• Athié, G., , and Marin F. , 2008: Cross-equatorial structure and temporal modulation of intra-seasonal variability at the surface of the Tropical Atlantic Ocean. J. Geophys. Res., 113, C08020, doi:10.1029/2007JC004332.

    • Search Google Scholar
    • Export Citation
  • Athié, G., , Marin F. , , Treguierd A. , , Bourlès B. , , and Guiavarch C. , 2009: Sensitivity of near-surface tropical instability waves to submonthly wind forcing in the tropical Atlantic. Ocean Model., 30, 241255.

    • Search Google Scholar
    • Export Citation
  • Boyer, T. P., , and Levitus S. , 2002: Harmonic analysis of climatological sea surface salinity. J. Geophys. Res., 107, 8006, doi:10.1029/2001JC000829.

    • Search Google Scholar
    • Export Citation
  • Chassignet, E. P., and Coauthors, 2009: U.S. GODAE: Global Ocean Prediction with the Hybrid Coordinate Ocean Model (HYCOM). Oceanography, 22, 6475.

    • Search Google Scholar
    • Export Citation
  • Cronin, M. F., , and McPhaden M. J. , 1999: Diurnal cycle of rainfall and surface salinity in the western Pacific warm pool. Geophys. Res. Lett., 26, 34653468.

    • Search Google Scholar
    • Export Citation
  • Cummings, J. A., 2005: Operational multivariate ocean data assimilation. Quart. J. Roy. Meteor. Soc., 131C, 35833604.

  • Delcroix, T., , and Henin C. , 1991: Seasonal and interannual variations of sea-surface salinity in the tropical Pacific Ocean. J. Geophys. Res., 96, 22 13522 150.

    • Search Google Scholar
    • Export Citation
  • Delcroix, T., , and McPhaden M. J. , 2002: Interannual sea surface salinity and temperature changes in the western Pacific warm pool during 1992–2000. J. Geophys. Res., 107, 8002, doi:10.1029/2001JC000862.

    • Search Google Scholar
    • Export Citation
  • Delcroix, T., , McPhaden M. J. , , Dessier A. , , and Gouriou Y. , 2005: Time and space scales for sea surface salinity in the tropical oceans. Deep-Sea Res. I, 52, 787813.

    • Search Google Scholar
    • Export Citation
  • Eldin, G., , Rodier M. , , and Radenac M. H. , 1997: Physical and nutrient variability in the upper equatorial Pacific associated with westerly wind forcing and wave activity in October 1994. Deep-Sea Res. I, 44, 17831800.

    • Search Google Scholar
    • Export Citation
  • Font, J., and Coauthors, 2010: SMOS: The challenging sea surface salinity measurement from space. Proc. IEEE, 98, 649665.

  • Fox, D. N., , Teague W. J. , , Barron C. N. , , Carnes M. R. , , and Lee C. M. , 2002: The Modular Ocean Data Assimilation System (MODAS). J. Atmos. Oceanic Technol., 19, 240252.

    • Search Google Scholar
    • Export Citation
  • Freitag, H. P., , McCarty M. E. , , Nosse C. , , Lukas R. , , McPhaden M. J. , , and Cronin M. F. , 1999: COARE Seacat data: Calibrations and quality control procedures. NOAA Tech. Memo. ERL PMEL-115, 89 pp.

  • Johnson, E.,, Lagerloef, G. , Gunn, and J. , Bonjean F. , 2002: Surface salinity advection in the tropical oceans compared with atmospheric forcing: a trial balance. J. Geophys. Res., 107, doi:10.1029/2001JC001122.

    • Search Google Scholar
    • Export Citation
  • Lagerloef, G.,, and Delcroix T. , 2001: Sea surface salinity: A regional case study for the tropical Pacific. Observing the Ocean in the 21st Century, Australian Bureau of Meteorology, 137–148.

    • Search Google Scholar
    • Export Citation
  • Lagerloef, G., , Swift C. T. , , and Le Vine D. M. , 1995: Sea surface salinity: The next remote sensing challenge. J. Oceanogr., 8, 4450.

