Recent observations and model studies of the earth’s radiative energy balance have focused attention on the earth’s top of atmosphere (TOA) energy balance. This is the balance between the shortwave energy absorbed by the earth, which is represented by a spatially and temporally averaged absorbed flux , and the emitted longwave energy, which is represented by the corresponding averaged emitted flux . The TOA average net flux FN is defined as the difference between the two over the averaged area and time, which may be a local, regional, or global average. A global nonzero net flux represents a measure of imbalance between the energy being absorbed and emitted by the earth for the time interval in question. It is of interest to ask what the natural variability of the net flux might be and whether, during times of climate change, signals of important climate change processes might be detected against this natural background variation; examples of these signals include evidence of ocean heat storage, the effects of El Niño, and the radiative effects of volcanic eruptions. In this paper, the authors review the significance of the net flux, survey the observational evidence from a range of satellite instruments over several decades, and analyze some of the most recent observations from the Clouds and the Earth’s Radiant Energy System (CERES) program to determine what signals and what natural variability might be expected in the TOA net flux. Based on this analysis, the use of broadband radiation measurements for global climate change studies can be assessed.
We are concerned in this paper with the net flux (difference between absorbed energy and emitted energy) at the top of the atmosphere (TOA) and its use as a measure of climate change. This paper sets out to examine the net energy flux balance at the TOA measured using observations from polar-orbiting spacecraft. The paper presents an unprecedented review of past and present observations and introduces a new analysis of the most recent measurements. We then discuss what broadband signal we can expect to detect and consider how broadband and spectrally resolved measurements might be used.
The radiative energy balance of the earth is fundamental to an understanding of climate and climate change. The earth system is not one of thermodynamic equilibrium, as reference to any elementary text book will confirm; the system is not isolated, because energy is flowing through it, so the production of entropy must be determined using nonequilibrium statistical mechanics to describe what actually is a quasi steady state. Energy from the sun is absorbed by the earth, and energy from the earth is radiated back to space, so as to maintain a balance between the two at the TOA. Between the arrival and exit of these two streams of energy, a huge array of individual processes cascade the incoming energy down a chain of decreasing energy quality and increasing disorder. The photon stream arrives as a flux of high energy, with relatively few photons, and departs as a larger number of low-energy photons. In between, work is done and entropy is created (for relevant background, see Kleidon and Lorenz 2005; Read 2004).
This is a very high-level view of the system. The details of all these processes are of course vital to our understanding of many aspects of weather and climate, and it is the purpose of advanced climate models to capture the significant details of all the processes, at least in approximations that provide a sufficient accuracy to allow accurate climate forecasts to be made. However, it is equally important that our fundamental understanding of the principles that lie behind these detailed processes is sound; otherwise, the computer models will simply not predict the future accurately, however detailed and complex they may be. We consider this energy balance to occur through the TOA fluxes of shortwave (SW) energy absorbed by the system, (x, y, t), and of longwave (LW) thermal energy emitted by it, (x, y, t). Here, x and y denote horizontal spatial coordinates (e.g., latitude and longitude) and t is time. Then, at a time t, the net TOA flux, FN averaged over Δx and Δy, in a time series that extends over a total period T, can be defined as the difference between these quantities, with the sign convention (note that the opposite sign convention is sometimes taken, in which net flux is the emitted flux minus the absorbed; e.g., Andrews 2000) as follows:
Because the absolute values of fluxes can suffer from significant systematic errors (poor accuracy), it is common practice to define the flux anomaly for a multiannual time series, in which the average annual cycle and the averaged value of the time series are subtracted from the time series. For example, for the net flux anomaly,
where F̃N(x, y, T) represents the averaged annual cycle over the whole time series.
For simplicity, we will not write the functional dependences explicitly in every equation: we will do that only when it is important to the argument. Figure 1 illustrates the properties of the net flux on a global basis, using a monthly average for April 2003, from the Clouds and the Earth’s Radiant Energy System (CERES) experiment [shown is the Terra Flight Model 1 Edition 2D–TOA monthly average geostationary interpolation product (FM1 Ed. 2D SRBAVG Rev 1 GEO); Wielicki et al. (1996)]. This image has values of x = y = 1°; because it is a single monthly average, t = 1 month. It can be seen that the net flux, broadly zonal in nature and broadly symmetric about the equator, has many interesting anomalies: for example, over the Sahara and the Pacific Ocean and in greater detail in many other places. Over the whole globe, the net radiation sums approximately to zero. In the long term, we might expect a precise summation to zero. However, we actually know rather little about how closely the net flux tracks zero on monthly, annual, or decadal time scales, and this is one of the questions addressed in this paper. Of course, the TOA net radiation also exhibits a strong annual cycle as the elevation of the sun varies, though this is not shown in Fig. 1.
