Satellite data have provided a wealth of information on the Earth system and have had a profound impact on operational numerical weather forecasting. Unlike ground-based instruments or airborne field campaigns, satellite data provide continuous global coverage, which facilitates the study and assimilation of distributions of atmospheric fields, as well as global model evaluation. However, satellite measurements sample continuously changing atmospheric fields only at discrete times and locations, depending on the satellite orbit as well as the measurement technique, which can result in a biased depiction of the atmospheric field.

Typically, the impact of orbital sampling has been evaluated by comparing a raw model field against a satellite-sampled one. For example, many studies have documented sampling errors for rainfall estimates e.g., and brightness temperatures , as well as O3, CO, temperature and a few other atmospheric parameters sampled by nadir-viewing instruments . Recently, evaluated the sampling bias in monthly and annual mean climatologies of O3 and H2O from 16 satellite instruments, including limb emission sounders, limb scattering sounders, solar occultation instruments and a stellar occultation instrument. They concluded that coarse sampling may introduce significant sampling uncertainties in climatologies, not only through nonuniform spatial sampling but, more importantly, through nonuniform temporal sampling, that is to say, producing regional monthly means using measurements that do not cover the entire month. As expected, the sampling bias was found to be the greatest in regions with large natural variability.

In this study we further evaluate the impact of the Aura Microwave Limb Sounder (MLS), the HALogen Occultation Experiment (HALOE) and the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) sampling patterns using the Canadian Middle Atmosphere Model (CMAM). MLS sampling provides a dense uniform pattern, while HALOE and ACE-FTS are representative of coarser solar occultation sampling patterns. We use HALOE and ACE-FTS sampling patterns because they are commonly used solar occultation datasets and, furthermore, because their sampling patterns are significantly different and thus representative of the range of observation patterns obtained by solar occultation instruments.

Our study has two purposes. (1) We expand upon previous studies by quantifying the sampling bias of these instruments affecting measurements of upper tropospheric and stratospheric temperature and trace gas species. (2) We investigate how differences in data coverage may affect the outcome of two illustrative atmospheric studies: trend detection and quantification of tropical vertical velocities. We assess the differences in the long-term (> 30 years) trends in temperature, O3 and CO estimated using datasets with different sampling patterns. Also, we characterize the impact of orbital sampling on derived lower-stratospheric tropical vertical velocities. These velocities are computed by correlating the lag of the water vapor “tape recorder” signal between adjacent levels . As such, they are likely an upper bound on the actual velocity . These vertical velocities are modulated by the quasi-biennial oscillation (QBO), seasonal cycles and El Niño–Southern Oscillation (ENSO) e.g.,.

This paper is organized as follows: Sect.  describes the satellite patterns and the model fields used. Section  briefly revisits sampling bias estimates, while the impact of sampling on the estimation of long-term trends as well as on trend detection is presented in Sect. . Section  addresses the impact of orbital sampling on derived tropical vertical velocities, and Sect.  summarizes our results. The results discussed in this study should be considered as example cases. Whether the results shown represent reasonable estimates of the true orbital-sampling-induced artifacts (e.g., in the sampling bias, in the inferred magnitude of the trends or in the derived tropical vertical velocities) may also depend on how well the model fields represent the real atmosphere.

We evaluate the sampling biases associated with constructing monthly zonal means from the raw and satellite-sampled data. The raw or sampled zonal means for a particular latitude bin for each pressure level are given by Zlx‾=1N∑ylx, where N is the total number of points, y, belonging to a latitude bin l and x is a placeholder variable for either the raw data, denoted by the superscript r, or the sampled data, denoted by the superscript s. Figure  shows examples of raw and sampled zonal means for temperature, O3 and H2O. The difference between the satellite-sampled zonal mean and the raw zonal mean gives the absolute sampling bias, that is to say,

SA=Zls‾-Zlr‾ or, in percentage, SP=Zls‾-Zlr‾Zlr‾×100. Figure  shows examples of the sampling biases for temperature, O3 and H2O for January 2005 CMAM30-SD fields. Relative biases are shown for trace gas species to accommodate their strong vertical gradients. These biases only display the impact of sampling the CMAM30-SD fields; as mentioned before, how well these biases represent the true atmospheric sampling biases will depend on how close the model fields are to the real atmospheric state.

