Estimation of the Impact of Sampling Errors in the VOS Observations on Air–Sea Fluxes. Part I: Uncertainties in Climate Means

a. Characteristics of sampling uncertainties in VOS flux fields

Sampling uncertainties in monthly VOS-based air–sea fluxes result from the inadequate representation of the synoptic variability by the irregularly sampled VOS observations. Many ICOADS reports contain certain individual variables (e.g., air temperature or wind), missing others (e.g., humidity or cloud cover). This implies different sampling uncertainties for different variables and affects the ICOADS Monthly Summary Trimmed Groups (MSTG), that is, 1° or 2° averages of basic variables (Woodruff et al. 1998). However, the flux computation requires exclusively those reports providing all variables needed for the proper application of bulk formulas. Figure 1a shows the average monthly mean number of air temperature (the best sampled variable) reports per 2° × 2° box for the period 1948–2002. Areas of substantial undersampling for air temperature and other individual parameters (not shown) are found in the Southern Ocean and Northern Hemisphere subpolar regions. This becomes especially true if only those reports that provide all parameters needed for the flux computations are shown (Fig. 1b). Their number is 2–15 times smaller than that for individual variables, showing south of 40°S for most 2° × 2° boxes less than 0.1 reports per month.

Figure 1c shows the temporal distribution of the total number of ICOADS reports (excluding drifting buoys) containing selected variables and all flux-related variables. The total number of air temperature and wind speed reports generally increased during 1948–2002. Until the late 1970s, the total number of cloud cover reports was comparable to those for air temperature and wind speed but started to decrease quite rapidly in the mid-1980s. The total number of reports containing all flux-related variables is substantially smaller throughout the whole period. The number of reports containing all flux-related variables did not change much during the last three decades, yet in relative terms their number actually decreased substantially. After the early 1970s the percentage of reports with all flux-related variables decreased to 10%–25% of the total number of reports in comparison to 40%–60% during 1948–70. Thus, for the surface flux computations the 1960s are still the best-sampled decade. Besides the moored buoys, whose installation has started in the 1980s, this can be explained by the extended installation of automatic packages, providing measurements of wind speed, air temperature, and SST onboard marine carriers starting from the early 1970s. Having such a package onboard, marine officers typically do not practice the observations of the variables not measured automatically (e.g., cloud cover).

In summary, Fig. 1 implies that sampling uncertainties in flux-related variables and computed fluxes are spatially dependent, being higher in the Southern Ocean than in the Northern Hemisphere midlatitudes. Moreover, different variables are influenced to a different extent by inadequate sampling. Sea–air fluxes are always more strongly influenced by sampling problems than individual variables are. Finally, sampling uncertainties are time dependent due to temporal changes in the number of observations. This is particularly true for the locations of the Ocean Weather Stations (OWS) in the North Atlantic and North Pacific, where most observations were terminated in the early 1970s.

b. Sea–air flux computations from the NWP surface variables

The NWP products (NCEP–NCAR, ERA-40, and ECF) used in this study provide the turbulent and radiative fluxes computed by the operational model at the sea surface. However, the use of different parameterization schemes at different NWP centers may introduce additional uncertainty in the comparative assessment. To estimate the pure influence of sampling on VOS fluxes, here we use the individual variables from different NWP products and recomputed the fluxes for every 6-hourly step for the periods covered by the different products.

