric heat budget through the divergent component of the atmospheric energy transports and their relationship to the SST field. A number of datasets are employed, as given in section 2. We first show in section 3 some intriguing anomalies in a case study of two January months that were very different in both the phase of ENSO and the North Atlantic Oscillation (NAO). We then explore in section 4 the time sequences in the tropical Pacific and expand to the global domain through a singular value decomposition (SVD) analysis of the cross covariance matrix between SST and the divergence of atmospheric energy, along with precipitation as a key indicator of the latent heating of the tropical atmosphere, outgoing longwave radiation (OLR) and estimates of the atmospheric diabatic heating. In this way, we attempt to clarify the role of surface fluxes and diabatic processes, and how they relate to SST variations. We show that at least two indices are needed to characterize ENSO variability and we propose a new index to help do so. Results hint strongly at significant lead and lag relationships which are related to the slow evolution of ENSO, but these are explored elsewhere. The consistency of results from the different datasets is discussed in section 5 and the conclusions are given in section 6.

2. Data and methods

Key data sets consist of a number of monthly mean derived products from the atmospheric reanalyses from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) and European Centre for Medium Range Weather Forecasts (ECMWF), as described in Trenberth et al. [2001a], for the period 1979 to 1993 for ECMWF and 1979 to 1998 for NCEP. The full resolution atmospheric reanalyses four-times daily on model coordinates were used to obtain the best accuracy possible for the atmospheric transports. The mass budget was first utilized as a constraint and adjustments are made to the vertically integrated mass flows to ensure a balance on a monthly mean basis. Then we computed for each month the vertically integrated total atmospheric energy transports ${\bf F_A}$ and their divergence $\nabla \cdot {\bf F_A}$. Diabatic heating is computed as a residual from the thermodynamic equation [ Trenberth and Solomon, 1994]. The vertically integrated moisture transports and other quantities, were also computed. The total energy consists of the potential and internal energy, the latent energy, and the kinetic energy, while the transports also include a pressure-work term so that the transport can be broken down into components from the dry static energy and the moist (or latent) component, which together make up the moist static energy, plus the kinetic energy. In addition we compute the tendencies in mass and atmospheric energy storage utilizing values at the beginning and end of each month. The energy tendencies are combined with the computed divergence of the vertically integrated atmospheric energy transports to give the net column change, which has to be balanced by the top-of-the-atmosphere (TOA) radiation $R_T$ and/or the surface fluxes $F_s$, see Trenberth and Solomon [1994] and Trenberth et al. [2001a] for details. Ignoring tendencies,

\nabla \cdot {\bf F_A} = R_T +F_s
\end{displaymath} (1)

where $F_s$ is directed upwards and $R_T$ downwards.

Over the oceans in the extratropics, Trenberth et al. [2001a] evaluate and compare results from the two reanalyses and show that they agree in their monthly mean anomaly time series with correlations exceeding 0.6 for the vertically integrated total energy divergence. The agreement is not as good in the tropics. Local errors of about 25 to 30 $W m^{-2}$ on T31 scales are inferred most places, although embedded within a signal of about 40 $W m^{-2}$ in the extratropics for monthly anomalies. Spatial and temporal averaging reduces these errors and the systematic errors are much less than in other approaches. We exploit the large spatial and temporal scales of ENSO to bring out the ENSO signal from the noise.

However, continuity problems with the ECMWF reanalyses arising from the positive reinforcement of biases in satellite radiances with those of the assimilating model first guess [ Trenberth et al., 2001b] undermine their utility for exploring climate variability. In addition, the implied ocean heat transports from the ECMWF reanalyses do not agree within error bars of direct oceanographic estimates whereas those from NCEP/NCAR do [ Trenberth and Caron, 2001]. The time series of tropical temperatures from the NCEP reanalyses also appear to be more consistent. Accordingly we use the NCEP-derived products to explore aspects of interannual variability.

Net surface fluxes from the ocean into the atmosphere can therefore be computed from (1) only when reliable net TOA radiation data are available, such as during Earth Radiation Budget Experiment (ERBE). This method avoids the substantial biases and uncertainties associated with bulk flux formulations, and spatial and temporal sampling, and is physically consistent with the global constraints. It is limited by the accuracy of especially the atmospheric energy transports, which have been extensively evaluated by Trenberth et al. [2001a], and Trenberth and Caron [2001]. ERBE data are available from February 1985 to April 1989, but we will also refer to results when we have only the atmospheric energy divergence available. The root mean square (rms) uncertainty in net TOA radiation is estimated [ Rieland and Raschke, 1991] to be 7.8 W m$^{-2}$ for the three satellite combination versus 11 W m$^{-2}$ for one satellite, with larger uncertainty in the absorbed solar radiation (ASR). The ERBE data contain discontinuities when the NOAA-9 satellite was lost, and we have adjusted the dataset to accommodate this. We have also filled in missing data, which is pervasive near the delimiter of the solar radiation. Trenberth [1997] describes the methods, changes and availability of the revised ERBE dataset (see

In 1998, new TOA radiation fluxes have become available from Clouds and the Earth's Radiant Energy System (CERES) instruments on the Tropical Rainfall Measurement Mission (TRMM) for the region equatorward of about 40$^\circ$  latitude. These fluxes are being evaluated to ensure their compatibility with earlier measurements, and results thus far (e.g., Wielicki et al., 1999) suggest good comparability, and so we will make cautious use of some of these as well. TRMM precesses through all local hours of the day every 23 days, and so this can lead to noise and aliasing of the diurnal cycle onto monthly means. Because 23 days is close to 2/3 month, the diurnal cycle aliases onto 3 monthly periods when using monthly means, with about 21% of the amplitude.