The variability of the shortwave, longwave, and net fluxes are clearly important to our understanding of the climate, how it works, and how it might change. Measurements of these parameters are required to challenge models of the system; in turn, the models must be able to reproduce the observed properties of such a fundamental aspect of global climate. Here, we address a number of questions that relate to our understanding of the balance between these energy fluxes, calling on a wide range of experimental measurements. Note that we specifically exclude an analysis of data from climate models for three reasons. First, such comparisons are major exercises that have been undertaken before (e.g., Cess et al. 1993, 1997; Potter and Cess 2004). Second, the use of “tuning” of the TOA fluxes in models complicates the interpretation of TOA fluxes and trends. Third and most importantly, we wish to establish experimentally and independently of models the real-world observed variability of the TOA net flux.
In this way, we propose to address the following questions: what are the time and space scales of variability of the earth’s radiative energy balance? How does the balance respond to perturbations? How close is the global TOA net flux to zero? Can broadband measurements achieve the accuracies needed to detect climate change phenomena such as changes in ocean heat storage? We will refer to a recent paper by Wong et al. (2006), in which decadal variations in net TOA flux and its consistency with ocean heat storage record were investigated.
2. The global energy balance, the net flux, and issues of equilibrium and steady state
If the power absorbed globally by the complete earth system from the solar energy flux is Pin and the power emitted to space in the infrared is Pout, we make the assumption that they are in balance in the long-term average if no further perturbations occur. However, instantaneously (meaning “instantaneous” on a short time scale in terms of typical climate scales, so the definition is dependent on the process in question) the equality between these fluxes may not be exact and may include a small component of “unbalanced energy,” Δp:
The Δp term can be thought of as “stored” energy if it is positive: that is, energy that has entered the system but is delayed in causing a surface or atmospheric temperature rise that would produce a balancing increase of outgoing thermal emission. For example, this may be associated with warming of the subsurface layers of the ocean through the circulation, following global warming at the surface. Thus, instantaneously there would be a net imbalance of energy at the TOA: that is, a nonzero globally averaged net flux, FN ≠ 0. If the forcing is removed (e.g., by stopping any further increase of greenhouse gases), after a certain characteristic time the net flux will return to zero. For example, if deep ocean circulations are involved, these characteristic time constants might be multiannual or decadal. Because there is a range of processes ranging from slow to fast, we might expect almost a continuum of response times from almost immediate to, for the slowest processes, centuries or millennia.
A negative Δp would represent incoming energy lost to the system on a time scale that is fast by comparison with the time constant for adjustment of the outgoing longwave energy flux (i.e., the time constant of the processes associated with thermal emission from the surface and lower parts of the atmosphere to space). In this case, the thermal response of the system would not have time to adjust immediately to the decrease in incoming energy. This might arise, for example, from a volcanic eruption, producing aerosol that reflects more shortwave energy back to space: such an event is fast enough that the thermal response (cooling) of the surface layers of the earth and its atmosphere cannot keep up, which would again produce a nonzero net flux, but in the opposite sense to the storage example. The characteristic time constants associated with these negative perturbations to the net flux are one or two years, which are determined, in the case of a volcanic eruption, by the time constants associated with the insertion and removal of volcanic aerosol into the stratosphere (tropospheric aerosol can be removed on much shorter time scales, through dynamical processes involving cloud, rain, and water vapor) and by the characteristic thermal response times of the system.
Of course, there are many different processes that instantaneously contribute to the energy imbalance term. For some of these, Δpi is positive (storage); for others, it is negative (loss). If we assume a total of k linear processes (linear at least for small perturbations), we can write the total effect as . We must recall that each of these k processes will have a different characteristic time constant, so there will be a wide spectrum of responses to any given perturbation. The total effect will presumably be one of a slowly changing continuum of processes.
where is the SW-averaged absorbed downwelling flux; is the LW-averaged emitted upwelling flux; S = S0/4; S0 ≈ 1361 W m−2 is the solar constant (Kopp et al. 2005); A is the albedo of the atmosphere; σ = 5.6696 × 10−8 W m−2 K−4 is the Stefan–Boltzmann constant; Ts ≈ 288 K is the global average surface temperature; TE ≈ 254 K is the effective blackbody emission temperature of the earth; Δpi is the unbalanced energy for the ith process; and g = σ(Ts4 − TE4)/σTs4 ≈ 0.40 is the normalized greenhouse parameter.
On the basis of Eq. (4), we might search for evidence from measurements of TOA net flux imbalances if we suspect the earth’s climate to be changing. However, as we note later, this would require an accuracy of a few tenths of W m−2. Theoretical studies using climate models are of value in judging how large a net flux signal (departure from zero) might be expected. To set the scene and the scale of likely net flux perturbation, we consider the work by Hansen et al. (2005) shown in Fig. 2.