For each month, instrument and pressure level, this bias was computed for all the latitude bins in which an instrument was able to sound the atmosphere. To summarize the potential sampling biases, we computed root-mean-square (RMS) biases over 1 year's worth of data. As an example, Fig.  shows these calculated RMS sampling biases for temperature, O3 and H2O for 2005. Overall, there is a direct correlation between the sampling biases and the variability of the geophysical parameters. For example, as noted by , O3 sampling biases for the three instruments are smaller in the tropics and larger at midlatitudes and in the polar regions, where variability is low or high, respectively. However, the biases in all regions are minimized by dense uniform sampling such as that of MLS.

Figure shows the mean and maximum sampling biases over all latitudes for the model year 2005 for all the atmospheric parameters studied. In general, HALOE and ACE-FTS sampling patterns produce mean and maximum sampling biases 1 order of magnitude larger than those of MLS. For example, for the occultation sensors, the temperature maximum sampling biases are about 10 K compared to 1 K for MLS. Similarly, in the middle stratosphere, H2O maximum sampling biases for the solar occultation instruments can be as large as 5 % compared to less than 1 %, and lastly, HNO3 maximum sampling biases can be as large as 50 % compared to less than 5 %.

We now evaluate the impact of orbital sampling on the representation of long-term trends. Accurate representation of long-term trends is crucial because they are indicators of climate change, as well as ozone recovery. To summarize the effect of the orbital sampling upon long-term trends we use Taylor diagrams , which provide a convenient method for visualizing statistics of how closely patterns match each other; in this case, they are used to depict the success of the satellite-sampled data in representing the variability found in the raw model fields. The similarity is quantified by their correlation coefficient, their centered RMS difference (RMSd) and their standard deviations. Simply, the centered RMSd is the RMS of the differences between the two anomaly time series.

In the diagrams shown, all data are normalized to the raw model standard deviation to facilitate showing different pressure levels in the same figure. In these diagrams, there are four things to consider: (1) the azimuth angle indicates the correlation between the satellite-sampled and raw data; (2) the point with normalized standard deviation of 1 and correlation of 1 is the reference point and corresponds to the raw model data; (3) the distance between any point in the figure and the reference point indicates the ratio of the centered RMSd and the raw model standard deviation (green contours); and (4) the distance between other points in the plot and the origin is the ratio between the satellite-sampled standard deviation and that of the raw model field.

Near-global (60∘ S–60∘ N) long-term (1979–2012) patterns are compared between satellite-sampled and raw model fields in Fig.  for all the atmospheric parameters evaluated in this study. Means were computed by averaging all data available between 60∘ N and 60∘ S with no effort to use only latitudes where the satellites sampled. This approach was taken to show the representativeness of near-global patterns. We did not expand this study to the latitudes poleward of 60∘ N or 60∘ S because ACE-FTS does not sample these areas for 4 months per calendar year and HALOE does not sample for 5 and 6 months at the South and North Pole, respectively (see Fig. ). Figure  shows the raw model standard deviations used to normalize these diagrams (black lines). Overall, the MLS-sampled data (circles in Fig. ) for all variables and all pressure levels are close to the reference point, indicating high correlation coefficients, low centered RMSd and the expected standard deviation (i.e., a standard deviation similar to that of the full model fields). The HALOE-sampled data (triangles) show intermediate performance, followed by the ACE-FTS-sampled data (squares), which show the weakest correlation and the largest normalized standard deviation. For example, this is easily seen in the CO Taylor diagram, where the MLS-sampled points all cluster tightly at the reference point, whereas HALOE-sampled points lie farther away and ACE-FTS-sampled points the farthest.