Sensible (Q_h) and latent (Q_e) heat fluxes were estimated using the Coupled Ocean/Atmosphere Response Experiment (COARE)-3.0 algorithm (Fairall et al. 2003), which is considered to be the least biased among the available surface flux schemes (Brunke et al. 2003). The NCEP–NCAR, ERA-40, and ECF air temperature and humidity (given at 2-m height) were adjusted to 10-m height, and surface wind speed (reported at 10 m) was adjusted to neutral stability using the flux-profile relationships from Fairall et al. (2003). The LW radiation was computed using the parameterization of Clark et al. (1974), used in Southampton Oceanography Centre (SOC) climatology (Josey et al. 1999). The different algorithms show quite a large range of estimates for turbulent heat fluxes (Blanc 1985; Kent and Taylor 1995; Hasse and Smith 1997; The WGASF Group 2000; Brunke et al. 2003) and for LW radiation (Fung et al. 1984; Bignami et al. 1995; Josey et al. 1997). Thus, quantitatively different results might be obtained for different schemes. However, we are focusing on the sampling impact on the flux fields. Qualitative similarity of the turbulent and LW schemes implies that our main conclusions will hold for most schemes.

For a proper computation of the SW radiation four observations per day (0000, 0600, 1200, and 1800 UTC) are not enough for an adequate description of the diurnal cycle, and as a result daily averaged SW fluxes will be biased. The SW flux diagnosed by the reanalyses is not a prognostic variable, but a 6-hourly average for the period of the reference time plus 6 h and thus accounts properly for the diurnal cycle. To apply the so-called hourly models designed for instantaneous measurements we computed the SW radiation, changing for each report the solar altitude around the clock with 30-min step for the midmonth date and the latitude varying within a corresponding 2° latitudinal belt, assuming the cloud cover and temperature to be constant (Gulev 2006, manuscript submitted to J. Atmos. Oceanic Technol.). In some regions diurnal variations in cloudiness and temperature may affect the results. This bias, however, is more important for climate means than for estimated sampling uncertainties. For the computations of instantaneous SW values we used the model of Malevsky et al. (1992), which has been employed for the construction of the Institut für Meereskunde (IFM) climatology (Lindau 2000). Its validation against observational data (Niekamp 1992; Gulev 1995) shows that it gives the smallest biases in comparison to the parameterizations of Reed (1977), Dobson and Smith (1988), and Lind et al. (1984). Instead of the astronomically driven Payne’s (1972) albedo, traditionally used in VOS computations, we applied the Girdiuk et al. (1985) albedo, which depends also on the cloud cover and gives more realistic values in high latitudes.

c. Simulation of the VOS sampling density in the NWP flux-related variables and fluxes

The regularly sampled flux-related variables and recomputed fluxes from the NWP products were subsampled to match the VOS sampling density. In different regions ICOADS provides from zero to several thousand samples per months in 2° × 2° boxes, whereas NCEP–NCAR, ERA-40, and ECF provide always 120 samples for a 30-day “month.” The limit of 120 samples per month is exceeded in VOS only over midlatitudinal areas of the Northern Hemisphere (Fig. 1). To simulate the VOS-like sampling for the NWP flux fields, 6-hourly data were matched to the dates and UTC hours of the ICOADS reports. If the ICOADS reports were not available at “standard” times (0000, 0600, 1200, and 1800 UTC), the adjacent snapshots were interpolated to the exact time of the VOS sample. In cases where more than one ICOADS report was available at one instant, the NWP fluxes were repeatedly used to simulate the oversampling of the VOS data. A similar procedure was used by Gulev et al. (2003b) for estimating sampling uncertainties in wave parameters. Da Silva et al. (1994) used a simplified version of this procedure for the comparison of University of Wisconsin–Milwaukee (UWM) and 12-hourly ECMWF operational fields. This procedure was applied to the turbulent fluxes, LW radiation, and the SW radiation recomputed for the “rotated around the clock astronomy” and midmonth date (Gulev 2006, manuscript submitted to J. Atmos. Oceanic Technol.).

After the procedure of subsampling, the computed fluxes and individual variables were averaged within 2° × 2° boxes. This procedure leaves gaps for each month in the unsampled 2° × 2° boxes. Application of different interpolation methods for gap filling gives yet another source of uncertainties of VOS products (see, e.g., Sterl 2001, 2004). In this study we applied the modified method of local procedures (Akima 1970) in order to produce flux fields on a regular grid, which was used for the development of the wave climatology (Gulev et al. 2003b). The idea behind this method is close to the krigging technique, but is much more computationally effective. Spatial smoothing was done using a two-dimensional Lanczos filter (Duchon 1979; Gulev et al. 2002). First, the flux products were interpolated on a half-degree grid and then the Lanczos filtering has been applied for 36 directions with the cutoff radius varying from 166 to 455 km.