Nimbus-7 wide field of view data exist from 1979 through October 1987 and have been compared with ERBE data by Kyle et al. [1990]. There are some modest biases shown to exist. For the common period, we have computed the climatologies of each and then taken the anomalies from all the Nimbus-7 datasets and added them onto the ERBE means to provide an adjusted Nimbus-7 data set that is more consistent with that from ERBE than the raw data. The wide field of view active cavity radiometer on Nimbus-7 has a footprint of 1000 to 2000 km across and thus radiation measurements are less accurate regionally. In addition, while the Nimbus-7 orbit remained stable for several years, it began to precess after about 1986, changing the time of day of the observation, see Kyle et al. [1993] for details on the data. It is possible that some spurious low frequency trends arise from drift in the zero level of the cavity radiometer. Some low frequency trends in the data set are therefore probably not physical. Also, a sharp discontinuity about November 1980 may have arisen from changes in algorithms used in the data processing necessitated by problems in channels 12 and 13 [ Kyle et al., 1993].

We also make use of the OLR data set from the NOAA series of satellites. However, the OLR contains inhomogeneities associated with different satellites and their different equatorial crossing times and orbital drift, and we use a version for which some of these have been adjusted with results from Waliser and Zhou [1997]. We apply the correction to the region between $\sim \pm$30$^\circ$(through July 1996 only) and taper the correction to zero near $\pm$30 degrees to smooth any discontinuities that might be introduced as follows: the region between $\pm$ 27.5$^\circ$latitude is fully corrected; the correction at $\pm$30$^\circ$is weighted 2/3 and also applied at $\pm$32.5$^\circ$ with 1/3 weight. There is no correction poleward of 32.5$^\circ$.

We use the SSTs from NCEP from the optimal interpolation (OI) SST analysis of Reynolds and Smith [1994] after 1982 and the empirical orthogonal function (EOF) reconstructed SST analysis of Smith et al.  [1996] for the period before then. The latter does not contain anomalies south of 40$^\circ$S. However, these SSTs are preferred to those in the global surface temperature dataset from the University of East Anglia and the United Kingdom Meteorological Office [ Hurrell and Trenberth, 1999], which is also employed to examine values over land. We also utilize the precipitation dataset from Xie and Arkin [1996, 1997], called the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP). Over land these fields are mainly based on information from rain-gauge observations, while over the ocean they primarily use satellite estimates made with several different algorithms based on OLR, and scattering and emission of microwave radiation.

Because large natural variability on synoptic timescales appears as weather noise in monthly means, and also spurious noise related to sampling is present (especially for SSTs, OLR, and net radiation), aside from the case study, we have smoothed the monthly anomaly fields used in the analyses with a binomial ${1\over 4} (1, 2, 1)$ filter which removes two month fluctuations.

Various exploratory analyses, including empirical orthogonal function analysis, have been employed, but the results deemed most enlightening have arisen from singular value decomposition (SVD) of the cross covariance matrix between two variables [ Bretherton et al., 1992], such as SST with the divergence of atmospheric energy, and both of those fields with OLR and precipitation. In addition we employ correlation and regression analysis to help define relationships.

SVD analysis brings out the spatial patterns and their associated time series (or expansion coefficients) that explain the maximal mean square temporal covariance between two fields. We use monthly mean fields which have been normalized by their standard deviation. One variable is designated the ``left'' field and one the ``right'' field. As well as obtaining the total squared covariance fraction (SCF) explained by the modes resulting from the analysis, we also obtain the correlation between the two time series for each mode as a measure of how well they agree. The modes are ordered by SCF ranking. Correlation or regression of the left (or right) time series with the left (right) field provides what is called the ``homogeneous'' patterns associated with each mode, while correlations and regressions with the opposite right (left) field provide the ``heterogeneous'' patterns. When the correlations between the time series are high, there is very little difference between the homogeneous and heterogeneous patterns, although the former are naturally stronger. However, the heterogeneous patterns are appropriate in order to judge the response of one field to the other.

The SVD analysis can be performed using only part of a domain and results projected to the rest of the domain using regression. Similarly, regression results can be derived for other fields to obtain associated correlative patterns. This is especially useful when essentially the same time series results for one field when combined in separate SVD analyses with several other fields, as is the case in the tropical Pacific.

3. An example of anomalous atmospheric energy transports

Figures 1 and 2 present summary results of the total divergent energy transport and its divergence $\nabla \cdot {\bf F_A}$, for two different Januaries, those of January 1989 (Fig. 1) and January 1998 (Fig. 2) based on the NCEP reanalyses. The bottom panel shows the actual vectors of the vertically integrated transport and its potential function, while the top panel shows the divergence. Similar results are obtained for the ECMWF reanalyses.

The overall climatology of this dataset has been documented and evaluated in Trenberth et al., [2001a]. However, to better appreciate the anomalous features seen in Figs. 1 and 2, in Fig. 3 we present the 20 year mean from 1979 to 1998 and the standard deviation of the anomalies. Then Fig. 4 shows the anomalies for January 1989 and 1998.

