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  • View in gallery

    Total number of SST observations in COADS for 1950–79.

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    Average monthly standard deviation of all Januarys between 1950 and 1979 that have greater than 10 observations month−1 for (a) surface wind (normalized by climatological Vs, as a percentage) and (b) cloud cover (as a percentage).

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    Annual mean net surface shortwave uncertainties (W m−2): (a) systematic, (b) random, and (c) total.

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    Pacific Ocean lag correlations, as a function of latitude, for the departures from the zonal means of (a) cloud cover and (b) surface wind speed.

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    Zonal and climatological annual mean global ocean surface net SW uncertainty bounds for (a) the full year, (b) DJF, (c) MAM, (d) JJA, and (e) SON.

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    Annual mean net surface longwave total uncertainties (W m−2). Color scale same as Fig. 3. (a) The full year, (b) December–February (DJF), (c) March–May (MAM), (d) June–August (JJA), and (e) September–November (SON).

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    Zonal and climatological annual mean global ocean surface net LW uncertainty bounds.

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    Annual mean latent heat uncertainties (W m−2) for (a) the exchange coefficient (systematic), (b) surface wind speed (systematic), (c) moisture gradient and correlation terms (systematic), and (d) the total. Note that Figs. 3, 6, and 8 have the same color scale.

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    Zonal and climatological global ocean surface LH uncertainty bounds for (a) the full year, (b) DJF, (c) MAM, (d) JJA, and (e) SON.

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    Annual mean sensible heat uncertainties (W m−2) for (a) the exchange coefficient (systematic); (b) wind speed, sea surface temperature, and surface air temperature (systematic), and (c) the total.

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    Zonal and climatological annual mean global ocean surface SH uncertainty bounds.

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    Annual mean net surface heat flux uncertainties (W m−2): (a) random, (b) systematic, and (c) total.

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    Zonal and climatological mean global ocean surface net heat flux uncertainty bounds for (a) the full year, (b) DJF, (c) MAM, (d) JJA, and (e) SON.

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    Zonal and climatological mean global ocean surface flux (black line is the adjusted Oberhuber) uncertainties (error bars) and the average (white line) ± one standard deviation (shading) of the AMIP simulations for (a) annual mean net shortwave radiation and (b) DJF latent heat.

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    Zonal mean DJF global ocean total LH flux total uncertainty (thin bars) and that resulting when the systematic surface wind speed uncertainty is reduced by 50% (thick bars).

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Uncertainties in Global Ocean Surface Heat Flux Climatologies Derived from Ship Observations

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  • 1 Program for Climate Model Diagnosis and Intercomparison, Lawrence Livermore National Laboratory, Livermore, California
  • | 2 Department of Land Air and Water Resources, University of California, Davis, Davis, California
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Abstract

A methodology to define uncertainties associated with ocean surface heat flux calculations has been developed and applied to a global climatology that utilizes a summary of the Comprehensive Ocean–Atmosphere Data Set surface observations. Systematic and random uncertainties in the net oceanic heat flux and each of its four components at individual grid points and for zonal averages have been estimated for each calendar month and for the annual mean. The most important uncertainties of the 2° × 2° grid cell values of each of the heat fluxes are described. Annual mean net shortwave flux random uncertainties associated with errors in estimating cloud cover in the Tropics yield total uncertainties that are greater than 25 W m−2. In the northern latitudes, where the large number of observations substantially reduces the influence of these random errors, the systematic uncertainties in the utilized parameterization are largely responsible for total uncertainties in the shortwave fluxes, which usually remain greater than 10 W m−2. Systematic uncertainties dominate in the zonal means because spatial averaging has led to a further reduction of the random errors. The situation for the annual mean latent heat flux is somewhat different in that even for gridpoint values, the contributions of the systematic uncertainties tend to be larger than those of the random uncertainties at most latitudes. Latent heat flux uncertainties are greater than 20 W m−2 nearly everywhere south of 40°N and in excess of 30 W m−2 over broad areas of the subtropics, even those with large numbers of observations. Resulting zonal mean latent heat uncertainties are largest (∼30 W m−2) in the middle latitudes and subtropics and smallest (∼10–25 W m−2) near the equator and over the northernmost regions. Preliminary comparison of zonal average fluxes suggests that most atmospheric general circulation models produce excessively large ocean surface fluxes of net solar heating and evaporative cooling when forced with realistic sea surface temperatures. It is expected that the method introduced here will be refined to produce increasingly reliable estimates of uncertainties in surface flux atlases derived from ship observations.

Corresponding author address: Dr. Peter J. Gleckler, PCMDI (L264), Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550.

Email: gleckler@pcmdi.llnl.gov

Abstract

A methodology to define uncertainties associated with ocean surface heat flux calculations has been developed and applied to a global climatology that utilizes a summary of the Comprehensive Ocean–Atmosphere Data Set surface observations. Systematic and random uncertainties in the net oceanic heat flux and each of its four components at individual grid points and for zonal averages have been estimated for each calendar month and for the annual mean. The most important uncertainties of the 2° × 2° grid cell values of each of the heat fluxes are described. Annual mean net shortwave flux random uncertainties associated with errors in estimating cloud cover in the Tropics yield total uncertainties that are greater than 25 W m−2. In the northern latitudes, where the large number of observations substantially reduces the influence of these random errors, the systematic uncertainties in the utilized parameterization are largely responsible for total uncertainties in the shortwave fluxes, which usually remain greater than 10 W m−2. Systematic uncertainties dominate in the zonal means because spatial averaging has led to a further reduction of the random errors. The situation for the annual mean latent heat flux is somewhat different in that even for gridpoint values, the contributions of the systematic uncertainties tend to be larger than those of the random uncertainties at most latitudes. Latent heat flux uncertainties are greater than 20 W m−2 nearly everywhere south of 40°N and in excess of 30 W m−2 over broad areas of the subtropics, even those with large numbers of observations. Resulting zonal mean latent heat uncertainties are largest (∼30 W m−2) in the middle latitudes and subtropics and smallest (∼10–25 W m−2) near the equator and over the northernmost regions. Preliminary comparison of zonal average fluxes suggests that most atmospheric general circulation models produce excessively large ocean surface fluxes of net solar heating and evaporative cooling when forced with realistic sea surface temperatures. It is expected that the method introduced here will be refined to produce increasingly reliable estimates of uncertainties in surface flux atlases derived from ship observations.

Corresponding author address: Dr. Peter J. Gleckler, PCMDI (L264), Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550.

Email: gleckler@pcmdi.llnl.gov

1. Introduction

Despite its importance for climate and climate change, the global-scale ocean surface energy balance is not well known. Deficiencies in our understanding result a from lack of quality observational data and the complex nature of the physical processes involved. Here, we focus on quantifying, as best as possible, the uncertainties associated with global ocean surface energy flux climatologies, which have been derived from surface observations. Individual sources of error will be examined to identify how they collectively propagate into total uncertainties in the estimates of annual and seasonal mean surface energy fluxes. The reduction of random uncertainties due to averaging techniques will be quantified. In most cases, we will not attempt to correct for the more problematic systematicbiases in the climatologies, an endeavor that is crucial to enhanced understanding and that represents an active area of investigation by many researchers.