  • Lagerloef, G., and Coauthors, 2008: The Aquarius/SAC-D mission: Designed to meet the salinity remove-sensing challenge. J. Oceanogr., 21, 6881.

    • Search Google Scholar
    • Export Citation
  • Le Vine, D. M., , and Abraham S. , 2004: Galactic noise and passive microwave remote sensing from space at L-band. IEEE Trans. Geosci. Remote Sens., 42, 119129.

    • Search Google Scholar
    • Export Citation
  • Le Vine, D. M., , Abraham S. , , Wentz F. , , and Lagerloef G. S. E. , 2005: Impact of the sun on remote sensing of sea surface salinity from space. Proc. IEEE Int. Geoscience and Remote Sensing Symp. (IGARSS), Vol. I, Seoul, South Korea, IEEE, 288–291, doi:10.1109/IGARSS.2005.1526164.

  • Le Vine, D. M., , Lagerloef G. S. E. , , Colomb F. R. , , Yeh S. H. , , and Pellerano F. A. , 2007: Aquarius: An instrument to monitor sea surface salinity from space. IEEE Trans. Geosci. Remote Sens., 45, 20402050.

    • Search Google Scholar
    • Export Citation
  • Lukas, R., , and Lindstrom E. , 1991: The mixed layer of the western equatorial Pacific Ocean. J. Geophys. Res., 96, 33433357.

  • McPhaden, M. J., 1995: The TAO array is completed. Bull. Amer. Meteor. Soc., 76, 739741.

  • McPhaden, M. J.,, and Coauthors, 2009: RAMA: The Research Moored Array for African–Asian–Australian Monsoon Analysis and Prediction. Bull. Amer. Meteor. Soc., 90, 459480.

    • Search Google Scholar
    • Export Citation
  • Picaut, J., , Ioualalen M. , , Delcroix T. , , Masia F. , , Murtugudde R. , , and Vialard J. , 2001: The oceanic zone of convergence on the eastern edge of the Pacific warm pool: A synthesis of results and implications for ENSO and biogeochemical phenomena. J. Geophys. Res., 106, 23632386.

    • Search Google Scholar
    • Export Citation
  • Ponte, R. M., , and Lyard F. , 2002: Effects of unresolved high-frequency signals in altimeter records inferred from tide gauge data. J. Atmos. Oceanic Technol., 18, 534539.

    • Search Google Scholar
    • Export Citation
  • Ray, R. D., 1998: Spectral analysis of highly aliased sea-level signals. Geophys. Res. Lett., 103, 24 99125 003.

  • Riser, S. C., , Ren L. , , and Wong A. , 2008: Salinity in ARGO. Oceanography, 21, 5667.

  • Servain, J., , Busalacchi A. , , McPhaden M. , , Moura A. , , Reverdin G. , , Vienna M. , , and Zebiak S. , 1998: A Pilot Research Moored Array in the Tropical Atlantic (PIRATA). Bull. Amer. Meteor. Soc., 79, 20192031.

    • Search Google Scholar
    • Export Citation
  • Schlax, M. G., , and Chelton D. B. , 1994: Aliased tidal errors in TOPEX/Poseidon sea surface height data. J. Geophys. Res., 99, 24 76124 775.

    • Search Google Scholar
    • Export Citation
  • Sharma, R., , Agarwal N. , , Momin I. M. , , Basu S. , , and Agarwal V. K. , 2010: Simulated sea surface salinity variability in the tropical Indian Ocean. J. Climate, 23, 65426554.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., , and Stammer D. , 1995: The global frequency–wavenumber spectrum of oceanic variability estimated from TOPEX/POSEIDON altimetric measurements. J. Geophys. Res., 100, 24 89524 910.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Standard deviation of HYCOM surface salinity fields computed based on 1-yr-long daily time series: (a) variability at periods longer than 2 days, including seasonal cycle; (b) variability at periods <14 days; and (c) the ratio of (b) over (a), showing that significant part of SSS variability is contained at short periods in many ocean regions.