These two months also happen to be ones where we have some reliable data from the TOA. Using the ERBE base period of February 1985 to April 1989 to establish a climatology for each month, we compute anomalies for the TOA for January 1989 using the ERBE data and for January 1998 using CERES data for the tropics (see Fig. 5). Anomalies are much greater in both the ASR and OLR fields (Fig. 6) and exceed 50 $W m^{-2}$ in both years but there is strong cancellation in their contribution to the net radiation. Differences are $<10$ $W m^{-2}$ except in very small spots plus the stratocumulus deck regions at about 20$^\circ$S off the west coasts of Peru in the Pacific and Australia in the Indian Ocean. Therefore, because the changes in the net TOA fluxes are of the order of $<$10 $W m^{-2}$, most of the field in Fig. 4arises from the net fluxes at the surface out of the ocean.

These two months were chosen because they occur at times of the peak in the most recent El Niño event (Fig. 2) and the major La Niña in 1988-89 (Fig. 1). The tropical Pacific will be discussed in more detail later. For the moment we note that in January 1989, when there was a strong cold dry tongue in the tropical eastern Pacific (Fig. 6), the net atmospheric divergence is as much as $>$150 $W m^{-2}$, and so the implication is that the clear skies allow solar radiation to contribute to a strong heat flux into the ocean. In contrast, in 1998, under mature El Niño conditions, when the ITCZ and SPCZ were combined as extensive areas of convection over the equatorial Pacific (Fig. 6), the net flux is mostly out of the ocean into the atmosphere. In terms of anomalies, the standard deviation of $\nabla \cdot {\bf F_A}$  for January is about 30 $W m^{-2}$ in the tropical Pacific (Fig. 3) and the anomalies range from less than $-$75 $W m^{-2}$ in January 1989 to $>$ 75 $W m^{-2}$ in January 1998 (Fig. 4).

There was a strong reversal of the Pacific-North American (PNA) teleconnection pattern in the northern extratropics between these months. In January 1988 the PNA index anomaly was -1.5 standard deviations versus +2.2 standard deviations for January 1998. In January 1989 this was part of sea level pressure anomalies exceeding +18 mb at 45$^\circ$N 180$^\circ$ in the Pacific signifying a weak and split Aleutian low pressure system. In contrast during January 1998, there was a deep well-organized Aleutian low with a sea level pressure anomaly of $-$12 mb. The result was a very different mean and transient flow out of Asia into the Pacific. The huge differences in the surface fluxes (Figs. 1 and 2) off Japan and over the Kuroshio extension region are a direct consequence of this. In January 1989, a broad region with heat fluxes into the atmosphere of over 100 $W m^{-2}$ peaked at just over 200 $W m^{-2}$, while in January 1998, the peak fluxes into the atmosphere for the monthly mean exceeded 350 $W m^{-2}$ but the areal extent of the fluxes $>100$ $W m^{-2}$ was not as great. In both years the monthly anomalies in $\nabla \cdot {\bf F_A}$ exceeded $\pm$75 $W m^{-2}$.

Also of note in these two figures is the huge contrast in the Labrador Sea. The Icelandic low switched from $<$990 mb in January 1989 to 1000 mb in January 1998, and in January 1989 there was a +15 mb anomaly in sea level pressure over Europe. A strong positive North Atlantic Oscillation (NAO) in January 1989 (+2.0 standard deviation anomaly) led to cold outbreaks over the northeast of Canada and Greenland, and resulted in fluxes of over 250 $W m^{-2}$ fluxes out of the ocean in the Labrador Sea compared with a flux into the ocean in the same region in January 1998, when the NAO was weak (index +0.1). These anomalies exceeded $\pm 105$ $W m^{-2}$ and are almost two standard deviation departures from the mean.

Overall, the patterns seen here are reasonable. As January is the northern winter, when heat preferably goes into the southern oceans and out of the northern oceans, following the sun, and the main atmospheric transports are into the northern hemisphere. There is a strong land-sea contrast, as expected. A few weird features show up, such as positive values over parts of the southern oceans and Antarctica that are not reproducible and clearly relate to quality of the analyses.

4. The tropical Pacific variability

We have examined the evolution of the anomaly fields of the divergence of the atmospheric energy transports using movie loops and statistical analysis. Not unexpectedly, there is a very high level of ``blinking'' on and off of anomalies in individual months, and even switches in sign from month to month which is partly caused by the effects of individual synoptic systems. The presence of a warm sector in a region at the end of one month followed by the cold sector of a cyclonic storm at the beginning of the next month leads to considerable weather-related noise, and part of the balance is with the local energy storage tendency terms. The magnitude of the noise is quite high in the extratropics, and especially over Antarctica and the Southern Oceans where the quality of the analyses is not as great [ Trenberth et al., [2001a]. However, we are more interested in underlying systematic patterns which indicate the changes in storm tracks and climate influences of the ocean on the atmosphere. Accordingly it proves to be desirable to smooth the monthly anomalies and suppress the very high frequency fluctuations from the analysis, as noted in section 2. While there remain considerable high frequency fluctuations in $\nabla \cdot {\bf F_A}$  in the extratropics, it proves not to be very coherent and so the tropical regions dominate in an analysis of the co-variability.

4.1 Time series of Niño 3.4 region

El Niño events tend to dominate the large-scale coherent patterns of divergent atmospheric energy transports, as will be shown below. Therefore to set the stage for subsequent analysis we present two key ENSO indices in Fig. 7. These are the Southern Oscillation Index (SOI) based upon Tahiti and Darwin pressures and the SST anomalies in Niño 3.4 region (170$^\circ$-120$^\circ$ W, 5$^\circ$N to 5$^\circ$S), which we henceforth refer to as Niño 3.4. (This shorthand is proposed to distinguish the SST anomaly area average over Niño 3.4 from area averages of other quantities over the same region). Higher than normal SSTs in this region go hand-in-hand with negative SOI values and signify an El Niño, while reversed signs indicate La Niña events.