To highlight the impact of these sampling differences, Fig.  shows trend estimates for near-global temperature at 10 hPa using the raw and satellite-sampled data. Three methods have been used to compute the trends. The first is a simple linear fit (an ordinary least square regression) through the points. In the second, we deseasonalize the data (we remove the observed climatological monthly mean at every grid point) before computing a linear fit. Lastly, we consider a trend model of the form Y=μ+ωt12+S+N, where Y is the monthly raw or sampled average measurements (temperature, CO or O3 concentration, etc.), μ is a baseline constant, ω is the mean trend per year, t is time in months, S is a seasonal mean component represented by S=a1sin⁡(2π12t+b1)+a2sin⁡(2π6t+b2), and N is the unexplained portion of the data assumed to follow a first-order autoregressive model [AR(1)]. That is, it satisfies

N=ϕN1+ε, where ϕ is the autocorrelation of the noise, computed and assumed temporally invariant, following , and ε is independent white noise variables with variance σε2. As pointed out by , ϕ has the effect of reducing the amount of information that would have been available in the same number of independent data points. Similar models have been used in many previous trend studies e.g.. As shown in Fig. , HALOE (ACE-FTS) sampling artificially reduces (increases) the trend estimates by about 10 % (25 %). Despite agreement on the sign of the trend, these sampling-induced artifacts will compromise the robustness of the derived temperature trends. We computed the trend using different methods in order to emphasize that using models that are more geophysically realistic, such as those that capture the seasonal component, may not have much impact on the estimated trends or, as pointed out by , on the trend statistical properties.

Figure shows how these sampling-induced trend artifacts vary with altitude. To avoid clutter, this figure only shows the differences in trend magnitude computed using Eq. (), but the ones computed using the other trend detection methods are similar. We show results for temperature, O3 and CO because these parameters exhibit clear trends at most pressure levels in the CMAM30-SD simulations and also because overall they can be accurately described by the model given by Eq. (). For O3 we only use data starting from 2000 to capture the expected period of O3 recovery. Overall, MLS sampling allows the estimation of the trend magnitudes to about 1 order of magnitude better than HALOE and ACE-FTS sampling, with accuracy better than 1 % at most pressure levels for temperature and CO and better than 10 % for O3.

Figure also shows the estimated number of years required to definitively detect these trends. When using Eq. (), the number of years, n*, needed to detect a given trend with a 95 % confidence level with a probability of 0.90 can be approximated by n*=3.3σN|ω|1+ϕ1-ϕ2/3, which indicates that trend detectability depends on three factors: (1) ϕ the autocorrelation of the residual between the data points and the trend model computed following ; (2) σN the standard deviation of the residual, which corresponds to the unexplained variability of the data; and (3) the absolute magnitude of the trend. It is also noted that σN is related to σε by σN2=σε21-ϕ2 in this trend model (Eq. ). Note that ϕ was computed for the raw as well as the satellite-sampled data. As shown in Fig. , trend detection using data with HALOE or ACE-FTS sampling will require considerably more years than using data with MLS sampling. This is due to an increase in the magnitude of σN resulting from the noisiness of the time series based on the HALOE or ACE-FTS sampling patterns (e.g., Fig. ). For example, at 1 hPa, the pressure level where the strongest temperature trend is found in CMAM30-SD, a 15-year record of MLS-sampled observations would be required to detect such a trend at the 95 % confidence level, while HALOE and ACE-FTS sampling would require 25 and 30 years, respectively. For O3 at 2 hPa, the pressure level where the strongest O3 trend is found in CMAM30-SD, the MLS sampling pattern would require about 11 years, while HALOE and ACE-FTS would require about 20 and 30 years, respectively. In addition, MLS sampling requires the same number of years as for the raw model fields; that is, the required number of years is only determined by the natural variability. We also performed this analysis using only the autocorrelation computed for the raw model data and found no significant differences.

We also investigated the effect of instrument noise, using and : σN=σε21-ϕ2+σI2nI, where σI is the instrument noise and nI is the number of measurements averaged. Typical noise estimates were taken from for MLS; , and for ACE-FTS; and and for HALOE. Since HALOE does not measure CO, we assumed the same error as given by for ACE-FTS. The effect of instrument noise was found to be negligible due to the high number of measurements even for HALOE and ACE-FTS (in a given month, around 70 000 for MLS, 600 for HALOE and 270 for ACE-FTS). These estimates of the length of the measurement record required to detect trends do not take into account the effects of a disruption of the measurements for a given period or aging of the instrument, both of which can induce artificial trends in the data that are not representative of the actual environmental trend studied.