  • View in gallery

    Surface salinity observations from TAO/PIRATA/RAMA moorings showing daily series (black), rapid (periods < 14 days) fluctuations (red), and annual cycle (blue). Moorings are labeled 1 through 9 and are located as shown at bottom panel.

  • View in gallery

    Aquarius measurement swath pattern showing the number of samples in 28 days on 1° grid.

  • View in gallery

    Values of parameter α, defined in Eq. (1), showing the impact of rapid variability on monthly salinity estimates computed from HYCOM solution as the RMS difference between “true” monthly averages (based on daily series) and aliased monthly averages (based on Aquarius sampling pattern). Note that in several coastal and tropical regions aliasing error α > 0.1 psu. For comparison, typical expected error for Aquarius surface salinity is 0.2 psu.

  • View in gallery

    As in Fig. 4, but with aliased monthly averages computed based on regular sampling every 3.5 days.

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    Aliasing effects based on in situ data: True (black line) and aliased (red dots) monthly averages computed based on Aquarius sampling intervals and their annual cycles (blue) obtained using corresponding series. The annual cycle is estimated as A cos[2πw0(tt0) + φ], where A and φ are annual amplitude and phase, w0 is the annual frequency, t is time, and t0 is the point the phase was calculated from.

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Assessing Temporal Aliasing in Satellite-Based Surface Salinity Measurements

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  • 1 Atmospheric and Environmental Research, Inc., Lexington, Massachusetts
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Abstract

The Aquarius/Satelite de Aplicaciones Cientificas-D (SAC-D) salinity remote sensing mission is intended to provide global mapping of sea surface salinity (SSS) fields over the next few years. Temporal and spatial averages of the satellite salinity retrievals produce monthly mean fields on 1° grids with target accuracies of 0.2 psu. One issue of relevance for the satellite-derived products is the potential for temporal aliasing of rapid fluctuations into the climate (monthly averaged) values of interest. Global daily SSS fields from a data-assimilating, eddy-resolving Hybrid Coordinate Ocean Model (HYCOM) solution are used to evaluate whether the potential aliasing error is large enough to affect the accuracy of the SSS retrievals. For comparison, salinity data collected at a few in situ stations over the tropical oceans are also used. Based on the HYCOM daily series, over many oceanic regions, a significant part of the total salinity variability is contributed by rapid fluctuations at periods aliased in the satellite retrievals. Estimates of the implicit aliasing error in monthly mean salinity estimates amount to 0.02 psu on average and >0.1 psu in some coastal, tropical, western boundary current, and Arctic regions. Comparison with in situ measurements suggests that HYCOM can underestimate the effect at some locations. While local aliased variance can be significant, the estimated impact of aliasing noise on the overall Aquarius system noise is negligible on average, when combined with effects of other instrument and geophysical errors. Effects of aliased variance are strongest at the shortest periods (<6 months) and become negligible at the annual period.

Corresponding author address: Nadya Vinogradova, AER Inc., 131 Hartwell Ave., Lexington, MA 02421. E-mail: nadya@aer.com

Abstract

The Aquarius/Satelite de Aplicaciones Cientificas-D (SAC-D) salinity remote sensing mission is intended to provide global mapping of sea surface salinity (SSS) fields over the next few years. Temporal and spatial averages of the satellite salinity retrievals produce monthly mean fields on 1° grids with target accuracies of 0.2 psu. One issue of relevance for the satellite-derived products is the potential for temporal aliasing of rapid fluctuations into the climate (monthly averaged) values of interest. Global daily SSS fields from a data-assimilating, eddy-resolving Hybrid Coordinate Ocean Model (HYCOM) solution are used to evaluate whether the potential aliasing error is large enough to affect the accuracy of the SSS retrievals. For comparison, salinity data collected at a few in situ stations over the tropical oceans are also used. Based on the HYCOM daily series, over many oceanic regions, a significant part of the total salinity variability is contributed by rapid fluctuations at periods aliased in the satellite retrievals. Estimates of the implicit aliasing error in monthly mean salinity estimates amount to 0.02 psu on average and >0.1 psu in some coastal, tropical, western boundary current, and Arctic regions. Comparison with in situ measurements suggests that HYCOM can underestimate the effect at some locations. While local aliased variance can be significant, the estimated impact of aliasing noise on the overall Aquarius system noise is negligible on average, when combined with effects of other instrument and geophysical errors. Effects of aliased variance are strongest at the shortest periods (<6 months) and become negligible at the annual period.