To further explore the atmospheric energy transports in the tropical Pacific, we average various quantities over the Niño 3.4 region. We present the vertically integrated divergence from both reanalyses, $\nabla \cdot {\bf F_A}$, as anomaly time series beginning in 1979 (Fig. 8). The ECMWF reanalyses cover the period through only 1993 and, as noted by Trenberth et al. [2001b], suffer from spurious variability and two major discontinuities in the tropics in late 1986 and early 1989. In both cases, the tropical atmosphere, as analyzed, spuriously jumped to warmer values below 550 mb and cooler above there, adversely affecting the computations of the moist static energy. The whole time series is therefore somewhat corrupted, but it is shown to illustrate the extent of the agreement with NCEP values from the positive anomalies in 1982 to the negative anomalies in 1983 and the positive anomalies again in 1986 of about the same magnitude. The time series from NCEP clearly identifies all of the ENSO variability seen in Fig. 7, with positive anomalies in $\nabla \cdot {\bf F_A}$  corresponding to the warm phase of the ENSO events.

Anomalies in TOA radiation for the Niño 3.4 region are shown in Fig. 9, all relative to the ERBE base period. The longest reasonably continuous time series related directly to radiation is that of OLR from the NOAA series of satellites. There is quite good agreement with the anomalies from ERBE (which used two of the same satellites) during the ERBE period but not very good agreement with broadband measurements from Nimbus-7, which appears to show spurious drifts. Similarly in 1998, there are disagreements and a positive offset between OLR measurements from CERES with those of NOAA, raising questions about both sets of data at these times. For net radiation, the only reliable data are from ERBE and relatively small variability in the Niño 3.4 region is evident with a range of $<4$ $W m^{-2}$. Nimbus-7 does provide a fairly long time series, although with a downward jump in 1980 that is likely spurious and with smaller variability over the common period. It nevertheless highlights the relatively small anomalies compared with those in Fig. 8, which continue with the CERES data.

We also examined averages of OLR over the more extensive region from 30$^\circ$N to 30$^\circ$S for systematic effects (Fig. 10). As expected, there is a large cancellation within this region and, instead of the up to $\sim$50 $W m^{-2}$ values in Fig. 9, the fluctuations are about $\pm$3$W m^{-2}$. However, we conclude that rather than revealing real changes with time, most of what is present are spurious changes related to orbital changes in the satellites, among other things. In particular, from 1989 to early 1995, NOAA-11 drifted in orbit such that its local equator crossing time changed from 1400 to 1730, and it is exactly when NOAA-11 was replaced that the time series jumps back to anomalies near zero. This evidence shows that the Waliser adjustments were insufficient to homogenize the series to better than about 3 $W m^{-2}$, and this spurious drift is slightly worse in the original uncorrected OLR data. Also in this figure are the values for CERES in 1998 relative to the ERBE climatology, and it immediately casts suspicion on its compatibility with the rest of the series.

Note that a 1$^\circ$C temperature change over a column of water of 130 m deep over 5 months corresponds to a surface flux of about 40 $W m^{-2}$. However, such a change over the Niño 3.4 region when redistributed throughout the 30$^\circ$N to 30$^\circ$S area amounts to about 1 $W m^{-2}$ and is not measurable because it is less than the noise.

The assessment of the net TOA measurements is that the interannual changes are most likely quite small and thus we can regard the atmospheric energy divergence as corresponding mostly to air-sea flux exchanges. However, we note the very strong resemblance between the NOAA OLR time series and the atmospheric energy divergence in the tropical Pacific, and that these strongly resemble the indices of ENSO (Fig. 7). Moreover, as these two datasets are entirely independent, the likelihood of these being chance relationships is very slim. Contemporary correlations for the smoothed monthly anomalies among these indices are given in Table 1. All are very high, exceed 0.75 in magnitude, and are highly statistically significant. For correlations between variables with persistence related to ENSO [ Trenberth, 1984] for the 240 months, this implies about 80 degrees of freedom and suggests statistical significance at the 5% level if the correlations exceed about 0.23.

The strong correlation between the tropical Pacific atmospheric energy divergence, and thus surface fluxes, arise primarily from the large ENSO events, revealed by the indices and shading in Fig. 7. The areal extent of the Niño 3.4 region is 6 $\times 10^{12}$ m$^2$ and thus the results of Trenberth et al. [2001a], which suggest random errors of $\sim$30 $W m^{-2}$ over 500 km scales, imply a random standard error of 6 $W m^{-2}$. This fits reasonably well with the coherence of the NCEP atmospheric energy divergence with the ENSO indices and strongly suggests that signals greater than 12 $W m^{-2}$ are significant. In the major El Niños over the Niño 3.4 region, the anomalies in 1982, 1986-87, 1992 and 1997 all exceed 40 $W m^{-2}$, with the implied surface heat flux out of the ocean into the atmosphere. From there, heat is transported to higher latitudes and elsewhere in the tropics and subtropics. Large-scale overturning is the dominant process in the latter regions while, in the extratropics, many processes are involved as teleconnections alter storm tracks and advection by the flow [ Trenberth et al., 2001c]. In 1982 and 1997, the biggest El Niño events, the anomalies exceed 60 $W m^{-2}$ for a few months. In addition, in these events the areal extent of the anomalous fluxes is much greater than just the Niño 3.4 region. At the other extreme, with the La Niña events during this period, the anomalies are not quite as large but they last a bit longer. In the Niño 3.4 region, for several months during mid-1983 to early 1986, anomalous heat fluxes into the ocean exceed 35 $W m^{-2}$, and during the 1988-89 event the anomalous fluxes exceed 50 $W m^{-2}$ for a few months.