Figure 2 shows an example of the methodology used and demonstrates the time-dependent influence of sampling on sea–air flux estimates in the Labrador Sea, playing a key role in driving the Atlantic general circulation (e.g., LabSea Group 1998). Figure 2a presents sensible heat fluxes in the Labrador Sea for January 1978 recomputed from the NCEP–NCAR reanalysis data and those computed from VOS data. The monthly mean sensible heat flux obtained from VOS is 6 W m⁻² smaller than that obtained from NCEP–NCAR if only data collocated in time are used. However, the total monthly mean sensible heat flux from NCEP–NCAR, using all 124 six-hourly values available, is 160 W m⁻² higher than that derived from all the 14 VOS reports. This highlights the significance that the effect of inadequate sampling may have. Note that we selected one of the best-sampled months (14 samples) during the period after 1973 when the typical sampling density in this region lies between zero to seven reports per month (Fig. 2b). During the period 1948–73 observations at OWS B (56.5°N, 51°W) contributed 80% to 90% of the total number of reports and nearly 98% of all winter observations in the Labrador Sea. Termination of the OWS B in 1973 resulted in a considerable drop in the number of VOS reports, especially in winter (Fig. 2b). Figure 2c shows winter [January–March (JFM)] differences between the fully sampled NCEP–NCAR sensible heat fluxes and those derived from the NCEP–NCAR 6-hourly values matching the VOS observations in a 4 × 4 degree box around the OWS B. During the period 1948–72 differences vary within 10 W m⁻² with an average of 2 W m⁻² and a standard deviation (std) of 8 W m⁻². However, after 1973, differences are positive for most years with a mean of 51 W m⁻² and a std of 34 W m⁻². Figure 2c shows that even for long-term averages, sampling biases may amount to as much as 50 W m⁻² in highly variable areas such as Labrador Sea. Similar conclusions can be drawn from the data of the LabSea experiment (LabSea Group 1998; Renfrew et al. 2002). During February–March 1997 the research vessel (RV) Knorr collected several hundred meteorological observations in the Labrador Sea (Renfrew et al. 2002). We selected for the same period only those VOS reports that do not belong to RV Knorr dataset (eight reports) and obtained an underestimation of the Knorr values (including additional eight VOS samples) of 105 and 71 W m⁻² for sensible and latent heat, respectively.

d. Estimation of sampling uncertainties

Sampling uncertainties depend on the sampling density and on the method used to carry out the subsampling. If VOS-like sampling is simulated according to the real time of the VOS reports, the squared difference between the monthly means of the regularly sampled variables or fluxes (x_o) and VOS-like sampled variables (x_u) gives the squared total sampling uncertainty, χ²:

View Expanded

Alternatively, the simulation of sampling can be carried out by randomly choosing n NWP data, n being the number of VOS observations for one particular box and month. This method has been traditionally used to estimate sampling uncertainties (e.g., Kidson and Trenberth 1988; Gulev et al. 2003b; Chang 2005). This procedure yields the random sampling error, δ, which is only associated with the number of samples available; the actual UTC times of observations are not considered. Following Gulev et al. (2003b), for each month and 2° × 2° box we repeated this procedure 20 times, yielding 20 estimates of δ_i, i = 1, . . . 20. The value 〈δ_i²〉^1/2, with 〈〉 being the averaging operator, gives an estimate of the monthly random sampling error. Sensitivity experiments for selected years show that dependence of δ on the number of simulations becomes 3–8 times weaker for i = 7 and becomes negligible for i > 14. For ECF, for which no atmospheric data were used to constrain the model, only random sampling errors were estimated. Although the model may quite successfully simulate basic characteristics of synoptic variability, it cannot be expected to reproduce particular synoptic events after some days when the impact of initial conditions goes to zero (loss of predictability).