Both HALOE and ACE-FTS provide better coverage in the extratropics than in the tropics (see Fig. ). Figure  therefore shows long-term pattern comparisons between satellite-sampled and raw data for trends derived using only data from 30 to 60∘ N. Figure  also shows the raw model standard deviations used to normalize these diagrams (purple lines). In general, HALOE- and ACE-FTS-sampled data correlation coefficients improved considerably over the near-global case, with a correlation coefficient no smaller than ∼ 0.6 and with a centered RMSd better than 1 raw model standard deviation (see Fig. ). MLS-sampled data are still closest to the reference point. Two variables can have similar trends but still perform poorly in Taylor diagrams due to either a lack of correlation or different standard deviations. In both cases, this will impact σN, resulting in an increase in the number of years required to statistically detect such a trend.

Figure is equivalent to Fig.  but for the 30 to 60∘ N latitude range. As for the near-global trends, ACE-FTS sampling still requires considerably more years to confidently detect a trend than does MLS sampling. HALOE, however, has a more uniform sampling density than ACE-FTS in this latitude range (see Fig. ), and thus the time required to detect a trend is more in line with that for MLS. Nevertheless, MLS sampling allows estimation of trends to about 1 order of magnitude better than HALOE and ACE-FTS sampling. As before, the effect of instrument noise was found to be negligible (for this latitude range the approximate number of measurements in a given month is 19 000, 220 and 70 for MLS, HALOE and ACE-FTS, respectively).

As shown, the ability to detect trends depends upon the natural variability and the correlation of the data. These in turn vary with the specific parameter as well as the location and height being studied. Studies of natural variability and autocorrelation of the data will help identify where to monitor to find more readily detectable trends, but such a study is outside the scope of this paper.

In this section we investigate the impact of orbital sampling upon derived tropical vertical velocities (a key metric for atmospheric circulation). The vertical velocities are calculated using the same approach as described by and . In short, we use time series of daily zonal mean water vapor data averaged between 8∘ S and 8∘ N (see Fig. ). We correlate these time series at different pressure levels and determine the time lag for the best correlation. The vertical velocity for the midpoint of each layer is simply computed by dividing the distance between the pressure levels (the altitude difference) by the lag. These calculations were performed using the raw model CMAM30-SD simulations as well as the satellite-sampled data. The vertical velocities derived from this method are a measure of the transport velocity averaged over 8∘ S–8∘ N and have been shown to agree well with the transformed Eulerian mean residual vertical velocity when in-mixing from the extratropics and vertical diffusion are small . Interpolation was used to fill the data gaps due to the sampling patterns. In the case of HALOE sampling, this implies linearly interpolating to fill gaps in June and December. For ACE-FTS, gaps are filled in January, March, May, July, September, November and December, when no measurements are made over the tropics (8∘ S to 8∘ N); thus, we are applying the analysis to highly interpolated data. Considering the degree of interpolation required, we do not recommend the use of ACE-FTS to derive tropical upwelling velocities, but we include this case merely as an illustrative example.

Figure (top) shows the vertical velocities averaged over 60–30 hPa derived using raw model fields as well as the satellite-sampled data. To quantify the impact of the different orbital sampling patterns, Fig.  (bottom) displays scatterplots between the raw fields and the satellite-sampled vertical velocities. The best correlation (R=1.00), the best line fit (1.07 x + 0.02, obtained using an ordinary least squares fit regression) and the smallest RMSd (0.005) are found when using the MLS sampling. ACE-FTS and HALOE sampling lead to non-negligible artifacts when deriving vertical velocities from the tape recorder.