Corresponding author address: Nadya Vinogradova, AER Inc., 131 Hartwell Ave., Lexington, MA 02421. E-mail: nadya@aer.com

1. Introduction

The Aquarius/Satelite de Aplicaciones Cientificas-D (SAC-D) salinity remote sensing mission, developed jointly by the U.S. and Argentine space agencies (Lagerloef et al. 1995, 2008; Le Vine et al. 2007), was launched in June 2011. The mission is dedicated to improving our knowledge of the global water cycle and will provide global maps of sea surface salinity (SSS)—a crucial variable in studies of large-scale ocean circulation and climate change (e.g., Riser et al. 2008; Delcroix et al. 2005; Lukas and Lindstrom 1991). Monthly mean salinity fields on a ~150-km global grid with an accuracy of 0.2 psu or better are intended (Lagerloef et al. 2008). The Soil Moisture and Ocean Salinity (SMOS) mission is currently flying with similar objectives (Font et al. 2010).

The prelaunch Aquarius measurement error requirements of 0.2 psu take into account all possible error sources, including sensor and geophysical random errors and biases. Many studies have been dedicated to estimating and reducing the error budgets for Aquarius (e.g., Le Vine and Abraham 2004; Le Vine et al. 2005). One potential error that remains poorly understood is related to the Aquarius sampling rate. The orbit repeat cycle of the Aquarius satellite is 7 days, with an irregular sampling interval that can vary with location from daily to once in 7 days, implying that variability at periods <14 days can alias into longer periods. Thus, the question arises as to whether potential aliasing errors are large enough to affect the accuracy of 0.2 psu that is targeted for the final salinity product.

The problem of temporal aliasing is one of the major concerns when designing any observational system. For example, the existence of unresolved variability in sea level, associated with large tidal signals (e.g., Ray 1998; Schlax and Chelton 1994) and nontidal high-frequency (HF) barotropic signals (e.g., Ponte and Lyard 2002), has been shown to lead to sizable aliasing errors in satellite altimetric measurements. The theory of aliasing in signal processing and related disciplines is well understood. For any random time series, the sampling interval Δt defines the highest resolvable frequency fN = 1/(2Δt), also known as the Nyquist frequency. If the record contains variability at frequencies >fN, such variability will be falsely located at lower frequencies. Contamination of the computed spectra by power at frequencies >fN is called aliasing or spectrum folding.

Although the nature of aliasing is well understood in theory, in practice the effects of aliasing are difficult to determine as they depend on the spectral characteristics of oceanic variability, which can vary in both space and time. One way to evaluate the impact of high-frequency variability is to compare measurements of the known, “true” oceanographic spectrum with a simulated “aliased” spectrum based on subsampled data. Such comparisons, which can be based on analysis of in situ data with high temporal resolution, have proved to be useful in many oceanographic applications (e.g., Ponte and Lyard 2002; Ray 1998; Wunsch and Stammer 1995). In studies of ocean salinity, however, in situ data coverage is sparse in time and space. Even the most extensive Argo data collection system samples only about every 10 days and does not profile at depths shallower than 5 m.

One of the few available datasets resolving SSS rapid variations comes from tropical mooring sites described in McPhaden (1995), Servain et al. (1998), and McPhaden et al. (2009). Delcroix et al. (2005) used these SSS data to describe high-frequency variability in the three tropical oceans. They found that typical standard deviations over 10-day-long records were about 0.1 psu, driven mostly by heavy local precipitation, but in some instances exceeded 0.2 psu. These rapid fluctuations, found in the eastern edge of the Pacific warm pool, have been attributed to the movement of SSS fronts across the observational array (Delcroix and McPhaden 2002; Picaut et al. 2001; Eldin et al. 1997), which can lead to daily SSS changes of more than 1 psu.