An important motivation for this study is to quantify the uncertainties in observationally based energy flux atlases so that they can be used to evaluate surface energy fluxes simulated by atmosphere and ocean general circulation models. The comparison of model-simulated energy fluxes with observationally based estimates to date has been of limited use because it is well known that there are large uncertainties in the atlases. It has also been known for some time that the present uncertainty in the net oceanic air–sea heat flux substantially exceeds the 10 W m−2 required to establish ocean and atmosphere energy budgets to the accuracy required for climate monitoring and prediction (cf. Dobson et al. 1982). Exactly how large these observational uncertainties are remains unclear, but this is precisely the issue that we will address in this study.

Few direct measurements of ocean surface energy fluxes have been made because they are extremely difficult and expensive. To overcome the lack of in situ measurements,parameterizations have been developed to estimate surface energy fluxes from commonly observed fields. Surface air temperature, sea surface temperature, dewpoint temperature, wind speed, and cloud cover are commonly measured or estimated by merchant ships of the volunteer observing fleet and research vessels. Using the parameterizations in conjunction with databases containing millions of these observations spanning three or more decades, atlases of monthly mean climatological global ocean surface heat fluxes have been developed (cf. Esbensen and Kushnir 1981; Hsiung 1986; Oberhuber 1988; da Silva et al. 1994).

Other observationally based techniques such as operational analyses (cf. Simonot and LeTreut 1987; Trenberth and Solomon 1994) and satellite retrieval techniques (Liu 1988; Darnel et al. 1992; Chertock et al. 1992; Li and et al. 1993) may be used to estimate large-scale surface energy fluxes. Here, we will restrict ourselves to the evaluation of ocean surface energy flux estimates resulting from surface marine observations.

Some studies (cf. Cayan 1992a) have focused on the interannual variability of ocean surface energy fluxes. Only in the northern oceans (the North Atlantic in particular) are there a sufficient number of surface observations available to study interannual variability in any reasonable way. It is our belief that models must have a credible simulation of the seasonal cycle before we can have faith in their ability to realistically capture interannual variability, and for this reason, we focus on the seasonal mean climatology. In any event, most available estimates are composite climatologies because the observations available in nearly all regions are too scant to provide reasonable estimates for an individual month.

In section 2, the data and parameterizations used in this study are described. In section 3, uncertainties in the observations and the parameterizations, as well as those due to sampling deficiencies, are summarized. The heat flux uncertainty analysis is described in section 4 for each term of the surface energy balance: the net surface shortwave(SW) and longwave (LW) radiation, the latent heat flux (LH), the sensible heat flux (SH), and the net surface heat flux (N = SW + LW + LH + SH). We define all fluxes to be positive downward. The analysis, its potential uses, and its deficiencies are discussed in section 5.

2. Data

We use a modified version of the Oberhuber atlas (1988) as the basis of our uncertainty estimates. Other atlases (cf. Esbensen and Kushnir 1981; Hsiung 1986; da Silva et al. 1994) could have been used, but we chose that of Oberhuber because it has been used extensively and the raw data required for the analysis that follows are available. It is not clear that the parameterizations used by Oberhuber are superior to other efforts, but for the most part, the results of our analysis are not sensitive to the choice of the atlas used, provided that certain corrections are made. This is not to suggest that the parameterization used in one atlas is not significantly better than that used in another, but rather that on a global scale, the uncertainties associated with all of them are of comparable magnitude.

To estimate the surface fluxes with the parameterizations that are outlined below, Oberhuber used a monthly climatology (Wright 1988) of the Comprehensive Ocean–Atmosphere Data Set (COADS, cf. Woodruff et al. 1987). This COADS product was based on data archived from the Voluntary Observing Fleet (VOF) of merchant vessels during the period from 1950 to 1979. The observed fields in the COADS climatology that are needed for the surface flux parameterizations are surface air temperature (2 m) Ta, sea surface temperature Ts, dewpoint temperature (2 m) Td, surface pressure Ps, and the more subjective estimates of total cloud cover C and surface wind speed (10 m) Vs. To give some sense of the number of observations available, Fig. 1 depicts the total number of sea surface temperature observations available during the 30-yr period. The distribution of available observations for theother fields used in this analysis is similar, but the number of observations of some fields (e.g., Ts) is much less than for Ta. There is a steady increase in the total number of observations taken during the 3 decades, but in general, those regions with relatively high or low sampling rates remain that way throughout the data collection period.

Oberhuber used the Wright (1988) 2° latitude × 2° longitude climatology; thus, the surface flux estimates are made with climatological monthly mean observations. This technique has been frequently referred to as the “classical” method. A more complex, but perhaps preferred, technique is to estimate the surface heat fluxes with the“sampling” method, whereby flux computations are made with individual measurements. We will return to this issue.

For the net shortwave radiation, Oberhuber made use of Reed’s (1977) parameterization
Q0ACZα
where Q0 is the monthly averaged surface clear-sky solar radiation reduced by atmospheric transmissivity (Zillmann 1972); α is the surface albedo, with a constant value of α = 0.06; Z is the solar noon altitude in degrees; and A is a coefficient with a constant value of 0.62. Oberhuber reduced Reed’s (SW) formulation by 10% without sound justification in order to adjust the annual mean meridional oceanic heat transport implied from the net surface heat flux N. In the analysis that follows, this reduction of (SW) is removed because Reed’s unaltered (SW) formula was judged to be the most accurate for monthly mean estimates in an extensive review by Dobson and Smith (1988).
That progress is slow in the large-scale estimates of the net longwave flux is evident in the fact that Oberhuber used the parameterization of Berliand (1960), which has been improved little in 35 years. The Berliand formula is written as
i1520-0442-10-11-2764-e2
where B is a function of latitude (varying from 1 at the poles to 0.5 at the equator), es is the air surface vapor pressure (derived from the observed dewpoint temperature), ε the emissivity of the sea surface, and α is the Stefan–Boltzman constant; Ta and Ts are in units of K.
To date, the only means of making large-scale estimates of the turbulent latent and sensible heat fluxes requires usage of the classical bulk formulas
i1520-0442-10-11-2764-e3
where qa is the surface (2 m) air specific humidity, and CE and CH are the exchange coefficients for LH and SH, respectively. The diagnostic variable qs is defined as the saturation specific humidity at Ps and Ts, while qa is derived from Td. Oberhuber has used the empiricallybased model of Large and Pond (1982) for CE and CH, with some modifications (Oberhuber 1988).