The top panel of Fig. 2 shows the individual radiative forcings included by Hansen et al. in a simulation of the changing climate as the concentrations of greenhouse gases CO2, CH4, and others are increased. Note the positive radiative forcing (a warming of the planet) resulting from increasing greenhouse gases and the opposing effect (cooling) caused by both background tropospheric and stratospheric (mainly volcanic) aerosols. The bottom panel of Fig. 2 shows the calculated net flux at the TOA. This shows two notable features: a series of negative “spikes” in the net flux, which coincide with volcanic eruptions (e.g., Pinatubo in 1991 and Krakatoa in 1883), and a slow rise in positive net flux from about 1960 onward, which Hansen et al. (2005) ascribe to increasing ocean heat storage as the earth warms and some of the additional energy in the system is distributed within the oceans.
Thus, according to these simulations, we should expect slow departures on the order of ΔFN = 1 W m−2 to occur on a decadal scale because of slow ocean circulation processes, because the whole ocean is involved in sequestering the surface warming and spreading the extra heat around the globe; on the other hand, according to these simulations, volcanoes have much shorter, opposing effects, perhaps lasting a year or two, of up to about −2 to −3 W m−2 (the reader is reminded that these figures are global averages). Figure 2 also suggests that this negative imbalance could become a more permanent feature if the rate of volcanic eruptions was greater, as it has been in the past, leading to a permanent cooling of the planet.
An important result is that the predicted magnitude of the Δpi terms is small (Hansen et al. 2005), which increases the difficulty of detecting them using satellite-borne radiometers against natural internal variability, instrument noise, absolute uncertainty, and sampling uncertainties. Current levels of absolute accuracy make this detection difficult. Work so far (Wong et al. 2006) has involved the use of anomaly data, which are less sensitive to absolute error. Despite this, we can see that it may be possible to provide a meaningful test of the validity of a model of the climate system if we demand that it satisfies observed TOA SW, LW, and net fluxes and possibly even limitations on the entropy production rate associated with all the internal processes that link and (Goody 2000).
3. Observational evidence: Measurements of TOA net flux
What is the evidence for departures of the global net flux from zero? We consider a number of sources. We begin by reminding ourselves of early studies that pioneered the idea of making measurements of global parameters such as FN from space. Although these early attempts may be of limited (and often poorly defined) accuracy, they have unique value in that they were taken in a period when no other global measurements existed. We therefore should try to use them as far as the inherent uncertainties will allow: we try to assess these uncertainties. We also take into account a range of more recent studies, including data from specific satellite sensors such as High Resolution Infrared Sounder (HIRS; Mehta and Susskind 1999), Advanced Very High Resolution Radiometer (AVHRR; Stowe et al. 2002), Earth Radiation Budget Experiment (ERBE; Barkstrom 1984), and the International Satellite Cloud Climatology Project (ISCCP; Rossow and Dueñas 2004), and we analyze some of the most recent observations from the CERES project (Wielicki et al. 1996). Other techniques, such as Earthshine (Pallé et al. 2004, 2005), the Global Dimming project, and others that provide only one of the two fluxes needed to deduce net flux or surface measurements only, as from the Baseline Surface Radiation Network (BSRN; Ohmura et al. 1998), have not been included, despite the high quality of some of these, notably BSRN.
a. Early results, 1962–95
It is important to take account of early estimates of the net flux, because these data provide a much larger time scale by which to judge climate variability. We will consider some early analyses of ERB data that were reported up to about 1998.
A number of these measurements are listed in Table 1. They range from early Nimbus experiments by Vonder Haar and coworkers in the 1970s (Vonder Haar and Suomi 1971; Ellis and Vonder Haar 1976), the Nimbus-6 ERBE wide- (Jacobowitz et al. 1979) and narrow- (Campbell and Vonder Haar 1980b) field-of-view (FOV) radiometers, Nimbus-7 ERB (Jacobowitz et al. 1984), the National Oceanic and Atmospheric Administration (NOAA) series of scanning AVHRRs (Lucas et al. 2001), the French Scanner for Radiation Budget (ScaRaB) radiometer that operated in 1994–95 (Kandel et al. 1998), and the ERBE scanner (1985–89; Barkstrom et al. 1989). Not all these data are reported with a comprehensive error analysis, so a rigorous uncertainty estimate is not possible. Instead, we have taken a simple average and calculated the scatter of results around this mean as some indication of the variability of the results. Over the period 1962–95, this yields a value of
Can we test to ascertain whether this standard deviation about the mean is reasonable? Strictly, we cannot, because not all the studies reported an error analysis. However, the range of uncertainties that are quoted in these works is quite sufficient to account for the standard deviation that we obtain, ±4.0 W m−2. For example, Kandel et al. (1998) give uncertainties of ±5.5 W m−2 for SW flux and ±2.3 W m−2 for LW flux (monthly average) for the ScaRaB radiometer. Barkstrom et al. (1989) quote ±5.5 W m−2 for ERBE, and Wielicki et al. (1995) quote a range of 1 − σ errors for the net flux for ERBE, from ±3.1 W m−2 in the monthly averaged regional 5-yr trend to ±6.4 W m−2 in the monthly regional-scale average.