4.2 SVD analyses

We performed several exploratory SVD analyses, using global domains as well as domains limited to the Pacific. We also explored results where one field was lagged relative to the other by $\pm$6 months. It was readily apparent that all results were dominated by ENSO events in the first two or three modes and that the evolution of ENSO necessitates more than one mode to explain the ENSO-related variability. Therefore, to focus the analyses on the Pacific, we have chosen to present results whereby the domain for the SVD analysis was restricted to that of the Pacific, although the results are not sensitive to this.

The main SVD analysis results we present are between $\nabla \cdot {\bf F_A}$  and SST for the first two modes. Results for SST with CMAP precipitation produce the same time series and pattern for SST, and therefore we also present results for correlative variables using regressions with the time series of the SVD modes.

Figs. 11 and 12 present the homogeneous correlation patterns of SST and $\nabla \cdot {\bf F_A}$  for the first two modes while Fig. 14 presents the time series. The corresponding patterns for precipitation are shown in Fig. 13 and the time series for the precipitation-SST SVD patterns are also given in Fig. 14. For $\nabla \cdot {\bf F_A}$  and SST, the SCFs for the two modes are 62.2% and 12.1% of the covariance in the Pacific domain (versus 39.5% and 15.4% for the global domain analysis). The $\nabla \cdot {\bf F_A}$  and SST time series are correlated 0.92 and 0.87 for the first two modes, and the maximum correlation is at zero lag. It is readily apparent that the time series of SVD1 are also highly correlated with ENSO indices, and for N3.4 the correlation is 0.90 for SST and 0.87 for $\nabla \cdot {\bf F_A}$. Of more interest is that the cross correlation is a maximum with N3.4 leading the other time series by 2 months (correlations 0.94 and 0.91, respectively). The precipitation time series are highly correlated with the others (0.93 with SST and 0.94 with $\nabla \cdot {\bf F_A}$) and in phase.

While the time series from SVD2 are negatively correlated with N3.4 at zero lag about $-$0.2 to $-$0.3, the correlations are 0.40 and 0.43 (SST, $\nabla \cdot {\bf F_A}$) with SVD2 leading by 10 months, and $-$0.65 and $-$0.48 with N3.4 leading by 7 months, strongly indicating the role of SVD2 in the evolution of ENSO. Thus SVD2 patterns with reversed sign occur some 10 months before SVD1, to be followed by SVD2 7 months later. For the 1979 to 1998 period, this sequence relates to the times of change of SSTs in Niño 4 (near the dateline) and Niño 1+2 (along the South American coast) regions, compared with those in the central tropical Pacific as given by SVD1 and Niño 3.4. Accordingly, we have formed a new index which we call the Trans-Niño index given by $ TNI =
SST_{{1+2}_N - SST_{4_N}}$ where the $N$ refers to normalization by the standard deviation of the SST anomalies for each time series [ Trenberth and Stepaniak, 2001]. The correlation of TNI with with the SST SVD2 time series is 0.8. Because N3.4 $\approx SST_{{1+2}_N} + SST_{4_N}$ it has zero correlation at zero lag with TNI and thus is orthogonal. Hence the combination of Niño 3.4 and TNI provides an efficient representation of ENSO through two different indices. The patterns associated with TNI are pursued in Trenberth and Stepaniak [2001].

The spatial patterns of SST in SVD1 reveal the strongest relationship with the Niño 3.4 region. The anomaly in that region extends throughout the tropical central and eastern Pacific of one sign and with boomerang-shaped opposite-signed anomalies at 20-30$^\circ$latitude in both hemispheres and in the far western equatorial Pacific. Positive values in the Indian Ocean, a weak dipole structure in the tropical Atlantic, negative values in the North Pacific and around New Zealand, and positive values in the southeast Pacific are all features associated with ENSO. Throughout the tropics there is a strong positive correlation with both the anomalies of associated precipitation and $\nabla \cdot {\bf F_A}$. Changes in precipitation depend upon the total field in which there is strong structure in the mean climatology, in particular the inter-tropical convergence zones (ITCZs) and the South Pacific Convergence Zone (SPCZ). Thus the dipole structure across 10$^\circ$N in the Pacific is emphasized in the precipitation, but not SSTs, as the ITCZ moves south and the SPCZ moves northeastward with El Niño. $\nabla \cdot {\bf F_A}$ is strongly related to both and seems to be in between, as is discussed next.

To show the actual anomalies corresponding to a unit standard deviation of the SST time series for SVD1, Fig. 15 presents the regression patterns for SST, precipitation, $\nabla \cdot {\bf F_A}$  and the vertically-integrated diabatic heating. The latter is derived as a residual from the NCEP reanalyses [ Trenberth et al., 2001a]. Anomalies in SST in the tropical Pacific slightly exceed 1.2$^\circ$C and correspond to a peak of 2.5 mm/day in the precipitation anomaly farther to the west near 170$^\circ$W on the equator, and about 18 $W m^{-2}$ in $\nabla \cdot {\bf F_A}$  and presumably the surface heat flux into the atmosphere. This would correspond to a surface evaporative rate of 0.6 mm/day. However, examination of results from the assimilating NCEP model integrations of the evaporation indicates only weak systematic associated evaporation anomalies of order 0.3 mm/day (not shown). For $\nabla \cdot {\bf F_A}$, anomalies just as large as in the eastern tropical Pacific, but of opposite sign, occur in the tropical western Pacific north of the equator. Of course for $\nabla \cdot {\bf F_A}$, the global mean has to be zero as the divergence of energy from one region shows up as convergence elsewhere. The diabatic atmospheric heating in Fig. 15 reveals heating of 50 $W m^{-2}$ in the Niño 3.4 region and cooling in a boomerang-shaped region to the west.