3. Measurement, parameterization, and sampling uncertainties

The analysis that follows is an extension of the work of Weare (1989), wherein uncertainties in Weare’s (1981a) tropical Pacific heat flux atlas were estimated. In this section, we summarize estimates of random and systematic uncertainties due to deficiencies in sampling, observing errors, and the parameterizations themselves. Most of these estimates have been cataloged from the work of various researchers involved in the quality control of observational data and by those who are active in parameterization development. In section 4, we will assess how these uncertainties propagate in the climatological estimates of global ocean surface heat fluxes.

a. Uncertainties in the observed fields

1) Random uncertainties

To compute surface fluxes with the parameterizations summarized in section 2 requires field observations of C, Vs, Ta, Ts, Td, and Ps. Random errors resulting from a single measurement of the directly observed quantities have been estimated (cf. Weare 1989; Taylor 1984) to be approximately ±1°C for Ta, Ts, and Td. These estimates are meant to represent any random error in the reading of the thermometer or a bias in any given instrument. A bias in a single thermometer will be considered a random error in the total dataset because many different thermometers were used to measure temperature within a given 2° × 2° grid cell during the 30-yr period.

The random uncertainty associated with the estimated (as opposed to measured) quantities of Vs and C are more elusive. Estimated reports of Vs in COADS are based on the official Beaufort equivalent scale of the World Meteorological Organization (WMO), code 1100 (WMO 1970). Using the Beaufort scale, visual estimates of the sea state are converted to wind speed using a conversion table. The situation is complicated by the fact that the fraction of reported observations measured with anemometers has been steadily increasing (cf. Taylor et al. 1994). Unfortunately there is no distinction between estimated and measured reports in the COADS monthly summaries (Woodruff et al. 1987), but for most locations and years, the number of anemometer wind measurements has been less than 20% of all reports. A multitude of random errors can arise in an estimate of surface wind speed. For example, the Beaufort scale is based on the sea state, which is dependent on the magnitude, duration, and area coverage of the wind. To get a sense of a typical random error in an estimate of Vs, we have examined the standard deviation of observations made within a given month, a product available in the COADS (1950–79) dataset. We calculate an “average” standard deviation (S) for each calendar month k,
i1520-0442-10-11-2764-e5
where N is the total number of years (t) with at least 10 observations for a given longitude (i)–latitude (j) 2° × 2° cell. For example, our January calculation was based on the up to 30 sample standard deviations (S) available for each January between 1950 and 1979. Note that by assuming that this averaged standard deviation is related to random uncertainties in measurements, we may be overestimating the random uncertainties since at least part of the standard deviation is a measure of actual variability.

As shown in Fig. 2a, in the North Atlantic the standard deviation (normalized by the climatological Vs) was found to be larger than elsewhere, presumably representing higher meteorological variability. We have assumed that outside the North Atlantic, the variability that exists is due predominantly to random errors (which again yields a conservative estimate of the uncertainty). With this measure, we rather subjectively estimate the random error for a single estimate of Vs to be 50%.

The estimates of C are reported in eigths, ranging from clear skies (0/8) to overcast (8/8). Such estimates made by the VOF are extremely subjective. We have evaluated the year-to-year variability of C in the same manner aswe did Vs in order to make a judgement on the random errors associated with such cloud cover estimates (Fig. 2b). In many areas, the variability is roughly 20%–25%. We again chose to be conservative by assuming that this variability is due mostly to random uncertainties in measurements and not actual variability. It is probable, however, that the uncertainty is a function of cloud cover itself. For clear and overcast skies, the random uncertainty in a given estimate is likely to be much less than for partly cloudy skies. Our estimate of the random error for a single observation of C is 2/8 (25%) for all conditions.

2) Systematic uncertainties

Assessing systematic errors in ship-based observations is perhaps more difficult than assessing random errors. Systematic errors of Ts are probably best understood. Measurements of Ts are usually made by sampling engine- intake water, which was found (Saur 1963) to be systematically too warm by roughly 0.7°C. Subsequent investigators have found that this discrepancy is a function of location and season and that other factors are also important. Before engine-intake seawater was commonly used for measurement, both insulated and uninsulated buckets were employed. In any case, it is difficult to make a rigorous estimate of these errors because the frequency of use of the three methods (engine intake, buckets insulated, and not insulated) is not known. Jones et al. (1991) have suggested that since 1950 discrepancies have been greatly reduced. An estimate of ±0.5°C will be used here for the systematic uncertainty in Ts.

It has become evident that systematic errors might also be present in Ta measurements (Weber 1985). Shifts in decadal means of Ta have been observed, which seem to be related to changes in the method of measurement. Kent et al. (1993) have attempted to correct biases from instrument exposure to sunlight and wind. Other factors may also contribute to error, such as the “heat island” effect of a ship’s hull. Despite progress in identifying sources of systematic errors, biases of either sign are possible, and they are likely to vary with circumstance. We will assume that the systematic uncertainty of Ta is also approximately ±0.5°C.

It has often been suggested that the systematic uncertainty in Td measurements is negligible because it is typically measured with a sling psychrometer, which should be well ventilated. Isemer et al. (1989) have assumed the systematic uncertainty in TaTd to be only 0.2°C. However, Kent et al. (1993) have shown that systematic errors in Td can arise from inadequate ventilation or a contaminated or imperfectly wetted wick. Each contribute to a decreased wet-bulb depression and consequently to an increased dewpoint temperature. The situation is more complicated, as there are several methods that are routinely-used to measure dewpoint, and without knowing which observations were made with which type of instrument, it is difficult to identify the relative importance of possible biases on the climatologies. We suspect that the error estimateof Isemer et al. (1989) is too small, and we will use 0.25°C as the systematic uncertainty in Td.

Sea surface (10 m) wind measurements are derived either from Beaufort estimates of the sea state or by direct anemometer measurement. There is no distinction in the COADS monthly summary between estimated and measured reports, and it is thus difficult to determine the relative importance of the errors resulting from the two methods. However, we do know that most of the data in the Wright (1988) climatology used by Oberhuber consist of estimated wind speeds (before 1970 there were few ships equipped with anemometers), and we have therefore assumed that the majority of the records are estimated wind speeds. Based on Atlantic Ocean observations, Isemer and Hasse (1991) have suggested that there is a systematic underestimate of Beaufort surface wind speeds on the order of 1.5 m s−1. Although Isemer and Hasse claim to have determined the sign of the bias, we make no attempt to correct the Oberhuber atlas, but we do use the Isemer Hasse correction as an estimate of the systematic error in the surface wind speed.

Fractional cloudiness estimates made by surface observers are fraught with uncertainty (Warren et al. 1988). However, systematic errors in observed quantities contribute to surface heat flux uncertainties only if the observed quantities or the averaging methods used in applying the observations to the parameterizations differ from the data or the averaging methods originally used to derive the parameterizations. For example, suppose a systematic bias exists in the estimates of C. The SW and LW radiation formulas [Eqs. (1) and (2)] were derived by fitting a wide range of these biased observations to relatively accurate direct (radiometer) measurements of the fluxes. Presumably, the resulting parameterizations will yield reasonable estimates, provided they are made with the biased data. Because all of the data used are estimated in a similar fashion, we assume that the systematic uncertainty in C affecting the radiation flux parameterizations is negligible. This is not to suggest that a significant systematic uncertainty in C does not exist.

Oberhuber chose to use a constant albedo (α = 0.06) in his use of the Reed parameterization. Payne (1972) found that the monthly mean α seldom departs from 0.06 by more than 0.01 equatorward of 60° in the Atlantic. We have used 0.01 for our estimate of the systematic uncertainty in the albedo. When sea ice is present this is clearly not appropriate, but in this study, we can adequately analyze only those areas of the ocean that are free of ice.