The difference between the squared total sampling error and the squared random sampling error, that is,

View Expanded

represents the squared actual sampling error, which is not random. It partly accounts for the fair-weather bias, which is associated with the fact that ships tend to avoid stormy conditions. However, for many poorly sampled regions actual sampling errors are dominated by the fact that ships tend to pass grid boxes during limited periods only (hence, e.g., providing several measurements of the same synoptic situation). In this case the actual VOS-like sampling effectively provides a smaller number of independent observations in comparison with the random sampling procedure.

Estimates of the total and random sampling errors are valid only for grid cells with at least one report per month. For the fully unsampled boxes, sampling uncertainty is represented by the spatial interpolation error, γ (G), which depends on the interpolation operator G used for the particular flux climatology to provide users with gap-free fields. This error was quantified by comparing the monthly means of the regularly sampled NWP variables and those implied by the interpolation procedure for the grid cells with no observations in ICOADS. Note that skills of the interpolation procedure and, therefore, the associated uncertainty will also depend on the sampling errors in the neighboring locations.

For individual flux-related variables there are two kinds of sampling uncertainties. The first one corresponds to individual parameters such as air temperature (Fig. 1a). The second one arises since more than one parameter has to be available simultaneously in order to estimate surface fluxes (Fig. 1b). We will call these two estimates “parameter-sampling errors” (χ_p, ξ_p, δ_p, γ_p) and “flux-sampling errors” (χ_f , ξ_f , δ_f , γ_f). All sampling uncertainties described above were estimated for meteorological variables as well as for air–sea fluxes (Q_h, Q_e, SW, LW, net heat flux) using 6-hourly data from NCEP–NCAR, ERA-40, and ECF and ICOADS reports for the corresponding periods. Our focus will be on the NCEP–NCAR-based results, which we will compare with 10 yr of ERA-40 and ECF.

a. Random sampling errors

The random sampling errors in air temperature, δ_p(T_a), scalar wind speed, δ_p(V), and total cloud cover, δ_p(C_n) for January and July for the period 1948–2002 (Fig. 3) represent the joint effect of the sampling density and the intensity of synoptic-scale variability of individual parameters. The largest winter values of δ_p(T_a) amount to 3°C in the poorly sampled Labrador and Greenland–Iceland–Norwegian (GIN) Seas in the Atlantic and Okhotsk and Bering Seas in the Pacific, as well as in the Southern Ocean. The smallest values of δ_p(T_a) ranging within 0.2°C are observed along the best-sampled ship routes in the midlatitudinal and tropical oceans, which are characterized by weaker synoptic variability. The largest random sampling errors in the scalar wind speed are higher than 3 m s⁻¹ in the cold season in the North Atlantic subpolar latitudes and in the Southern Ocean and drop to 0.1–0.4 m s⁻¹ in well-sampled areas. Random sampling errors in the total cloud cover vary from several percent in well-sampled regions to 15%–25% in the poorly sampled subpolar regions of the Northern Hemisphere and Southern Ocean. Random sampling errors in specific humidity (not shown) generally follow the spatial distributions of δ_p(T_a) and have maximum values of 2–3 g kg⁻¹ in the poorly sampled regions of the subpolar North Atlantic in winter.

The ratio between the “flux sampling” errors (δ_p) and the “parameter sampling” random errors (δ_f) varies from 1.5 to 2 in the Northern Hemisphere midlatitudes to values slightly higher than 1 in the Southern Ocean. Comparison of zonal averages of (δ_f) and (δ_p) (Fig. 4) shows that values of δ_f(T_a) are larger than those of δ_p(T_a) by 0.1°–0.3°C in the Northern Hemisphere midlatitudes and by 0.08°–0.15°C in the Southern Ocean. The highest values are typically found during the cold season. For the wind speed, the largest differences (about 0.8 m s⁻¹ in winter and 0.3–0.5 m s⁻¹ in summer) are observed in the Northern Hemisphere midlatitudes. Zonally averaged differences between the values of δ_f(C_n) and δ_p(C_n) (not shown) vary from 2% to 8% with the maximum found in the Northern Hemisphere midlatitudes. A qualitatively similar distribution is observed for specific humidity typically in the range 0.1–1.8 g kg⁻¹ (not shown).