Although Delcroix et al. (2005), Lagerloef and Delcroix (2001), and others have discussed potential sampling errors in planned satellite salinity missions, their studies are necessarily based on only a few selected locations. A global assessment of such errors has not been documented yet and is the main focus of this study. For these purposes, we analyze SSS model estimates, which are available globally and at high (daily) sampling rates. The model results compare well with those based on the few available in situ measurements and provide a good zero-order estimate of potential aliasing effects in space-based SSS records.

2. Model and data

The numerical estimates of SSS are based on the integrated model/data system Hybrid Coordinate Ocean Model (HYCOM) (Chassignet et al. 2009). The solution uses a global, eddy-resolving, high-resolution ocean model constrained to a variety of ocean datasets through an assimilation scheme. The current configuration (GLBa0.08/expt_90.8) uses the Navy Coupled Ocean Data Assimilation (NCODA) system (Cummings 2005) for ingesting surface observations, such as satellite altimetry and satellite sea surface temperature, and vertical temperature and salinity profiles derived from both in situ measurements (Argo floats, XBTs, buoys) and from sea surface height anomalies through the Modular Ocean Data Assimilation System (MODAS; Fox et al. 2002). Atmospheric forcing includes wind stress, heat, and freshwater flux provided by the Navy Operational Global Atmospheric Prediction System (NOGAPS). Output from HYCOM permits a good assessment of temporal sampling issues in the presence of eddies and other short-scale features. The output of the HYCOM simulations is also used in the Aquarius data simulator. For our purposes we use one year of daily salinity fields, covering the period from May 2009 (start date of the GLBa0.08/expt_90.8 configuration) to May 2010, allowing one to examine variability at periods longer than 2 days, including the seasonal cycle.

The available HYCOM near-surface salinity fields represent an average over the top 3 m of its original hybrid vertical grid (isopycnal in the stratified open ocean, sigma coordinates in shallow coastal regions, and fixed pressure-level coordinates in the surface mixed layer or nonstratified seas). The horizontal grid is configured to represent the global ocean and consists of a Mercator grid between 78°S and 47°N with equatorial resolution and a bipolar patch for regions north of 47°N, where the poles are shifted over land to avoid a singularity at the North Pole. Before analyses, the original HYCOM output was remapped from curvilinear to a regular latitude–longitude grid following the procedure described by A. Srinivasan (personal communication, 2010). To approximate the large (~100 km) footprint of the Aquarius beams, HYCOM output was averaged from the original high-resolution grid onto 1° grid.

In situ estimates of aliasing errors are based on daily salinity series collected at nine tropical mooring stations from the Tropical Atmosphere Ocean (TAO) project in the Pacific (McPhaden 1995), the Pilot Research Moored Array in the Tropical Atlantic (PIRATA) program in the Atlantic (Servain et al. 1998), and the Research Moored Array for Africa–Asian–Australian Monsoon Analysis and Prediction (RAMA) in the Indian Ocean (McPhaden et al. (2009)), and made available by the TAO Project Office of the National Oceanic and Atmospheric Administration (NOAA) and the Pacific Marine Environmental Laboratory (PMEL). Surface values correspond to salinity sampled at 1-m depth. The measurements are quality-controlled and have been described in detail in previous publications (e.g., Delcroix et al. 2005; Freitag et al. 1999), with errors in the moored salinity time series being generally about 0.02 psu. These programs include SSS records that have been routinely collected since 1970 and might contain time periods with no data. To avoid large time gaps in the salinity series, we choose records with more than one year of continuous sampling. The records vary in length from about 2 to 10 years within the last decade.