The uncertainty estimates summarized here are listed in Table 1. We will use these to examine how uncertainties collectively propagate in the estimate of surface heat fluxes. Although the list may not be complete, we feel it is a reasonable representation of the dominant uncertainties in the observed quantities. Note the uncertainty estimates listed in Table 1 are meant to represent the uncertainties in the observed quantities that contribute to the uncertainties in the surface heat fluxes. As pointed out earlier, there may very well be substantial systematic biases in the estimatesof C, but these are in effect built into the parameterizations and thus are not included in Table 1.

b. Parameterization and direct measurement flux uncertainties

Random and systematic errors in surface heat fluxes can result even if there are no errors in the observed quantities of the VOF. This is because the development of the parameterizations relies on the relatively few high-quality, but imperfect, direct observations to represent a nearly limitless combinations of possible states in nature. When possible, we divide these uncertainties into those due to the instrumentation used to make direct observations and those due to errors in the parameterizations.

Systematic uncertainties in direct measurements (made before or specifically for the development of the parameterizations) of radiative fluxes have been estimated by Simpson and Paulson (1979) to be approximately ±5%. Included in their estimates were problems due to the effects of ship motion, shadowing effects of ship hulls, and radiometer calibration. More recently Frohlich and London (1986) have suggested that the error in the SW marine measurements can be reduced to 1%–2%. Hourly measurements taken for 6 yr aboard the Oceanographer were used for an extensive validation of the Reed parameterization (Reed 1982). The pyranometers aboard the Oceanographer were carefully calibrated, and the systematic errors in the SW measurements probably did not exceed 2%. We will use 2% as our estimate of the SW instrumentation uncertainty. Direct measurements of LW are more difficult and less frequent, and thus we have decided to use the higher estimate of 5% made by Simpson and Paulson.

Dobson and Smith (1988) compared the various SW formulas with direct observations made on ships and on several open ocean islands. They found that for climatological estimates, the Reed model was in closest agreement with observations. Parameterizations that were designed to account for cloud type information (such as low, middle, and high) appeared to have little advantage, although this conclusion may not apply to parameterizations based on and used for estimates of SW over land (cf. Davies et al. 1985). With a large number of observations, Dobson and Smith (1988) found that the Reed formula yielded estimates that differed systematically from the direct measurements by no more than 8 W m−2 at three separate ocean weather stations (59°N, 19°W; 52°N, 20°W; and44°N, 60°W), where hourly measurements are available for 15, 14, and 12 yr, respectively. Reed (1982) tested his parameterization by using data from the Oceanographer, which traversed through many meteorologically varying regions from 7°S to 66°N in the Pacific Ocean. Six years of hourly visual estimates of C are available from this extended cruise, along with hourly accumulations from radiometers. Making use of the data from this extended expedition, the Reed parameterization was found to have a standard error (based on one standard deviation) of approximately 6.5% (Reed 1982). Since a wide range of conditions were surveyed with reasonable sampling and duration (hourly, for multiple years), we have chosen to use this value (6.5%) to represent the systematic uncertainty of the Reed parameterization. This may be a slight underestimate because the observations taken aboard the Oceanographer were not global in extent. Finally, with regard to the dominant random uncertainty, we assume that it is due to the estimate of C, not the parameterization itself.

Uncertainties associated with LW parameterizations have been examined by Simpson and Paulson (1979) and Fung et al. (1984). Both studies emphasize that uncertainty estimates themselves are limited by the lack of direct measurements over the open ocean, of which there are far fewer than for the SW. The results of Simpson and Paulson suggest that under cloudy conditions there is a random error of roughly 5 W m−2 associated with the Berliand formula. (Note that this differs from the case of random uncertainties associated with the SW parameterization, which were considered negligible because it was based on many more observations.) Fung et al. (1984) estimated the systematic uncertainty of the Berliand formula to be 5 W m−2 under all conditions. We will use the estimates of Simpson and Paulson (1979) and Fung (1984) for our measures of the random and systematic uncertainties in Oberhuber’s use of the Berliand formula, but it must be emphasized that these uncertainties are particularly subjective because there are so few direct measurements available for validation.

Blanc (1987) compared a variety SH and LH exchange coefficients with “direct” measurements (eddy correlation and dissipation techniques) and suggested that the systematic uncertainty associated with both coefficients is on average about 12%, which apparently includes the uncertainty in the direct measurements. In another study (Anderson and Smith 1981), it was found that the majority of methods used to model the exchange coefficients yield random uncertainties of about 20%. It is generally believed that these estimates are reasonable for winds between 2 and 11 m s−1 (cf. Large and Pond 1981), but that outside this range the random uncertainties are likely to be higher. The estimate of random and systematic uncertainties made by Blanc (1987) and Anderson and Smith (1981) will be used here. It is worth noting that many investigators (e.g., Kent et al. 1993; Isemer and Hasse 1991) have demonstrated that the exchange coefficients used in the global atlases of Esbensen and Kushnir (1981), Hsiung (1986),and Oberhuber (1988) were larger than eddy-correlation estimatestes by 5%–15%. It is possible that these higher values compensate for systematic underestimates in the winds derived from the Beaufort scale (Isemer and Hasse 1991).

Uncertainty estimates associated with the surface flux parameterizations are summarized in Table 2. For the radiation fields, no attempt is made to partition the uncertainties into the various terms in each formula, and all parameterization uncertainties of the LH and SH are attributed to the turbulent exchange coefficients.

c. Uncertainties due to sampling deficiencies

How many observations are required to make a reasonable estimate of a climatological monthly mean flux field? For the case of normally distributed random errors, the overall uncertainty is reduced by N−1/2, where N is the total number of observations. Several investigators (cf. Cayan 1992b; Weare 1992) have demonstrated at a number of locations in the Tropics and midlatitudes that given a sufficient sample size, it is reasonable to assume that the year-to-year variability is normally distributed. Thus, for most circumstances, simple sampling theory is applicable and will be used here. However, sampling errors that are not random can arise in a number of circumstances.

A spatial sampling bias could result if merchant ships routinely sampled one area of a grid cell more than other areas. This might be important in coastal areas and especially along sharp gradients such as those exhibited by the western boundary currents. The possibility of such a bias was considered by Weare and Strub (1981b) and found to be of much less importance than those due to parameterization or measurement uncertainties, especially in the open ocean. Moreover, any spatial bias here is thought to be much smaller than that in Weare’s (1981) study because the observations used by Oberhuber have been accumulated in 2° × 2° grid cells rather than 5° × 5° cells. Gulev (1994) has carefully analyzed spatial biases in the North Atlantic and has subsequently developed parameterization corrections. Although such modifications to the parameterizations are likely to be important for studies of variability, their influence is small compared to the dominant uncertainties that we consider here.