The largest random sampling errors in sensible heat flux (Figs. 5a,b) during boreal winter amount to as much as 60 W m⁻² in the Labrador and GIN Seas in the North Atlantic as well as in the western marginal seas of the Pacific. For the latent heat flux (not shown) the largest sampling errors are observed in the Southern Ocean, varying from 40 to 60 W m⁻² during the cold season and being 20%–30% smaller in austral summer. Random sampling errors in radiative fluxes (Figs. 5c–f) are smaller than those in the turbulent fluxes and amount to 10–15 W m⁻² for SW radiation and to 20 W m⁻² for LW flux. The highest δ_f(SW) values (>15 W m⁻²) are observed in the Southern Ocean during austral summer and in the North Atlantic subpolar latitudes during boreal summer, when the actual values of SW radiation are relatively high. Locally, the high values of δ_f (LW), ranging from 20 to 40 W m⁻², are observed in the subpolar latitudes of the North Atlantic during boreal winter. Random sampling errors in the net heat flux (not shown) were estimated from the individual values of the net fluxes. The largest values may amount to as much as 40–80 W m⁻² and observed during the cold season in the subpolar North Atlantic and North Pacific and in the Southern Atlantic and Indian Oceans.

b. Total and actual sampling errors

The total sampling errors, χ, which take into account the actual VOS-like sampling, show spatial patterns very similar to those obtained for random sampling errors (not shown); their magnitude, however, is generally larger. Zonal differences between the total and random sampling errors (Fig. 6) represent the actual sampling uncertainties ξ according to Eq. (2). The largest values of ξ_p (T_a) amount to 2°–3°C in winter in the Northern Hemisphere subpolar latitudes and from March to October in the Southern Ocean south of 60°S. For the wind speed the largest differences of about 1.5 m s⁻¹ are observed in the subpolar latitudes of the Northern Hemisphere during the cold season, reaching a maximum of 2.5–3 m s⁻¹ in the subpolar northwest Atlantic. In the Southern Ocean ξ_p (V) varies from 1 to 1.7 m s⁻¹ and does not show as clear a seasonal dependence as was found in the Northern Hemisphere.

Figure 6c shows that the actual sampling adds up to 20 W m⁻² to the zonal random sampling errors in Q_h in the Northern Hemisphere subpolar latitudes during boreal winter. January and July maps of the actual sampling errors in Q_e (Figs. 7a,b) are somewhat different from those for the random sampling errors. The highest winter values of ξ_f(Q_e) of up to 30 W m⁻² are observed in the subpolar North Atlantic, in the Gulf Stream area and in the midlatitudinal northwest Pacific, implying total sampling errors from 50 to 80 W m⁻². The highest July values (30–50 W m⁻²) are evident in the South Pacific and Atlantic Oceans. In many poorly sampled boxes of the Southern Ocean (less than three–five reports per month) the values of χ_f(Q_e) and δ_f(Q_e) are quite close to each other. This shows that the total sampling error in this area is to a lesser degree determined by the actual sampling. The errors in Q_h show a similar behavior in this area (not shown). The highest winter values of ξ_f(LW) (Figs. 7c,d) range from 15 to 30 W m⁻² in the subpolar North Atlantic and from 10 to 20 W m⁻² in the North Pacific. The highest July values of ξ_f(LW) of up to 30 W m⁻² are found in the Southern Ocean. Zonally averaged actual sampling errors in SW radiation (Fig. 6d) show maxima of 10–20 W m⁻² during the respective summer seasons of both hemispheres. Figure 8 shows the total sampling errors in the net sea–air heat flux for January and July. Representing the combined effect of the uncertainties in all flux components, the values of χ_f(Q_n) reach a maximum of 70–100 W m⁻² in the subpolar North Atlantic in boreal winter. Maximum winter values of χ_f(Q_n) in the North Pacific are smaller and range from 30 to 50 W m⁻². Total sampling errors in the net heat flux in the Southern Ocean vary from 40–60 W m⁻² in January to 50–80 W m⁻² in July. The smallest values of χ_f(Q_n) are observed along well-sampled ship routes and lie within 10–15 W m⁻².