We might ask if more recent work on uncertainties can throw more light on the variation of the mean we give earlier for the older experiments. Much welcomed, for example, is a recent paper by Loeb et al. (2009) that provides a valuable and very thorough description of the uncertainties of the CERES and ERBE LW, SW, and net fluxes. These authors quote 2 − σ (95%) uncertainties of ±7.5 W m−2 for the ERBE day plus night LW case and of ±4.0 W m−2 for the SW case. Combining these errors quadratically (if independent) would result in ±8.5 W m−2 for the ERBE net flux uncertainty. CERES is found to be about half this value, at about ±4.5 W m−2 in the net flux at the 2 − σ level. This more detailed and exacting analysis enables us to draw two conclusions. First, bearing in mind that this latest work quotes 2 − σ errors, the absolute values of ERBE net flux uncertainty reported in Loeb et al. (2009) broadly support the 1 − σ result for the monthly/regional average (±3.1 W m−2 in monthly averaged regional 5-yr trend to ±6.4 W m−2 in the monthly regional-scale average) quoted in Wielicki et al. (1995). Second, these updated error analyses would be quite sufficient to explain the standard deviation in the mean of the older measurements that we considered earlier. At least we can say that the standard deviation of the mean that we obtain is fully able to account for the value we have obtained without necessarily looking for other causes, such as natural variability. Of course, this does not mean that significant natural variability is or is not occurring; merely, it means that measurement accuracy is a dominating effect.
b. ERBE/ERBS, HIRS, AVHRR, and ISCCP results, 1985–99
Here, we look for information on the net flux within detailed analyses from the ERBE systems, which is published in Wielicki et al. (2002) and in modified form in Wong et al. (2006). Figure 6 of Wong et al. (2006) shows, among other things, measurements of the anomalies (strictly, they show the anomaly in the reflected, not the absorbed SW radiation), , and ΔFN for the tropical latitude range 20°N–20°S for the years 1985–99 from the ERBE/Earth Radiation Budget Satellite (ERBS) nonscanner wide-field-of-view radiometer (Ed 3, Rev 1 deseasonalised tropical mean dataset). Also shown in the figure are flux anomalies derived from two other sources (the HIRS instrument provides LW only, so it was not included; Mehta and Susskind 1999). These other sources were the AVHRR sensor (AVHRR Pathfinder ERB data for both LW and SW; Stowe et al. 2002); and the data derived from the ISCCP version FD cloud archive for both LW and SW (Zhang et al. 2004). All data were shown as anomalies using the average from 1985–89 as a baseline. Because these results are comprehensively discussed in Wielicki et al. (2002) and Wong et al. (2006), we shall reserve our comments here only to the relevance of this work to our study of the variability of net flux.
Wong et al. (2006) point out that the datasets agree to within a few W m−2, except for the AVHRR data. In the latter case, it appears that issues of intercalibration between different satellite sensors in the AVHRR series and probably of orbit/sampling problems cause much larger variations. Because the HIRS measurements do not give an estimate of net flux, there were only two datasets (the ERBS nonscanner and the ISCCP results) that could be compared for net flux. Wong et al. suggested that the net flux variability for these two datasets was in the range ±2 to ±4 W m−2, outside the period affected by Pinatubo. Inspection of the results in Wong et al. (2006) shows that the variability in the net flux is up to about 5 W m−2 on a month-to-month time scale and larger (up to about 10 W m−2) on multiannual time scales. The peak net flux anomaly caused by Pinatubo is clearly visible and was found to be a factor of 2 larger for the ISCCP data than for ERBS (the eruption causes a perturbation of about −6.5 W m−2 in ΔFN, as observed by ERBS, and about −13 W m−2 for ISCCP). This feature of the ISCCP analysis is now understood to be attributed to a double correction for aerosol scattering and is not due to any other cause (B. A. Wielicki 2009, personal communication).