Similar relationships seem to hold for SVD2 in the tropics (not shown). However, the relationships among variables is quite different in the extratropics, and some parts of the tropical Atlantic. The positive correlations between SST and the other variables in the tropics in SVD1 patterns reverse in the North and South Pacific polewards of about 30$^\circ$. In these regions, the evidence suggests that the atmosphere predominantly drives the ocean changes, so that a divergence of energy out of a region is associated with increased flux out of the ocean and colder SSTs, consistent with changes in the atmosphere arising from teleconnections -- an atmospheric bridge -- from the tropics [ Lau and Nath, 1994; Trenberth et al., 1998].

5. Discussion

Precipitation is a direct indicator of the latent heating in the atmosphere, and this is a substantial part of the tropical atmospheric diabatic heating. The diabatic heating is sometimes called $Q_1$, and, ignoring a tiny frictional heating component, vertically integrated is given by

Q_1 = R_T +F_s +L(P-E)

where $P$ is precipitation and $E$ evaporation in the column, and $L$ is the latent heat of vaporization. The term $LE$ cancels a part of $F_s$ leaving the surface radiation and sensible heat flux. Therefore, $Q_1$ is not a driver of changes in moist static energy or total energy (cf. (1)) because changes in the state of moisture are internal and simply change the dry static energy at the expense of the moisture content. For this reason there is a strong compensation between the dry static energy and the latent component which occurs as the convergence of moisture in the low levels is realized as latent heating.

We have presented deduced covariability among a number of fields from several different datasets associated with ENSO. Qualitatively the results make reasonable sense but quantitatively several do not, and are in fact inconsistent. Trenberth and Guillemot [1998] evaluated the hydrological cycle in the NCEP reanalyses and concluded that the interannual variability in the tropical Pacific was much too weak (by about a factor of two). Comparisons of precipitable water and precipitation from the reanalyses with other sources, such as the CMAP precipitation dataset used here, suggest that this is the case. This also suggests that the variability in latent heating released in the atmosphere in the NCEP model is too low and it probably leads to underestimates of the diabatic heating. On the other hand, estimates of $\nabla \cdot {\bf F_A}$  are believed to be somewhat more robust owing to the cancellation of some errors, as the moisture is converted into latent heating. There is further suspicion that the estimates of precipitation from CMAP underestimate the amounts in the central Pacific associated with El Niño. Alternative evidence from other precipitation estimates suggests that there should be a net positive precipitation anomaly, and thus latent heating anomaly, when averaged over the tropics associated with warm ENSO events [ Soden, 2000]. Our results indeed suggest that there is large cancellation in OLR throughout the domain 30$^\circ$N to 30$^\circ$S and, because precipitation estimates over the ocean are in large part dependent on an algorithm that uses OLR, this may be artificially built into the CMAP estimates.

For the central tropical Pacific in warm ENSO events, from the regressions, we would conclude that about a 1$^\circ$C SST anomaly is associated with maximum rainfall anomalies of 2.5 mm/day, but this is suspected to be underestimated, as noted above. Even so it corresponds to diabatic atmospheric latent heating of over 70 $W m^{-2}$, yet the indirect estimates from the NCEP reanalyses yield only 50 $W m^{-2}$. Similarly, estimates of evaporation from the NCEP reanalyses appear to be underestimates as they are at odds with the rainfall rates and $\nabla \cdot {\bf F_A}$. However, patterns of evaporation with ENSO are complex as they depend upon not only air-sea temperature differences and relative humidity, but also wind speed (see Deser [1989] for an analysis of these dependencies and estimates of actual evaporation with ENSO events). Note that these estimates come from several different datasets, each with strengths but also weaknesses, and the latter undermine a quantitative physically consistent picture.

Nevertheless, in both SVD patterns in the tropics, positive SST anomalies are associated with increased heat flux into the atmosphere (presumably mainly latent energy through surface evaporation, as found by Deser [1989]). In contrast, increased convective precipitation and decreased OLR occur in somewhat different locations governed by where the surface convergence occurs, and this depends on the mean precipitation patterns, the mean SST and gradients in SST [ Lindzen and Nigam, 1987]. The released latent energy forms a source and driver for the dry static energy, leading to a divergence of the atmospheric transports largely through large-scale overturning that is governed by the diabatic heating internal to the atmosphere, but does not relate well to surface fluxes.

The implication is that the local surface flux of heat from the ocean to the atmosphere damps the SST anomaly, especially through evaporative surface heat fluxes which provide fuel for the precipitation. Transport of energy by the atmosphere occurs from regions of precipitation excess to regions of deficit and it is in the clear sky regions where the energy can most efficiently radiate to space (as seen in the OLR). The alternative is that some energy is transported to higher latitudes by midlatitude baroclinic storms. The tropical transport of energy, however, also drives the transport of moisture from the evaporative sources to the precipitation sinks in the low level return flow of the overturning circulation. $\nabla \cdot {\bf F_A}$  is primarily related, through the associated surface fluxes, to the source of moisture, which is transported by the low level atmospheric circulation and released as precipitation. To the extent that steady overturning dominates the circulation then these two are directly linked through the driving by the diabatic heating, and latent heating in particular, and the transport of the moisture to the regions where precipitation is realized.