Oberhuber’s SW estimate was made with a monthly mean COADS product, which includes some nighttime observations. This could lead to a possible bias in the flux estimates, particularly in areas of marine stratus, wherethe diurnal variability can be important. Hahn et al. (1995) have attempted to quantify this bias, which apparently is largest in the Arctic winter and can reach as much as 8%. We will not account for this bias because it can easily be removed by using daytime-only cloud cover atlases such as that developed by Hahn et al. (1995), and here, our interest lies in those uncertainties for which there is no immediate solution. Day–night biases may also exist for LH and SH due to variations in the winds and air–sea gradients of moisture and temperature, but we believe that these are much smaller than other uncertainties considered here.

Another possible problem may result from what is commonly referred to as a “fair weather” bias. Kent and Taylor (1995) noted that fewer observations have been taken at high latitude during the winter months. However, they suggest that this does not necessarily result in a bias if the observations available are randomly distributed with respect to weather conditions. Testing this possibility, they concluded that there does not appear to be significant rerouting of ships during periods of high winds. It is important to note that such biases can occur, particularly in high latitudes, but we will make no attempt to quantify them here.

With the sampling method, individual flux estimates are determined from ship reports and are subsequently averaged over the period of sampling. With the classical technique, meteorological variables are averaged first and flux computations are made with these averaged quantities [e.g., with the classical method LH = LH(Vs, Ts, Td)]. Oberhuber and most others have made use of the classical method because it greatly simplifies the task and is generally regarded to be a reasonable approximation of the sampling method. Many studies (Esbensen and Reynolds 1981; Hanwana 1987; Simpson and Paulson 1979; Simmonds and Dix 1989) suggest that the classical method gives a reasonable approximation, but leads to minor discrepancies when comparisons are made with the more correct approach of computing the fluxes before averaging. Josey et al. (1994) found thatthe monthly LH flux estimated with the classical method overestimates the sampling method by 2–4 W m−2 in summer and roughly 7 W m−2 in winter. While these biases are not negligible, we will see that they are small compared to several other LH uncertainties. In any case, not all investigators agree upon the importance of the method used (e.g., Gulev 1994). For the SH, Josey et al. (1994) found the differences between the two methods to be on the order of 1 W m−2 and, consequently, much smaller than the interannual variation estimate of the North Atlantic (Cayan 1992a). This is in contrast to the study of Fissel et al. (1977), who found the biases in SH resulting from the classical method to be important. On the other hand, an important result of the Fissel et al. study (1977) is that extreme weather events did little to alter the climatological estimates of the LH and SH fluxes. Clearly, further studies are needed, preferably at a variety of locations to fully justify or refutethe classical method of computing surface fluxes with VOF data.

4. Ocean surface heat flux uncertainties

To estimate how the uncertainties summarized in sec~tion 3 propagate into uncertainties in the surface heat fluxes, we make use of basic sampling theory (Taylor 1982), which is briefly summarized here. Consider the special case of a variable F, which is a function of two variables x and y. To first order, the uncertainty estimate σF for a single measurement of x and y is
i1520-0442-10-11-2764-e6
where σx and σy are the random and systematic uncertainties in x and y, and ρxy is the correlation between x and y. If x and y are independent, they will not be correlated and, thus, the third term in Eq. (6) will vanish. If they are fully dependent (ρxy = 1), then Eq. (6) yields the maximum possible propagation of the uncertainties. In cases where where x and y are anticorrelated (ρxy < 1) or the partial derivatives with respect to F are negative, the third term in Eq. (6) will act to reduce σF.
If we are estimating uncertainties from a collection of measurements of each observable, as opposed to Eq. (6), which is based on only a single measurement of x, then, for instance, the first term on the right-hand side of Eq. (6) may be expanded to
i1520-0442-10-11-2764-e7
where σx,sys and σx,ran are estimates of the systematic and random uncertainties of x, respectively. Random uncertainties will be reduced by f(N) = N−1/2 because, as we have already pointed out, simple sampling theory is reasonable for our analysis. We will generalize the methodology outlined here to account for more than two variables.

a. Surface net shortwave radiation

The uncertainty resulting from Oberhuber’s use of the Reed SW parameterization (which we have corrected as described in section 2) may be formulated using Eqs. (6) and (7). Using the uncertainties listed in Tables 1 and 2, the total uncertainty in the SW is
i1520-0442-10-11-2764-e8
Only the third term in Eq. (8) has a partial differentiation [as in Eq. (6)] because all the other uncertainties in Tables 1 and 2 are estimated as percentages of uncertainty of the SW. We have assumed here that all possiblecorrelation terms are zero because each term in Eq. (8) represents an independent source of error. The random uncertainty reduction factor is f(N) = N−1/2, where N is the total number of observations within a given grid cell for a particular climatological month.

In order to properly account for seasonal variations in the uncertainties, the climatological monthly mean uncertainties are first computed. Estimates of the climatological annual and seasonal means are then derived from the root- mean-square of the monthly mean estimates. This procedure is used to estimate the uncertainties for each component of the surface energy balance.

Uncertainties in the climatological annual mean net SW are shown in Fig. 3. Gray areas over the oceans indicate that for at least one climatological month there were fewer than 10 observations of total cloud cover available for theentire 30-yr period. Figure 3a shows the SW systematic uncertainties (instrumentation and parameterization), which are spatially homogenous and range from approximately 5–10 W m−2 in the northern oceans to 15–20 W m−2 in the Tropics. The random uncertainties associated with C (Fig. 3b) are between 5 and 10 W m−2 in the northern oceans and greater than 25 W m−2 in the Tropics and southern oceans, except along common routes for merchant ships, where there are many more observations.

The total uncertainties in the annual mean SW shown in Fig. 3c are between 10 and 20 W m−2 in the northern oceans, with a slightly greater contribution resulting from systematic uncertainty. In the Tropics and the southern oceans, random uncertainties dominate.

This assessment of uncertainties demonstrates the relative importance of the various sources of error and how they vary spatially. However, it is desirable to reduce this information into a more compact form. The most obvious measure is to examine the zonal means of the uncertainties, which would be a useful first step in the validation of surface heat fluxes simulated by climate models. The random uncertainties can be reduced by spatial averaging in a manner analogous to what we have done with the uncertainties at each 2° × 2° grid cell. For instance, if thereare M grid boxes along a line of latitude, we can estimate random uncertainty in the zonally averaged SW by
σ[SW],ranσSW,rangM
where the square brackets denote a zonal average and g(M) is the function representing the reduction of random errors when averaging spatially. If the random uncertainties associated with each grid box are independent of one another, then g(M) = M−1/2. However, an assumption of spatial independence is probably not reasonable for some variables such as C. An observer may estimate clear-sky or overcast conditions quite well, but partly cloudy conditions with much more uncertainty. We cannot directly estimate how σC,ran varies spatially, but we do know how C varies. Therefore, to estimate the possible impact of the spatial dependence of σC,ran, we compute the spatial lag correlations of C and presume that they are similar to those of σC,ran. The lag correlation enables us to estimate the number of degrees of freedom and hence an appropriate value of g(M). Figure 4a shows the spatial lag correlations for the departures from the zonally averaged January monthly mean climatology of C at each latitude in the Pacific Ocean. The maximum correlation is clearly in the Tropics. As a length scale of dependence, we have chosen to use the number of grid cells at which the lag correlation drops to Lcuttoff = 0.4. For example, at 30°N, the lag correlation of the departure from the zonal average of C is 0.4 after seven grid cells; thus, g(M) = (M/7)−1/2. Tests demonstrated that our results are not very sensitive to Lcuttoff.