Along with the reported variability of ±2 to ±4 W m−2, which showed structure at periods from months to years, Wong et al. (2006) report evidence for changes in the net flux between the two 4-yr periods 1985–89 and 1994–97, based on their analysis. These are reproduced here in Table 2 for ERBS wide-FOV Ed 3, Rev 1 for the ISCCP FD and also for the AVHRR data. Despite the misgivings of Wong et al. (2006) about the latter dataset, a remarkably close range of values for the change in net flux between the two periods, +0.7 to +1.8 W m−2, is evident. Given the background variability of up to ±4 W m−2, this magnitude of signal must be at the limit of detection. It is noted from Table 2 that the ISCCP FD data for the SW show a decrease over this period of −2.40 W m−2, which is extremely close to the −2.10 W m−2 reported for ERBS. However, the SW trend for AVHRR is of opposite sign, at +0.7 W m−2.
c. CERES, 2000–present
A new generation of polar-orbiting ERB measurements from satellites has been introduced in the CERES experiment (Wielicki et al. 1996). Three CERES instruments have been launched into low Earth orbit, on the Tropical Rainfall Measurement Mission (TRMM), Terra, and Aqua satellites of NASA. Terra was launched in March 2000, and Aqua was launched in July 2002; both are still operating in tandem at the time of this writing. We are in an unprecedented period of measurement opportunities, because our planet is observed by ERB instruments on Terra and Aqua and also on Meteosat [the Geostationary Earth Radiation Budget (Harries et al. 2005) experiment is currently operating on Meteosat-8 and Meteosat-9]. In recent publications, SW radiation measurements of the CERES instruments have been carefully examined by Loeb et al. (2007a,b), with a particular eye on comparing these results with the Earthshine measurements (Pallé et al. 2004, 2005), which have shown a large rise in reflected solar radiation since about 2000.
The two papers by Loeb et al. have examined the SW reflected radiation (i.e., the albedo of the earth) for both the tropical zone (30°N–30°S) and on a global basis. The authors show deseasonalised monthly anomalies for the Terra and the Aqua instruments for August 2002–March 2005 and fit linear functions to these data. The instruments are affected by a spectral degradation, the effect of which is better accounted for in Terra instruments (N. Loeb 2007, personal communication). This causes a small drift of Aqua regression line, but the authors believe that this effect is not present for the Terra instrument.
The gradient of the linear fit for SW data for Terra CERES was found to be +0.031 W m−2 per decade; for Aqua CERES, it is −3.5 W m−2 per decade. Loeb et al. (2007b) discuss in great detail the statistics of this comparison, as well as a number of others. These analyses seem very conclusive and indicate little support for the large excursion of SW anomaly between the years 2000 and 2005 obtained by the Earthshine experiment (Pallé et al. 2005; Wielicki et al. 2005). These measurements produced a trend in albedo anomaly that is larger but in the same sense as ERBE up to the year 2000, but they thereafter show an increase of albedo (Pallé et al. 2004), whereas Wielicki et al. (2005) obtain a continuing decrease from the ERBE data.
Figure 3 data, provided by T. Wong and N. Loeb, show the net flux measured by three instruments: ERBE/ERBS nonscanner from 1985 to 1999 (see earlier discussion), CERES/Terra from 2000 to date [Ed 2D SRBAVG Rev 1 product, archived at the Langley Distributed Active Archive Center (DAAC)], and CERES/Aqua from 2002 to date (Ed 2A SRBAVG Rev 1 product). Linear fits have been made to each of the three elements to the data: the two ERBE periods and CERES. Two sets of curves are shown, one for 20°N–20°S, with a time resolution of 36 days for ERBE and 30 days for CERES, and the other for quasi-global (actually 60°N–60°S) data, with resolutions of 72 and 30 days, respectively. The higher values of net flux for the tropical data reflect, of course, that the net flux is a measure of the net input of energy, which in equatorial regions is strongly positive (see Fig. 1). In the quasi-global case, the net flux is nearer to zero, as expected. In the tropical case, the annual cycle shows a double positive peak, which is caused by the movement of the sun in and out the 20°N–20°S band.
In the quasi-global ERBE case, the relatively poor sampling of the annual cycle by this instrument gives rise to the rather angular shape. In the CERES case, the much improved sampling by this instrument gives rise to much smoother curves in both the tropical and quasi-global cases. The gaps in the data are caused by instrument change over or malfunction; we shall comment further later on the possibility of improving the accuracy of the net flux time series shown in Fig. 3 through the use of intercalibrations using measurements taken by CERES TRMM in 1998 and 2000.
Many interesting features emerge from Fig. 3 that are relevant to our interest in the stability of the net flux. The mean level of net flux for the tropical band is between about 62 and 67 W m−2, and this mean value (and indeed the extremum values) does not show a consistent shift with time or in the transition between ERBE and CERES. However, we can see a year-to-year variability in the range ±2 to ±4 W m−2. We note that the agreement in the overlap period between the two CERES instruments (on the Terra and Aqua satellites) is excellent.
For the near-global data, the sampling of the CERES instrument is more regular and includes greater sampling of polar regions. Therefore, the CERES data were sampled so as to include only 60°N–60°S, to be more consistent with the ERBE observations. The mean level of net flux lies in the range 21–25 W m−2. If the CERES data were not subsampled in this way, then the full global net flux cycle lies much closer to zero, ranging between about −5 and +15 W m−2. The two CERES instruments overlap is excellent.