Here we have outlined the contemporary relationships among several important climate variables. The evolution of ENSO and the implicit lag relationships manifested in the SVD1 and SVD2 patterns suggest that a systematic exploration of lead and lag relationships is warranted. However, the slow evolution of ENSO (as outlined for instance in Barnett et al. [1991] and Zhang and Levitus [1996]) is complex and expands the scope of this work to a point where it is necessary that these aspects should be pursued elsewhere [ Trenberth and Stepaniak, 2001; Trenberth et al., 2001c].

6. Conclusions

We used a case study which contrasted two different Januaries to illustrate the magnitude and importance of the variations from year to year in the atmospheric total heat or, more generally, energy budget. Anomalies in the extratropics in the surface fluxes between the ocean and atmosphere and the corresponding divergent energy transports within the atmosphere can exceed 120 $W m^{-2}$ in individual months, especially where regime-like behavior, such as that associated with the NAO, prevail. More generally, synoptic activity in the atmosphere adds large high frequency variability to the atmospheric transports and the surface fluxes.

In the tropics, the variability is not as large in magnitude but it extends over larger regions and is more persistent in time. A strong signal emerges associated with ENSO, in which the evidence suggests that the ocean mainly drives the atmosphere in terms of thermal forcing. Ample evidence from many studies has, however, shown how the ocean is driven by the atmospheric winds in the tropics. The surface fluxes damp the SST anomalies and provide energy to drive the atmospheric circulation. Because a key component of the surface fluxes arises from evaporation, which moistens the atmosphere, the atmospheric response depends on where the moisture is converged and realized as latent heating thus driving the large-scale overturning in the atmosphere and transporting energy to the sink regions.

The SVD analysis reinforces the primacy of ENSO as the dominant coupled mode of variability, as represented by time series of N3.4, although with clear evidence of the slow evolution of ENSO adding complexity. Changes in SST of about 1$^\circ$C in the central and eastern Pacific correspond to changes in surface fluxes and atmospheric divergence of $\sim$20 $W m^{-2}$. More than double these amounts occur in major ENSO events and thus surface flux anomalies of 50 $W m^{-2}$ over extensive regions can result for several months, thereby accounting for much of the change in ocean heat content. However, the positive and negative regions in the atmospheric divergence have to balance, unlike the changes in SST. The negative feedback between SST and surface fluxes can also be interpreted as showing the importance of the discharge of heat during El Niño events and the recharge of heat during La Niña events. Relatively clear skies in the central and eastern tropical Pacific during La Niña allow solar radiation to enter the ocean, apparently offsetting the below normal SSTs. Instead of warming the ocean locally, the heat is carried away by ocean currents and through adjustments brought about by Rossby and Kelvin waves, so that the heat is stored in the western tropical Pacific. This is not simply a rearrangement of the ocean heat, but also a restoration of heat in the ocean. Similarly, during El Niño, the loss of ocean heat, especially through evaporation into the atmosphere, is a discharge of the heat content, and both contribute to the life cycle of ENSO. These observations support the picture put forward by Barnett et al. [1991] based mainly on model results in which the SST anomalies are created by ocean dynamics and the response to wind forcing, and not local surface fluxes. However, they have been difficult to establish from observations and quantitative aspects are still uncertain. Nevertheless, the role of the surface fluxes and the diabatic component of the ENSO cycle should not be underestimated.

The positive correlations between $\nabla \cdot {\bf F_A}$  and SSTs in the tropical Pacific are reversed at higher latitudes and in some parts of the tropical Atlantic and Indian Oceans. A surprisingly strong pattern emerges over the South Pacific, although data are few in that region, and it seems to have a wave-2 structure which makes it similar in structure to the so-called Antarctic Circumpolar Wave [ Peterson and White, 1998]. However, current evidence suggests that it is driven by ENSO and mostly confined to the Pacific.

The exploration of the TOA energy budget exposes small but spurious changes in OLR of up to 5 $W m^{-2}$ that appear to be associated with orbital drift and changes in equator crossing times of satellites that have yet to be adjusted for in the datasets. We also note that recent CERES results from TRMM are incompatible with earlier ERBE results and those from the NOAA series of satellites. We further comment on the inconsistencies arising among the pictures of ENSO from the different datasets, which suggests that improved, more continuous and consistent observations and analyses are essential to make further progress.

We have also exposed intriguing lead and lag relationships among the variables and time series, in particular between SVD 1 and SVD 2, and between both with N3.4. The evolution of ENSO necessitates more than one mode to explain the ENSO-related variability, a point often not adequately appreciated by a number of analyses which simply use one ENSO index to ``remove'' the effects of ENSO linearly from time series [e.g., Jones, 1989; Christy and McNider, 1994; Zhang et al., 1996; Wigley and Santer, 2000]. We propose a second time series, TNI, as a simple second index important in the evolution of ENSO [ Trenberth and Stepaniak, 2001]. Other aspects of the evolution will be explored in Trenberth et al. [2001c].


This research was sponsored by NOAA Office of Global Programs grant NA56GP0247 and the joint NOAA/NASA grant NA87GP0105. We thank Bruce Wielicki for help with the CERES data.


Barnett, T. P., M. Latif, E. Kirk, and E. Roeckner, On ENSO physics, J. Clim., 5, 487-515, 1991.

Bretherton, C. S., C. Smith, and J. M. Wallace, An intercomparison of methods for finding coupled patterns in climate data, J. Clim., 5, 541-560, 1992.