The uncertainties in the zonal average global ocean SWfor the four seasons and the annual mean are shown in Fig. 5 in the form of upper and lower error bars. Both random [reduced by the latitude-dependent function g(M)] and systematic uncertainties are accounted for. Note that even in the Tropics the zonal average systematic uncertainties dominate, which demonstrates the effectiveness of spatial averaging as a means of reducing the magnitude of the random uncertainties. The annual mean zonal average total uncertainties vary from ±10 W m−2 in the northern oceans to at least ±20 W m−2 in the Tropics.

b. Surface net longwave radiation

Using an equation similar to Eq. (8), the total uncertainties in the net longwave flux LW have been estimated. In most regions, these total LW uncertainties (Fig. 6) are dominated by random uncertainties in C; all other random uncertainties are comparatively small. Only in the northern oceans do systematic uncertainties in e, Ta, Td, and Ts compare with the random uncertainty. The zonal annual means of the LW uncertainties are shown in Fig. 7. The random uncertainties are principally associated with C, and thus they are reduced in a manner analogous to the SW. Note that the LW uncertainty estimates are even more subjective than those made for the other heat fluxes. The importance of this deficiency is somewhat diminished by the fact that the magnitude and spatial variation of the LW are much less than those of the SW and LH.

c. Latent heat flux

Our estimate for the LH uncertainty is based on
i1520-0442-10-11-2764-e10

Pressure dependence in the qs uncertainty terms have been ignored because they have little effect. There are also no terms including ρCE,Vs or ρCE,(qaqs), but these are believed to be smaller than ρVs,(qaqs). The three largest uncertainties related to the LH flux, all of which are systematic, areshown in Fig. 8. In contrast to our findings for the radiative fluxes, the LH random uncertainties (not shown) in all regions are small in comparison to the systematic uncertainties. Figure 8a shows the annual mean systematic uncertainty due to the exchange coefficient CE. In many areasof the northern oceans, they are less than 10 W m−2, but in the Tropics and midlatitudes, they are in excess of 15 W m−2. Over the western boundary currents, they are greater than 20 W m−2. The systematic uncertainty in the LH flux due the surface wind speed, which is shown in Fig. 8b, is evidently the most serious source of systematic errors. In many regions, these uncertainties are greater than those due to the exchange coefficient, exceeding 20 W m−2 in much of the Tropics. In the eastern portion of the midlatitude oceans, they are smaller than in the west because the uncertainties are a function of the flux itself and are generally higher in the west, owing to the relatively dry air flowing eastward off the continents over the western boundary currents. Systematic uncertainties due to (TdTs) and from the correlation between surface Vs and (TdTs) are combined and shown in Fig. 8c. The correlation is calculated using the 30 monthly means for each calendar month [monthly values of Vs(TdTs) are available], and is small in most areas, except over the western boundary currents. The resulting uncertainties are much smaller than those in Figs. 8a and 8b. Correlation uncertainties between CE and Vs or (TdTs) are similar to those between Vs and (TdTs). The total LH uncertainties are shown in Fig. 8d. Nowhere are they less than 10 W m−2, and in western tropical oceans, they exceed 30 W m−2. Along the western boundary currents, the total LH flux uncertainty is nearly 50 W m−2. These results do not suggest that more of the same types of observations would substantially reduce LH uncertainties, but rather that methods to correct for existing errors are necessary. Estimates of Vs may improve (e.g., Isemer and Hasse 1991), but prospects for reducing exchange coefficient uncertainties are less encouraging. Finally, it is important to note that the exchange coefficient uncertainties are dependent on the uncertainties in Vs and, thus, the relative importance of these two terms (Figs. 8a and 8b) must be considered carefully. Further tests are necessary.

The zonal mean LH flux uncertainties for the annual and seasonal means are shown in Fig. 9. We we have reduced the zonal average uncertainties associated with Vs in the same manner as we have with C in the SW and LW because it is possible that the random uncertainty associated with a visual Vs estimate is a function of Vs itself. The corresponding (see section 4a) Vs lag correlations are shown in Fig. 4b. At 30°N, the estimated number of degrees of freedom is M/10, based on the same criterion (Lcuttoff = 0.4) as used for the lag correlations of C.

The random uncertainties resulting from all temperature measurements are presumed to have little spatial dependence, as they were recorded under many different circumstances. They were consequently reduced as M−1/2 and are barely discernible in the zonal mean figures. Unfortunately, even though we can justify reducing the random uncertainties substantially, the zonal means of the total LH uncertainties are at least ±25 W m−2 at most latitudes.

d. Sensible heat flux

The SH systematic uncertainties due to the exchange coefficient are shown in Fig. 10a, and in Fig.10b both the (TaTs) and Vs systematic uncertainties are shown. The absolute uncertainties in both figures are small, but the relative uncertainties are at least as large as those of the LH flux. All random uncertainties and the correlated uncertainties between Vs and (TaTs) are included in the total SH uncertainties in Fig. 10c. Over the western boundary currents, the total uncertainties are in excess of 15 W m−2, but elsewhere they range between 5 and 10 W m−2. The relative importance of the random and systematic uncertainties is analogous to that of the LH. The annual mean zonal averages of the SH flux uncertainties are shown in Fig. 11.

e. Net surface heat flux

To estimate the propagation of uncertainties into the net surface heat flux, we must account for possible correlations between each component of the surface energy balance, as follows:
i1520-0442-10-11-2764-e11

The partial derivatives in the correlation terms [compare with Eq. (6)] are not included in Eq. (11) because they are all unity (e.g., [(∂/∂N)SW][(∂/∂N)LW] = 1·1). Tests suggest that only the first two correlation terms(ρSW,LW and ρLH,SH) have an effect on our estimate of σN that is not negligible. The LH and SH uncertainties are clearly correlated to some degree since they both result from uncertainties in surface wind speed measurements, and both exchange coefficients depend upon estimates of atmospheric stability in the boundary layer. For each calendar month, we calculated the correlation for the 30 yr of data between Vs (qaqs) and Vs(TaTs) and have used this as a measure for ρLH,SH. In most regions, ρLH,SH was less than 0.25, but a notable exception was a rather high correlation (0.6–0.7) over the western boundary currents in the winter months.

Another potentially important correlation exists between the SW and LW estimates because both parameterizations are strong functions of C. Ideally we would estimate ρSW,LW as we did ρLH,SH because it gives us a measure of the correlation at each grid point. Instead, we have estimated ρSW,LW for each month based on the spatial correlation between SW and LW along each line of latitude because the COADS summary does not provide all the time-averaged quantities needed (e.g., T4sesC2) to make the gridpoint calculation are available via the COADS summary. There is a rather strong anticorrelation at most latitudes (−0.5 to −0.95) because the downward (and consequently the net) LW increases with C as SW decreases. The negative correlation leads to a minor reduction in the estimate of σN.