If the net flux anomalies for the tropical 20°N–20°S zone are formed from Fig. 3 [following Eq. (2)], we obtain the set of curves shown in Fig. 4. The common average annual cycle [F̃N in Eq. (2)] was obtained interpolating CERES data to a 36-day grid (i.e., ERBE), and the resulting time series was then averaged with ERBE data to form a seasonal cycle of 10 values per year to be subtracted from the absolute ERBE flux. In the same way, measurements from ERBE were interpolated to create a seasonal cycle of 12 values per year to be subtracted from CERES time series. For completeness, we also show the LW and SW anomalies to illustrate the degree of variability of the flux anomalies in this monthly 20°N–20°S average data. Peak-to-peak variations of the net flux anomaly are between ±2 and ±4 W m−2. Slow variations with a period of a few years have amplitudes of ±2 W m−2. The signal of Pinatubo is clear, at about −5 W m−2 in the net flux anomaly: note that partial compensation occurs between the LW and SW effects of the volcanic cloud.
To suppress the high-frequency variation, we have smoothed these data with a 6-month running mean. If we continue to use a single average annual cycle for the entire 1985–2006 period, we obtain the smoothed curve shown in Fig. 5. This shows an interesting cycle of period between about 2–4 yr in the SW and LW anomalies, which is less prominent in the net flux. It is not clear what these interannual variations might be due to (though the period is in the range typical of ENSO events, which should be further investigated). The net flux shows variability on the annual time scale.
In this smoothed version, it is easier to see that the data show large variability, outside that due to Pinatubo, from about ±2 to ±4 W m−2, possibly departing more from the zero line with time from the ERBE to the CERES data. However, if we take each of the three blocks of data separately (i.e., ERBE from 1985–93 and 1994–98 and CERES from 2000–05) and form a separate annual cycle for each period, a substantial part of the variability disappears, as we see in Fig. 6, where this has been done. We find that these departures from zero all collapse to within about ±0.5 W m−2 of zero.
Therefore, the largest part of the variability outside Pinatubo seen in Fig. 5 is due to there being differences in the mean annual cycle between the data blocks, which may of course include absolute error of intercalibration. These differences vary between less than ±1 W m−2 for the Aqua springtime peak to about ±5 W m−2 in the worst case, for ERBE. It is interesting to speculate as to whether these differences in the annual cycle are caused by some interannual variability of the climate system or are due to instrumental uncertainties. A very recent paper (published during the review of the present paper) by Loeb et al. (2009) has investigated the uncertainties in the TOA net (and constituent) fluxes for the CERES experiment, concluding that the 2 − σ uncertainty in the monthly average net flux is ±4.2 W m−2. This suggests that the interannual variability in the annual cycle could be fully explained as due to absolute error.
It is noticeable in Fig. 7 that the variability between the annual cycles has decreased between ERBE and CERES, also suggesting an instrumental and not a geophysical cause. However, we do note that, although the spring Aqua annual cycle curves lie closely on top of one another, the northern summer minimum and autumn peaks show larger interannual differences (nearer ±1.5 W m−2), which may indicate a small residual geophysical effect.
This variation of the averaged annual cycle between data blocks nevertheless represents something of a dilemma. Whether it is caused by limitations of absolute accuracy (as seems likely from Loeb et al.) or real-world interannual variability, it nevertheless represents a significant (circa ±4 W m−2) uncertainty in a parameter, the TOA net flux, that is a crucial parameter in climate studies (e.g., in terms of ocean heat storage) or of other processes, perhaps involving clouds. So, it is extremely important to devise ways of removing this uncertainty or of understanding its cause more precisely.
The problem of data gaps and the absolute accuracy of the data on either side of them can be approached in several ways: for example, by using data from CERES TRMM to span the gap between ERBS and CERES Terra. To address the whole issue of absolute accuracy in a more fundamental way, however, Loeb et al. (2009) have put forward a procedure in which a model estimate of ocean heat storage (+0.85 ± 0.15 W m−2; see Hansen et al. 2005) is taken to be correct and the measured fluxes are adjusted toward these calculated fluxes, within the range of uncertainty appropriate to the measurements. This approach is interesting, but the residual interannual variability of about ±1.5 W m−2 mentioned earlier, if confirmed, might remain a problem to be resolved.
To summarize, this initial analysis of the net flux signals in the combined ERBS–CERES dataset indicates the following:
The absolute net fluxes detected by the ERBE and the CERES experiments indicate an interannual variability in the range ±2 to ±4 W m−2 for the tropics and smaller, perhaps ±1 to ±2 W m−2, for the quasi-global case (Figs. 3, 4). The tropical (20°N–20°S) net flux shows a mean value of about 62–67 W m−2 and an annual amplitude of about ±20 W m−2. In the quasi-global case, the corresponding values are 21–25 W m−2 and ±15 W m−2 (Fig. 3).