c. Dependencies of the sampling uncertainties on the number of samples and the intensity of synoptic variability

Understanding how sampling errors depend on the number of samples may provide insights into how many measurements are needed to obtain heat fluxes of a prescribed accuracy. Weare and Strub (1981) and Weare (1989) for the Tropics and Cayan (1992) for the midlatitudes found that about 10 observations per month per 5° box guarantee unbiased estimates of turbulent fluxes. However, Legler (1991) accounted for the intramonthly variability and concluded that the accurate computation of, for example, monthly mean wind speed in midlatitudes requires from 90 to 170 reports. Chang (2005) analyzed the sampling impact on monthly sextile statistics of ICOADS SLP and found that 20–30 observations are needed for unbiased esti mation. We sorted all monthly estimates of χ and δ for the 55-yr period into classes of the number of samples from 1 to 120. The number of estimates available reduces from 3–5 × 10⁵ for 1< n < 5 down to 1000–5000 for the n > 50. The dependence of sampling errors on n shows quite a large scatter, implying large uncertainties of the approximation. To minimize these uncertainties, sampling errors for parameters and fluxes were normalized:

View Expanded

where σ(x) is the intramonthly standard deviation of the variable x, estimated from the regularly sampled NWP data. Normalized sampling errors decrease with the number of samples from a value of about 1 for n = 1 (for both δ and χ) to 0.06–0.1 (for δ) and 0.15–0.20 (for χ) for n > 40 (Fig. 9). For large enough n the total sampling errors are typically 2–3 times higher than random errors. Dependencies of the normalized sampling errors on the number of samples n_x can be approximated as follows:

View Expanded

where a_χ, a_δ, b_χ, and b_δ are empirical coefficients that were determined by a least squares approach using all data. Numerical values for these coefficients are given in Table 1 for all sea–air flux components and can be further used for the estimation of the sampling errors for a given number of reports per month and 2° boxes. The fastest decrease of sampling errors with n is found for the SW radiation and the slowest for sensible heat flux, implying that less observations are needed for the adequate estimation of monthly SW radiation in comparison to more highly variable turbulent fluxes, which require more reports for obtaining the accurate monthly mean.

d. Uncertainties due to interpolation and extrapolation in data-void areas

Being also formally associated with sampling density, interpolation errors, γ, by nature are somewhat different from the sampling uncertainties described above. They depend on the procedure of spatial interpolation applied, on the arrangement of data-void locations, and the spatial correlation of variables being analyzed. Additionally, sampling uncertainties in areas surrounding data-void grid cells have an impact on the interpolation errors (e.g., Kent et al. 2000). Figures 10a–d show the interpolation uncertainty for the wind speed and sensible heat flux, estimated by comparing regularly and VOS-like sampled NCEP–NCAR monthly fields. For wind speed, the largest January values of γ_f(V) exceeding 2 m s⁻¹ are observed in the Labrador and GIN seas in the Atlantic, whereas in the Sea of Okhotsk and subpolar northwest Pacific γ_f(V) may amount to 3 m s⁻¹. During austral summer the interpolation error can amount to 2–3 m s⁻¹ in the southeast Pacific and southwest Indian Ocean. The interpolation errors in sensible heat flux (Figs. 10c,d) vary from several watts per meter squared in the Tropics and midlatitudes during the warm season to 60 W m⁻² in the subpolar latitudes of the North Atlantic and North Pacific and to 30–50 W m⁻² in the Southern Ocean during the cold season. In the poorly sampled Labrador Sea and northwestern Pacific, interpolation errors can be 10%–30% higher than sampling errors (Figs. 5 –8), largely explaining the total uncertainty associated with inadequate sampling.