Figures 12a–12c show the random uncertainties, the systematic uncertainties, and the total uncertainties in the net surface heat flux. The random uncertainties range from 5–15 W m−2 in the northern oceans to 25–50 W m−2 in the Tropics and subtropics. The systematic uncertainties are between 15 and 30 W m−2 in the northern oceans and between 30 and 45 W m−2 elsewhere, except in the western boundary currents, where they are in excess of 45 W m−2. Thus, both random and systematic uncertainties are important in the net heat flux, although the systematic uncertainties are larger in most regions. Zonal mean uncertainties for the net surface heat fluxare shown in Figs. 13a–e. Note that at most latitudes the uncertainties suggest that not even the sign of the annual mean net surface heat flux is known.

5. Discussion

A methodology to define uncertainties associated with ocean surface heat flux calculations has been developed and applied to a revised version of the Oberhuber(1988) global climatology, which utilizes a summary of the COADS surface observations. Systematic and random uncertainties in the net oceanic heat flux and each of its four components at individual grid points and for zonal averages have been estimated for each calendar month and for the annual mean.

The most important uncertainties of the 2° × 2° gridcell values of each term in the surface energy balance are described. Random uncertainties in the tropical annual mean net shortwave flux that result from errors in cloudiness estimates are greater than 25 W m−2. In the northern latitudes where the large number of observations substantially reduces the influence of these random errors, the systematic uncertainties associated with the utilized parameterization are largely responsible for total uncertainties in the shortwave fluxes and usually remain greater than 15 W m−2. In the zonal means, the systematic uncertainties are the most important at all latitudes, because spatial averaging has led to a further reduction of the random errors. The situation for the annual mean latent heat flux is somewhat different because even for gridpoint values the contributions of the systematic uncertainties tend to be larger than those of the random uncertainties at all but the highest northern latitude locations. Uncertainties in latent heat flux are greater than 20 W m−2 for nearly all locations south of 40°N and in excess of 30 W m−2 over broad areas of the subtropics, even those with large numbers of observations. The resulting zonal mean uncertainties of latent heat flux are largest (∼30 W m−2) in the middle latitudes and subtropics and smallest (∼15–25 W m−2) near the equator and over the northernmost regions.

One of the primary goals of this research has been to introduce a methodology that provides an improved means of evaluating the agreement between observations of surface heat fluxes and those simulated by atmospheric and oceanic general circulation models. Simulated surface energy fluxes have been found to vary tremendously (cf. Lambert and Boer 1989; Gleckler et al. 1995). Preliminary results in the validation of surface heat fluxes as simulated by 30 atmospheric GCMs in the Atmospheric Model Intercomparison Project (AMIP, Gates 1992; Randall and Gleckler 1995) suggest that calculated uncertainties will prove to be useful in the evaluation of model simulations. Two examples are illustrated in Fig. 14, showing the total uncertainties based on the modified Oberhuber atlas and the 30 AMIP model means, with the one standard deviation range of the individual model results about those means. For the annual mean net surface shortwave flux, Fig. 14a shows that the mean model values are greater than the adjusted Oberhuber estimates plus our calculated uncertainties (SW + σSW) at all extratropical latitudes. Furthermore, in the midlatitudes, very few models have surface shortwave fluxes in the range of the observations. Figure 14b shows a similar comparison for the simulated and estimated DJF latent heat fluxes. Despite the fact that our uncertainty estimates for the LH are very large, they suggest that south of about 20°N, the mean of the models yields a rate of evaporation that is greater than our uncertainty bounds. In the low latitudes, the evaporation in virtually all models exceeds our range of uncertainties. It is interesting to note that the apparent biases in the surface shortwave and latent heat seem compensatory. This is however likely to be coincidence, because the latent heat flux is largely constrained by the SSTs, which are prescribed and therefore independent of the simulated surface radiative fluxes.

The confidence that can be placed in a comparison such as that shown in Fig. 14 depends upon the calculated uncertainties and the mean values of the chosen climatology. The uncertainties are based upon 1) estimates available from the published literature of the fundamental uncertainties in the basic observations and parameterizations used in the heat flux calculation, and 2) statistical analyses of the COADS summary to reduce random uncertainties in space and time. Actual uncertainties differ from one atlas to another depending on the choice of parameterizations, bias corrections in the observations, methodology (classical vs sampling), etc. However, it is our belief that this analysis illuminates the relative importance of fundamental uncertainties and how they vary in both spaceand time, and we expect that repeating this analysis with other atlases would yield similar results. The mean flux estimates of the different atlases can yield a systematic bias in our uncertainty estimates, which relates back to the confidence one can place in a comparison of our uncertainties with models such as that in Fig. 14. We have found that in the summer hemisphere da Silva’s SW is larger than the corrected Oberhuber SW by as much as 15 W m−2, but that the differences between Oberhuber and da Silva for the other fluxes are small compared to our estimated uncertainties. Further tests are needed to fully understand the differences between the Oberhuber and da Silva SW estimates. If da Silva’s SW proves to be more reliable than the corrected Oberhuber SW, then we recommend using the error bars in Fig. 5 in conjunction with da Silva’s estimate. This is reasonable only becausethe uncertainties outlined in Tables 1 and 2 apply in both cases, and both used the same (Reed 1977) parameterization. Incidentally, the conclusions drawn here concerning Fig. 14a do not change if one replaces Oberhuber’s mean with that of da Silva.

The largest influences in the magnitudes of all of the illustrated flux uncertainty estimates are our choices of the fundamental uncertainties listed in Tables 1 and 2. The estimates of the systematic uncertainties in the basic observations and the parameterizations are not only difficult to establish, but are strongly influenced by attempts to correct for one or more of the recognized systematic errors. One of the best researched systematic errors is the one associated with the conversions of Beaufort estimates of sea state to wind speeds. This has been the subject of a recent international workshop (Diaz and Isemer 1995). As a consequence of this and related work, da Silva (1994),in his recent climatology, chose to minimize this bias by an adjusting to the reported wind speeds. The affect of this adjustment on our uncertainties has been estimated by repeating our analysis of the total uncertainties in the latent heat flux with the systematic uncertainty of wind speed in Table 1, reduced by 50%. Figure 15 illustrates the zonally averaged uncertainties about the Oberhuber mean December–February latent heat fluxes based on calculations with and without this reduction. This figure suggests that reducing the biases associated with wind speed estimates is helpful, but the uncertainties in the LH remain large due to the uncertainties in the exchange coefficient and the air–sea moisture gradient.

In our analysis, the Wright COADS summary was used to calculate correlations and the g(M) factor [Eq. (9)], which reduces random uncertainties in space. Results using another climatology are likely to be very similar since there is no reason to believe that these correlations are sensitive to the time period or total number of the observations. Our zonal average results may be influenced by our rather arbitrary choice of a cutoff of correlation of 0.4 to estimate the number of degrees of freedom associated with the reduction in the influence of the random uncertainties, but tests have suggested that the uncertainty estimates are not highly sensitive to this critereon.