High-frequency (unfiltered), intermonthly variability in the net flux anomaly is typically up to about ±2 W m−2, with slower (multiyear to decadal) variations also up to ±2 W m−2; Pinatubo is very clear (Fig. 4).
After smoothing with a 6-month filter, the net flux anomalies show very small (few tenths of 1 W m−2) variations on the monthly scale; interesting interannual variations of up to ±3 W m−2 on ENSO-like periods; and clear evidence of the Pinatubo eruption (Fig. 5).
The smoothed anomalies show that using separate average annual cycles for each data “block” produces a net flux closer to zero, with less variability. Using separate annual cycles for the three main data blocks, 1985–93, 1994–99, and 2000–06, largely removes the lower-frequency variability seen in the anomaly formed using a single average annual cycle. There remains a variability, well centered on zero, of ±0.5 to ±1 W m−2. However, it is not clear whether the interannual variability in the annual cycle and offset is due to real climate signal or error resulting from sampling and instrumental effects (Figs. 6, 7), though the work by Loeb et al. (2009) indicates that absolute uncertainty may be the dominant source of error.
Overall, although the detection of slow (decadal) increases in net flux on the order of ≤1 W m−2 is obviously easier if smoothing is applied, at frequencies higher than those we wish to detect (according to Nyquist sampling rules), we nevertheless must be aware that climate variation signal may be lost or misinterpreted unless great care is taken in forming anomalies from the absolute signal variation. Interannual variability in the annual cycles subtracted from the data may contain real signal of change.
This analysis has, in passing, confirmed that the intrinsic precision being achieved by the CERES instruments is excellent. The interannual sensitivity to changes in net flux appears to be better than ±1 W m−2. However, the benefits of such precision have to be realized amidst measurement uncertainties (especially because of absolute uncertainty and sampling the cloud field) that are serious. In the present situation, it would seem that, because some real signal variability may be contained within the year-to-year annual cycle variability, the discussion of interannual and decadal variability in net flux anomalies should not assume that real signals on the order of ±1 W m−2 can be reliably detected.
Nevertheless, the possibility exists of further improving the intercalibration of data blocks by using any interconnecting measurements. It was noted (N. Loeb 2007, personal communication) that measurements taken by CERES TRMM in 1998 and 2000 overlap both ERBS and CERES Terra (albeit only for one month), and can therefore be used, in principle, to intercalibrate the observed values.
The problem of experimentally determining the net TOA radiative energy balance of the earth and using this information to draw conclusions about any global planetary energy imbalances or to monitor the evolution of the earth’s climate is an extremely difficult one. Nevertheless, it is clear from our study that the state of the art of measurements of LW, SW, and therefore net fluxes has developed to a state of very high quality, which makes their use in global net energy balance problems at least a possibility.
The problems that face us include the requirement for high absolute and relative radiometric accuracy (accuracy and precision) and long-term stability in the spaceborne instruments and their calibration; sampling the high degree of variability in space and time of the atmosphere and the cloud field; the rather weak mathematical tools we have available for sampling the highly variable system that faces us; and trying to do this with a global observing system that is generally not optimized for climate monitoring (often being driven more by the requirements of meteorology on one hand and one-off research programs on the other).
We have presented the evidence of the observations; both early measurements; and more recent, better-calibrated systems. We have found significant variability in the net flux and its components, the magnitude of which depends on the degree of smoothing of the data. Early work, up to the late 1980s, shows a standard deviation in the mean of 10 independent measurements of about ±4.0 W m−2 in a mean of 4.1 W m−2. More modern measurements in the 1990s and 2000s show variability of between ±2 and ±4 W m−2, depending on smoothing. Generally, this variability lies within a few W m−2 of zero and is fairly symmetric about zero. Recent work (Loeb et al. 2009) published while the present paper was reaching the end of its review stage suggests that, of the primary sources of uncertainty, that resulting from absolute calibration dominates (at as large as ±4.2 W m−2 for CERES), whereas other error sources, such as sampling error and real geophysical variability, are about one order of magnitude lower. In our work, unexplained variability of up to ±1.5 W m−2 in interannual fluxes measured with the same instrument suggest that the uncertainty resulting from processes other than absolute calibration might be a little larger than ±0.5 W m−2, perhaps closer to ±1.5 W m−2, but this remains to be more accurately assessed. For now, it would appear that the dominant cause of variability in the net flux is due to absolute calibration uncertainty.