Interpolation uncertainties in the latent heat flux (not shown) are 10% to 30% higher than those for the Q_h in the midlatitudes and Tropics and 20%–50% smaller in the subpolar latitudes. Zonally averaged interpolation uncertainties in the SW and LW radiation (Fig. 11a) vary within 5 W m⁻² in the Tropics and midlatitudes and increase to about 20 W m⁻² in the subpolar latitudes of the Northern and Southern Hemispheres during the cold season. Figure 11b shows that from 50°S to 40°N total sampling uncertainties in the net heat flux are 30%–60% larger than interpolation errors. However, in the northern and southern subpolar latitudes interpolation errors may become larger than the sampling errors with the locally highest differences in the poorly sampled and semi-isolated Labrador and GIN Seas and in the Sea of Okhotsk.

How sensitive are these results to spatial interpolation schemes? We tested successive correction, used by Josey et al. (1999) and da Silva et al. (1994) and krigging, applied by Lindau (2000), for the northwest and southern Atlantic. Table 2 compares the values of γ, obtained using these methods and the modified method of local procedures used in this study. Area-averaged estimates vary within the range of ±10% with better skills of the local procedure method in the Labrador Sea and of successive correction in the Southern Ocean. Krigging, although quite skillful on average in the Lab- rador Sea, may result in locally high uncertainties and therefore in higher standard deviations. Nevertheless, the spatial structure and the ratio between the interpolation uncertainties and other sampling errors remain similar when estimated using different algorithms.

a. Comparison with ERA-40 reanalysis

To compare estimates of sampling errors derived from the NCEP–NCAR reanalysis with alternative data, we performed similar computations with ERA-40 reanalysis and compared the results for the period 1992–2001. This period in both reanalyses is largely affected by observational data, which were somewhat different for NCEP–NCAR and ERA-40 (Kalnay et al. 1996; Uppala et al. 2005). January and July maps of the total sampling uncertainty of ERA-40 sensible heat fluxes for 1992–2001 (Figs. 12a,b) are very similar to those for NCEP–NCAR for the same period. Because of poor sampling of the Southern Ocean in the 1990s, especially during austral winter, many grid cells in the southern Indian and Atlantic Oceans remained data void. In most areas the sampling uncertainty estimated from ERA-40 is somewhat larger than that derived from NCEP–NCAR (Figs. 12c,d). Global differences are 1.4 W m⁻² for January and 1.6 W m⁻² for July. Spatial distributions for the uncertainties in the latent flux derived from both reanalyses (not shown) are also very similar to each other with the higher values of χ(Q_e) for ERA-40 (global differences 3.6 W m⁻² for January and 4.1 W m⁻² for July). Other flux-related variables and fluxes (SW and LW) also show slightly higher sampling uncertainties derived from ERA-40 data compared to NCEP–NCAR. This can most likely be explained by the higher-resolution model used for ERA-40 (T159 versus T62 in NCEP–NCAR) and, thus, potentially higher magnitudes of synoptic variability simulated in by the ERA-40 system. Our analysis shows that intramonthly standard deviations of surface variables and fluxes are systematically higher in ERA-40 in comparison to NCEP–NCAR by 1%–2% to 10%–20%. If we normalize the sampling uncertainties with standard deviations [Eq. (3)], the differences between the errors derived from two reanalyses become very small and do not show any regular pattern with the global mean deviations closely matching zero (Figs. 12e,f) and the pattern correlation exceeding 0.9, which is in line with the above explanation. Remarkably, the dependencies of χ̂(n) derived from ERA-40 are hardly distinguishable from those obtained from NCEP–NCAR. In Fig. 13 we show approximations of χ̂(n) derived according to Eq. (4) from NCEP–NCAR and ERA-40 for the period 1992–2001. They practically coincide with each other, implying that Eq. (4) is also valid for sampling uncertainties derived from ERA-40 data.