Previous studies have shown variability in middle stratospheric tropical vertical velocities on the order of up to ±40 % associated with the QBO and ENSO . To better understand the impact of these sampling-induced artifacts, we fit the following model to the monthly vertical velocities wTR=q⋅QSI[t-tq]+e⋅MEI[t-te]+c, where wTR is the vertical velocity derived from the tape recorder, QSI is a QBO shear index, MEI is the multivariate ENSO index, c is a baseline constant, q and e are constants modifying the magnitude of the QSI or MEI, and tq and te are the QSI or MEI time offsets, respectively. The QSI is calculated from the difference in the Singapore zonal winds at 50 and 25 hPa . The MEI is determined using a combination of the principal component analysis of sea level pressure, sea surface temperature, zonal and meridional surface winds, surface air temperature, and cloudiness as described by . Figure a shows the time series of the QSI and the MEI, along with the vertical velocities averaged over 60–30 hPa derived using raw model fields. As can be seen, these vertical velocities are clearly correlated with the QSI but also show a strong relationship with the MEI in some years. Figure b–e displays the results of fitting the model described by Eq. () to the raw (panel b) and satellite-sampled (panels c–e) derived vertical velocities. The time offsets were fitted using the raw model fields and then imposed onto the satellite-sampled data. We do not fit a modeled seasonal cycle, such as the one described by Eq. (), because the methodology used suppresses the seasonal cycle . As shown, this model is able to capture most of the variability in the derived vertical velocities. The fits are primarily driven by the QSI, with MLS sampling overestimating its influence by 3.8 % (the differences in q in the equations shown in Fig. ), while HALOE and ACE-FTS sampling underestimate it by 30.7 and 31.5 %, respectively. The impact of the sampling is more pronounced for the MEI (the differences in e), with MLS, HALOE and ACE-FTS underestimating its influence by 11, 64 and 122 %. We emphasize that these sampling-induced offsets to the strength of the modulation effects of the QBO and ENSO on the circulation are only applicable to CMAM30-SD fields. These fields may not accurately represent the stratospheric tropical vertical velocities and, consequently, the actual sampling offsets could be different. As such, they should be considered only as potential biases.

The changes in tropical upwelling associated with QBO and ENSO assessed here have been shown to alter O3 transport to the midlatitude lower stratosphere and to account for approximately half the interannual variability in midlatitude tropospheric O3 . It has been hypothesized that this observed relationship between stratospheric upwelling changes and changes in tropospheric O3 may provide an emergent constraint on the tropospheric O3 response to long-term strengthening of the circulation associated with greenhouse gas increases. If so, accurate quantification of the variability in tropical vertical velocities is crucial to reducing uncertainties in estimating this response.

In this paper we evaluate the effect of orbital sampling on satellite measurements of stratospheric temperature and several trace gases. In particular, we quantify the impact of sampling in terms of the sampling bias. To illustrate the impact of orbital sampling on the outcome of representative atmospheric studies, we also quantify the induced differences in the inferred magnitude of trends and their detectability, as well as the induced differences in derived tropical vertical velocities. We calculate these sampling-induced artifacts by interpolating CMAM30-SD model fields (used as a proxy for the real atmosphere) to the real sampling patterns of three satellite instruments – Aura MLS, HALOE and ACE-FTS – to allow us to compare a dense uniform sampling pattern characteristic of limb emission sounders to the coarse nonuniform sampling patterns characteristic of solar occultation instruments.

The results suggest that overall

coarse nonuniform sampling patterns, such as the ones from HALOE and ACE-FTS, can introduce sampling biases about 1 order of magnitude greater than those from dense uniform sampling patterns, such as the one from MLS. For example, we found a temperature maximum sampling bias of about 10 K compared to 1 K and H2O maximum sampling biases as large as 5 % as opposed to less than 1 % in the middle stratosphere. These results corroborate the results of and .

Stratospheric changes such as a possible increase in the circulation and trends in temperature and O3 are signatures of greenhouse gas warming and stratospheric O3 recovery. Thus, our ability to accurately measure these changes is crucial for detecting anthropogenic influences on climate.

All the data used in this study are publicly available. CMAM30-SD fields can be found in the Canadian Centre for Climate Modelling and Analysis webpage (http://www.cccma.ec.gc.ca/data/cmam/output/CMAM/CMAM30-SD/index.shtml). MLS data are available from the NASA Goddard Space Flight Center Earth Sciences (GES) Data and Information Services Center (http://disc.sci.gsfc.nasa.gov/Aura/data-holdings/MLS/index.shtml). HALOE data are available from the HALOE GATS webpage (http://haloe.gats-inc.com/download/index.php). ACE-FTS data are available from the ACE Public Datasets webpage (http://www.ace.uwaterloo.ca/public.html).