3. Methods

The monthly aliasing error (α) is defined here in terms of the ability of aliased measurements sampled within a given month to represent the true monthly mean value. To compute α, we compare monthly averages computed based on daily series (true; T) with monthly averages computed based on values sampled using the Aquarius measurement swath pattern. For each month m, we compute the difference between the true and aliased monthly means (αm) and define aliasing error α as the root-mean-square (RMS) of these departures:
e1
where m = 1, … , n, and n range up to 12 in HYCOM 1-yr analysis or more for in situ analysis depending on the record length. Monthly means are defined here as averages over 28 days, similar to the definition of the Aquarius monthly mean product (Lagerloef et al. 2008).
It is also useful to look at the amount of observed variability that may be due to aliasing as a function of frequency. In a similar manner, we define the true and aliased spectra, ΦT and ΦA, to be those based respectively on daily series and subsampled series. Subtraction of the true spectrum from the aliased one and then dividing by it provides an estimate of the percentage of variance in the subsampled series that is due to aliasing:
e2

To obtain the Aquarius sampling pattern, we use Aquarius level-2 orbital simulator data containing geolocations for along-track data records. The satellite is in repeat orbit that provides global coverage in 7 days, using two independent samples from the ascending and descending passes at each location. Within this 7-day repeat cycle, there are 103 such passes, each of them consisting of three elliptical beam footprints with dimensions of 76 km × 94 km, 84 km × 120 km, and 96 km × 156 km (Lagerloef et al. 2008). The three footprints are aligned across the ~390-km swath width and sample the ocean every 6 s along track. To determine the Aquarius sampling map, we compute how many individual observations occur within each 1° grid cell during a week of sampling. Given 1-day temporal resolution of HYCOM and in situ estimates, we neglect any satellite sampling within each day, counting them as a single measurement. Observation from each beam is considered as an independent measurement and mapped on the product grid if the center of the beam falls within the cell boundaries. As the satellite uses an exact 7-day repeat orbit, the amount of samples within 28 days is obtained by multiplying weekly maps by 4.

4. SSS variability

We begin with examining variability in SSS using numerical and in situ estimates, defined throughout the paper in terms of standard deviation. Since the estimates we are using here differ by time period, location and length, we remove the time mean from both numerical and in situ salinity records and deal with anomalies.

Figure 1a examines HYCOM-based estimates of SSS variability at periods longer than 2 days including the seasonal cycle. Typical values of 0.1–0.2 psu are found in most of the open oceans, with several regions exhibiting much higher variability (>1 psu). To first order, the large-scale features of SSS variability reflect variability in evaporation–precipitation (EP) (e.g., Boyer and Levitus 2002) with enhanced variability in the tropical regions, the Indian Ocean, and some regions in the Southern Ocean. There are, however, deviations from the EP patterns with noticeable influence from horizontal advection in the regions of major currents (e.g., Johnson et al. 2002) and in the tropical Pacific and Atlantic convergence zones (e.g., Delcroix and Henin 1991). In addition, local processes affect SSS variability at regional scales. For example, high SSS variability is clearly visible in northern high latitudes due to salt/freshwater release during the ice formation/melting process. River runoff is another major local process affecting SSS variability in regions off the Amazon and Congo Rivers and in the northern Bay of Bengal, as discussed by Boyer and Levitus (2002) or Delcroix et al. (2005).

Fig. 1.
Fig. 1.

Standard deviation of HYCOM surface salinity fields computed based on 1-yr-long daily time series: (a) variability at periods longer than 2 days, including seasonal cycle; (b) variability at periods <14 days; and (c) the ratio of (b) over (a), showing that significant part of SSS variability is contained at short periods in many ocean regions.

Citation: Journal of Atmospheric and Oceanic Technology 29, 9; 10.1175/JTECH-D-11-00055.1

Figure 1b shows high-frequency changes in SSS. For our purposes, high-frequency variability refers to signals at periods <14 days that can potentially alias into longer periods. The HF signal is computed by applying a high-pass filter to the original series to remove anomalies at periods >14 days. Many regions where the total variability is high—including the tropics, the Bay of Bengal, the Gulf Stream, and the Amazon and Congo Rivers—also show relatively strong (>0.2 psu) HF signals. Some areas in northern high latitudes, such as near eastern Greenland and in the Barents and Kara Seas, also show sizable HF fluctuations (>0.1 psu). There are, however, fewer regions of enhanced variability in the Arctic compared to Fig. 1a, suggesting the dominance of processes with longer (likely seasonal) time scales.