Set against these considerations, the purpose of this paper was to investigate whether ERB measurements are in reality capable of making useful measurements that can be applied to tests of climate model predictions or to monitor the state of the planetary system. Earlier, we set up a number of specific questions (section 1), and the answers we have found on the basis of this study are in the following subsections.
a. What are the scales of variability of the earth’s radiative energy balance? How does this balance respond to perturbations?
The observations show that volcanic eruptions can disturb primarily the SW component of the energy balance, and over a period of a few years this can cause a global imbalance of about −10 W m−2 (loss of energy to the planet; see Fig. 4). In the tropics, this is larger, perhaps greater than −15 W m−2. If large eruptions were more frequent, as they have been in the geological past, negative imbalance would be larger and more frequent, eventually leading to a new balance as a colder world.
Outside of large perturbations such as volcanoes, there is evidence that the net balance varies on a time scale of 2–4 yr or so, with a smaller amplitude of a few W m−2 about a mean, which we can only assume is within a few W m−2 of zero (Figs. 5, 6). Because ENSO/La Niña events involve the exposure of relatively colder or warmer seawater to the atmosphere in the Pacific, then we should expect ENSO to cause variations in the energy storage term in Eq. (4). Thus, the slow, monotonic increase in the ocean heat storage suggested in work by modelers (e.g., see Fig. 2) should be thought of as being modulated with this sort of period by ENSO. Slow variations such as those seen in Figs. 5 and 6 could be signals of ENSO modulating the amount of stored energy (Köhl and Stammer 2008).
On the time scale of one or two months, the high-frequency variability of the net flux of up to ±4 W m−2 seen within the observations of each individual sensor (Fig. 5) seems to be random, probably driven by the variability in the cloud field.
b. How close is the global TOA net flux to zero?
The few observations that do exist for the 1970s up to the mid-1980s indicate that the net flux balance of the planet was between 0 and 8 W m−2. We have no quantitative possibility of assessing the statistical significance of this result, because of the absence of error analysis in some of the published results, so it might be more correct in saying that the result indicates that it is statistically unlikely, on a 1 − σ basis, that the net flux was negative during this period.
In the 20 yr since 1985, there is no evidence that global FN is significantly out of balance, within a few W m−2 (Figs. 3, 4). The problem of an absolute determination of net flux is extremely difficult because of limitations in absolute accuracy and (to a lesser extent) because of sampling errors.
Because of the absolute measurement difficulties, researchers use relative measures such as net flux anomaly. Recent observations of this parameter (Figs. 3, 5, 6) indicate that, other than at times of volcanic eruptions, departures from zero net flux anomaly are near ±1 W m−2 for time scales of 6 months and longer and within ±2 to 4 W m−2 on a monthly time scale.
As well as we can tell, during the 6–18 months after a major volcanic eruption, the planet might be out of balance by about −10 W m−2. Outside such events, the planet appears to be usually within a few W m−2 of balance.
c. Can broadband measurement achieve the required accuracies needed to detect climate change phenomena such as changes in ocean heat storage?
The instantaneous instrumental precision possible with modern, well-designed systems is probably high enough (ca. few ×0.1 W m−2), though the issue of stability and drift of components of the instrumentation is still a limitation (Wong et al. 2006).
The most serious limitation would appear to be the uncertainty associated with absolute calibration (Loeb et al. 2009), though significant uncertainty also arises from sampling errors.
Given the evidence of the last 20 yr of observations, however, the natural variability of the climate system and the sampling uncertainties indicate that reliably detecting a change of TOA net flux of about +1 W m−2 over a decade is extremely challenging. If an adequate system of multiple satellite instruments and careful intercalibration between them are not available, then the task will remain almost impossible. To achieve this requires either (i) absolute calibration accuracy in each sensor and in its sampling to be able to interpolate across data gaps or (ii) overlapping measurements of instruments with high precision and good time and space sampling. Future “benchmark” climate measurement systems will focus on both the intercalibration and the need for traceable, high absolute accuracy.
In the future, a combination of broadband measurements (which are relatively inexpensive and can be deployed on several satellites) plus spectrally resolving instruments (more expensive, but on fewer platforms) may be optimal. The resolved spectrum contains more independent pieces of information than a broadband radiometer, but it is more complex and difficult to calibrate as well. The combination should be developed in unison to optimize the system.
We are grateful to colleagues in the CERES project at the NASA Langley Research Center for the supply of CERES data. In particular, Drs. Dennis Keyes, Bruce Wielicki, and Takmeng Wong were most helpful. Data for Table 1 appeared in a Ph.D. thesis by Dr. Laila Read, and Dr. James Hansen provided Figure 2. Our thanks go to Dr. Norman Loeb for his help and for comments on the draft manuscript.
We acknowledge valuable comments from two reviewers, who drew our attention to a valuable paper on CERES uncertainties, which was published after the review of this paper.
Corresponding author address: John E. Harries, Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom. Email: email@example.com