The mean values of the Oberhuber analysis also depend upon a prior assessment of the possible systematic biases in the observations and parameterizations and attempts to adjust them. For example, the turbulent exchange coefficients for LH and SH in the atlases of Oberhuber and others are believed by many to be too high (Isemer et al. 1989). High values of CE and CH were apparently needed to compensate for the wind speed estimates being systematically too low (Isemer and Hasse 1991). These two biases tend to compensate for each other in the calculation of the mean. Given the remaining controversies, we have retained both of these biases in our analysis. A future application of this analysis may yield a different perspecitve on the relative importance of these uncertainties.

Some authors (Darnel et al. 1992) have argued that the greatest potential for improvements in global long-term mean estimates of surface heat fluxes is through the use of satellite observations. Our results tend to confirm this assertion with respect to the radiative fluxes. Figure 3 illustrates that at individual grid points the uncertainties in the shortwave flux are dominated by the random uncertainties associated with estimates of cloud fraction. A number of authors (e.g., Li et al. 1993; Chertock et al. 1992) have pointed out that these can be reduced considerably by the use of frequent, high-resolution satellite observations of reflected solar radiation. Satellite observations are less useful in estimating surface longwave radiation (Darnel et al. 1992), but they too may also produce estimates with smaller random errors. For the moment, it is not clear whether satellite estimates of surface radiative fluxes have smaller systematic biases than those associated with the parameterizations utilized herein. On the other hand, the modeled cloudy-sky SW absoprtion utilized in all satellite-derived estimates of surface shortwave radiation has recently been questioned (Cess et al. 1995), and surface-based estimates may be more reliable at present.

Our results are less encouraging concerning the possiblity of satellite measurements helping to reduce the uncertainties in the latent heat flux. As is illustrated in Figs. 8 and 9, the largest contributions to the LH uncertainties are the systematic uncertainties associated with the basic observations and the parameterizations. Satellite-based methodologies for estimating LH (Liu 1988) rely upon the same bulk parameterizations used to construct surface- based flux climatologies. The difference is that satellite estimates of wind speed, temperatures, and humidities are used. Since the systematic uncertainties in the parameterizations remain the same as those discussed here and the systematic uncertainties of satellite estimates of wind speeds and humidities are not insignificant, these satellite estimates are unlikely to have smaller uncertainties than the surface based estimates. They are, however, proving to be useful for studies of variability (e.g., Liu 1988).

In addition to helping in the evaluation of surface heat fluxes simulated by general circulation models, the methodology outlined here allows one to interpret the relative importance of the various errors accumulated in large-scale surface heat flux estimates and how they vary in space and time. This methodology may therefore be helpful in developing a strategy for practical future observational programs. At this point, the uncertainty estimates resulting from the application of the method are only meant to be rough guidelines. It is expected that they will be fine-tuned and hopefully reduced in the years to come. Some possible biases have not been quantified here (such as use of the classical method) and will need to be evaluated in future applications of the method.

Observational programs such as the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment, the World Ocean Circulation Experiment, and the Global Energy and Water Experiment are expected to yield a wealth of information for the analysisof surface heat fluxes. For the moment, however, there appears little hope that our ability to measure surface heat fluxes on a global scale will improve by as much as 50%. Despite this rather discouraging scenario, it is important to develop new products using improved parameterizations and corrections for biases in available data. They are, in fact, necessary steps toward improving our understanding. Moreover, improved observational products may also be attainable even with existing resources. Taylor et al. (WCRP-23 1989) have outlined strategies for standardizing procedures of VOF measurements, and have suggested that it may be possible to optimize the utility of the global-scale network of VOF data simply by further improving procedural and instrumentation standards.

Uncertainty estimates for zonal average surface energy fluxes can be obtained from the corresponding author as monthly, seasonal, or annual means for each ocean basin.

Acknowledgments

This work was performed under the auspices of the Department of Energy Environmental Sciences Division by the Lawrence Livermore National Laboratory under Contract W-7405-ENG-48. We are grateful to the many who have enabled us to make use of their data.

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Fig. 1.
Fig. 1.

Total number of SST observations in COADS for 1950–79.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 2.
Fig. 2.

Average monthly standard deviation of all Januarys between 1950 and 1979 that have greater than 10 observations month−1 for (a) surface wind (normalized by climatological Vs, as a percentage) and (b) cloud cover (as a percentage).

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 3.
Fig. 3.

Annual mean net surface shortwave uncertainties (W m−2): (a) systematic, (b) random, and (c) total.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 4.
Fig. 4.

Pacific Ocean lag correlations, as a function of latitude, for the departures from the zonal means of (a) cloud cover and (b) surface wind speed.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 5.
Fig. 5.

Zonal and climatological annual mean global ocean surface net SW uncertainty bounds for (a) the full year, (b) DJF, (c) MAM, (d) JJA, and (e) SON.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 6.
Fig. 6.

Annual mean net surface longwave total uncertainties (W m−2). Color scale same as Fig. 3. (a) The full year, (b) December–February (DJF), (c) March–May (MAM), (d) June–August (JJA), and (e) September–November (SON).

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 7.
Fig. 7.

Zonal and climatological annual mean global ocean surface net LW uncertainty bounds.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 8.
Fig. 8.

Annual mean latent heat uncertainties (W m−2) for (a) the exchange coefficient (systematic), (b) surface wind speed (systematic), (c) moisture gradient and correlation terms (systematic), and (d) the total. Note that Figs. 3, 6, and 8 have the same color scale.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 9.
Fig. 9.

Zonal and climatological global ocean surface LH uncertainty bounds for (a) the full year, (b) DJF, (c) MAM, (d) JJA, and (e) SON.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 10.
Fig. 10.

Annual mean sensible heat uncertainties (W m−2) for (a) the exchange coefficient (systematic); (b) wind speed, sea surface temperature, and surface air temperature (systematic), and (c) the total.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 11.
Fig. 11.

Zonal and climatological annual mean global ocean surface SH uncertainty bounds.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 12.
Fig. 12.

Annual mean net surface heat flux uncertainties (W m−2): (a) random, (b) systematic, and (c) total.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 13.
Fig. 13.

Zonal and climatological mean global ocean surface net heat flux uncertainty bounds for (a) the full year, (b) DJF, (c) MAM, (d) JJA, and (e) SON.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 14.
Fig. 14.

Zonal and climatological mean global ocean surface flux (black line is the adjusted Oberhuber) uncertainties (error bars) and the average (white line) ± one standard deviation (shading) of the AMIP simulations for (a) annual mean net shortwave radiation and (b) DJF latent heat.

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Fig. 15.
Fig. 15.

Zonal mean DJF global ocean total LH flux total uncertainty (thin bars) and that resulting when the systematic surface wind speed uncertainty is reduced by 50% (thick bars).

Citation: Journal of Climate 10, 11; 10.1175/1520-0442(1997)010<2764:UIGOSH>2.0.CO;2

Table 1.

Uncertainty estimates of observed fields that contribute to flux uncertainties.

Table 1.
Table 2.

Uncertainty estimates associated with bulk parameterizations.

Table 2.
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