Christy, J. R., and R. T. McNider, Satellite greenhouse signal, Nature,367, 325, 1994.

Deser, C., Meteorological characteristics of the El Niño/Southern Oscillation phenomenon, Ph. D. thesis, Univ. Washington, Seattle, 1989.

Hurrell, J. W., and K. E. Trenberth, Global sea surface temperature analyses: multiple problems and their implications for climate analysis, modeling and reanalysis, Bull. Am. Meteorol. Soc., 80, 2661-2678, 1999.

Jones, P. D., The influence of ENSO on global temperatures, Clim. Monitor, 17, 80-89, 1989.

Kyle, H. L., A. Mecherikunnel, P. Ardanuy, L. Penn, and B. Groveman, A comparison of two major Earth radiation budget data sets, J. Geophys. Res.,95, 9951-9970, 1990.

Kyle, H., et al., The Nimbus Earth radiation budget (ERB) experiment: 1975 to 1992, Bull. Am. Meteor. Soc., 74, 815-830, 1993.

Lau, N. -C., and M. J. Nath, A modeling study of the relative roles of tropical and extratropical SST anomalies in the variability of the global atmosphere-ocean system, J. Clim., 7, 1184-1207, 1994.

Lindzen, R. S., and S. Nigam, On the role of sea surface temperature gradients in forcing low-level winds and convergence in the tropics, J. Atmos. Sci.,44, 2418-2436, 1987.

Peterson, R. G., and W. B. White, Slow oceanic teleconnections linking the Antarctic Circumpolar Wave with the tropical El Niño-Southern Oscillation, J. Geophys. Res.,103, 24,573-24,583, 1998.

Reynolds, R. W., and T. M. Smith, Improved global sea surface temperature analyses using optimum interpolation, J. Clim., 7, 929-948, 1994.

Rieland, M., and E. Raschke, Diurnal variability of the earth radiation budget: Sampling requirements, time integration aspects and error estimates for the Earth Radiation Budget Experiment (ERBE), Theor. Appl. Climatol., 44, 9-24, 1991.

Smith, T. M., R. W. Reynolds, R. E. Livezey, and D. C. Stokes, Reconstruction of historical sea surface temperatures using empirical orthogonal functions, J. Clim., 9, 1403-1420, 1996.

Soden, B. J., The sensitivity of the tropical hydrological cycle to ENSO, J. Clim., 13, 538-549, 2000.

Trenberth, K. E., Signal versus noise in the Southern Oscillation, Mon. Weather Rev., 112, 326-332, 1984.

Trenberth, K. E., Using atmospheric budgets as a constraint on surface fluxes, J. Clim., 10, 2796-2809, 1997.

Trenberth, K. E., and C. J. Guillemot, Evaluation of the atmospheric moisture and hydrological cycle in the NCEP/NCAR reanalyses, Clim. Dyn., 14, 213-231, 1998.

Trenberth, K. E., and A. Solomon, The global heat balance: Heat transports in the atmosphere and ocean, Clim. Dyn., 10, 107-134, 1994.

Trenberth, K. E., J. M. Caron, and D. P. Stepaniak, The atmospheric energy budget and implications for surface fluxes and ocean heat transports, Clim. Dyn., in press, 2001a.

Trenberth, K. E., D. P. Stepaniak, J. W. Hurrell, and M. Fiorino, Quality of reanalyses in the tropics, J. Clim., 14, in press, 2001b.

Trenberth, K. E., and J. M. Caron, Estimates of meridional atmosphere and ocean heat transports, J. Clim., submitted, 2001.

Trenberth, K. E., and D. P. Stepaniak, Indices of El Niño evolution, J. Clim., 14, in press, 2001.

Trenberth, K. E., J. M. Caron, D. P. Stepaniak, and S. Worley, The evolution of ENSO and global atmospheric temperatures, J. Geophys. Res., submitted, 2001c.

Trenberth, K. E., G. W. Branstator, D. Karoly, A. Kumar, N-C. Lau, and C. Ropelewski, Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperatures, J. Geophys. Res., 103, 14,291-14,324, 1998.

Waliser, D. E., and W. Zhou, Removing satellite equatorial crossing time biases from the OLR and HRC data sets, J. Clim., 10, 2125-2146, 1997.

Wigley T. M. L., and B. D. Santer, Differential ENSO and volcanic effects on surface and tropospheric temperatures, J. Clim., submitted, 2000.

Wielicki, B. A., T. Wong, D. F. Young, B. R. Barkstrom, and R. B. Lee III, Differences between ERBE and CERES tropical fluxes: ENSO, Climate change or calibration? in Proceedings of the Tenth American Meteororloical Society, Conference on Atmospheric Radiation, 48-51 American Meteorological Society, Madison, WI, 1999.

Xie, P, and Arkin, P. A., Analyses of global monthly precipitation using gauge observations, satellite estimates, and numerical model predictions, J. Clim., 9, 840-858, 1996.

Xie, P, and Arkin, P. A., Global precipitation: A 17 year monthly analysis based on gauge observations, satellite estimates and numerical model outputs, Bull. Am. Meteor. Soc., 78, 2539-2558, 1997.

Zhang, R-H, and S. Levitus, Structure and evolution of interannual variability of the tropical Pacific upper ocean temperature, J. Geophys. Res.,101, 20,501-20,524, 1996.

Zhang, Y., J. M. Wallace, and N. Iwasaka, Is climate variability over the North Pacific a linear response to ENSO? J. Clim., 9, 1468-1478, 1996.

Julie Caron