b. Comparison with ECMWF seasonal forecasts

Next, the impact of the use of actual data on the estimated sampling errors is investigated. VOS-like random subsampling is applied to wintertime seasonal integrations with the ECMWF model, ECF, in which no actual data were assimilated and the model used was very similar to the one used to carry out the ERA-40 reanalysis. As was mentioned above, the focus is on random sampling errors only, which are conceptionally better to understand for these seasonal integrations due to the fact that individual synoptic systems cannot be reproduced. Figures 14a,b show January maps of the random sampling uncertainties in the sensible and latent heat fluxes derived from ECF for the period 1992–2001. Again, the spatial patterns are quite comparable with those obtained for NCEP–NCAR and ERA-40 reanalyses with the highest uncertainties in poorly sampled and highly variable subpolar latitudes of the Northern Hemisphere and Southern Ocean. Differences between ECF and ERA-40 sampling errors (Figs. 14c,d) may locally amount to 10–15 W m⁻², being larger than the differences between the estimates derived from the two reanalyses. For both sensible and latent heat fluxes systematically higher sampling uncertainties in ECF were identified in the midlatitudinal and subpolar North Pacific and systematically higher uncertainties in ERA-40 were found in the subpolar North Atlantic. This can be attributed to systematic errors of the ECMWF model climate in simulating synoptic variability for the two ocean basins (Jung 2005). This explanation is supported by the fact that the normalized sampling uncertainties are quite close to each other with a pattern correlation of 0.84 and with no regular pattern for the difference fields. Figure 13b shows the scatterplot of the normalized random sampling uncertainties in the latent heat flux derived from the ERA-40 and ECF data. Despite some reasonable scatter, the slope of the orthogonal regression closely matches 1 with intercept of nearly zero. Thus, analysis of two alternative NWP datasets supports our conclusions based on NCEP–NCAR data.

c. Comparison with independent VOS observations

To further assess how skillful the reanalyses are in simulating the magnitude of synoptic and mesoscale variability, we performed another regional comparison. To this end sampling uncertainties were estimated using exclusively those VOS data that were not included into ICOADS. Using the data collected under the SECTIONS program in the Newfoundland basin (Gulev 1994, 1999) we selected those boxes in which the SECTIONS data provide more than 120 reports per month and the ICOADS provides less than 30 reports per month. Altogether six monthly time series were selected for 1987, 1988, and 1990 (Table 3). For these time series we performed the procedure of subsampling as described in section 3 by matching ICOADS reports with independent meteorological data from the SECTIONS collection. The flux estimates from SECTIONS data were computed using the same algorithms listed in section 3. Diagnosis of this small subset shows that the NCEP–NCAR reanalysis underestimates the magnitude of intramonthly variability by about 10% for wind speed and 3%–5% for other surface variables. On average, sampling errors obtained from SECTIONS data are 16% ± 5% higher than those obtained from NCEP–NCAR reanalysis data (Table 3). If the effect of the magnitude of synoptic variability is removed by normalization, then the estimated sampling errors are very similar for the SECTIONS and NCEP–NCAR reanalysis data (Table 3). Another independent dataset collected by the RV Knorr in Labrador Sea during one month of 1996 (LabSea Group 1998; Renfrew et al. 2002) also shows 6%–10% higher magnitude of synoptic variability in ship observations compared to NCEP–NCAR reanalysis data and, hence, implies higher actual sampling uncertainties. As with the other datasets described in this study, differences in estimated sampling uncertainties between the RV Knorr and NCEP–NCAR reanalysis data become small when normalized data are used.