To illustrate how much rapid changes contribute to the total signal, we compute the ratio of HF to total variability (Fig. 1c). Over many oceanic regions, a significant part of the total salinity variability is contributed by rapid fluctuations. On average, about 20% of the total variability is contained at high frequencies, but the ratio exhibits significant geographical variations. In the northern and southern high latitudes and some open-ocean regions, the ratio is small (<10%), reflecting the dominance of the seasonal cycle in SSS variability. In contrast, there are tropical regions where rapid variations amount to at least 50% of the total variability. In such regions, the Aquarius temporal sampling rate can potentially impact the quality of the monthly salinity fields where variability in the aliased band can be >0.1 psu (see Fig. 1b).

Figure 2 shows daily SSS time series collected at the TAO/RAMA/PIRATA mooring stations, together with annual and HF signals at corresponding locations. Many stations are characterized by significant HF variations (shown in red), with the values of standard deviations ranging from 0.03 psu in the Atlantic Ocean to 0.26 psu in the Indian Ocean (see Table 1). Delcroix et al. (2005) examined variations in SSS at the equatorial mooring stations that correspond in our notations to stations 1, 4, 5, 6, and 7. They computed the values of rapid changes in SSS based on periods of <10 and <30 days. Similar to our results, rapid changes in the equatorial oceans range between 0.05 and 0.1 psu, with larger amplitudes found in the Atlantic (station 1). These rapid changes in tropical SSS could be induced by heavy precipitation, which is typical in the Atlantic and Pacific intertropical convergence zones (Delcroix et al. 2005), or by changes in freshwater transport by the North Equatorial Countercurrent, which can exhibit short-term variations, including changes due to wind-induced current instabilities (Athié et al. 2009) or related to equatorial mixed Rossby–gravity waves (e.g., Athié and Marin 2008). Apart from the strong annual cycle, which is a major signal in most of the Indian Ocean and in the Pacific and Atlantic intertropical convergence zones, HF variability accounts for a significant part of the total SSS variability and has the potential to alias monthly averages if unresolved.

Fig. 2.
Fig. 2.

Surface salinity observations from TAO/PIRATA/RAMA moorings showing daily series (black), rapid (periods < 14 days) fluctuations (red), and annual cycle (blue). Moorings are labeled 1 through 9 and are located as shown at bottom panel.

Citation: Journal of Atmospheric and Oceanic Technology 29, 9; 10.1175/JTECH-D-11-00055.1

Table 1.

Standard deviation of high-frequency (<14 days) signals computed based on in situ (σD) and HYCOM (σH) fields at the mooring stations. Values in parenthesis are standard deviation based on full high-resolution HYCOM fields. Values αD and αH show the impact of rapid variability on monthly SSS fields, estimated according to Eq. (1) based on in situ and HYCOM fields, respectively. Units are psu. Values of r indicate the percentage of the observed variance due to aliasing at the selected frequencies (2, 4, and 12 months), estimated from in situ data according to Eq. (2).

Table 1.

5. Aliasing effects

a. Aquarius sampling pattern

The Aquarius measurement swath pattern in Fig. 3 displays spatial complexity. The local sampling interval varies by location, with a minimum of 4 daily samples per month in the tropics to the extreme case of 28 daily samples per month in high latitudes. The sample rate shows zonal dependency and increases toward higher latitudes as the orbits converge toward the poles. Table 2 shows the mean number of samples per month in a 1° box, averaged over 10° latitude bands. Lagerloef et al. (2008) estimated similar sampling intervals but based on 150 km2 boxes (see their Table 2). Notice that defined in this way, each latitudinal band in their Table 2 contains a different number of such boxes, gradually decreasing toward higher latitudes from ~266 at the equator to ~112 toward the poles and, accordingly, a larger number of samples per equal-area box. Thus, to compare their numbers with those in Table 2, one should scale their values by 360/2πR cosφ/150 km, where 360 is the number of bins in equally spaced 1° grid, R is the earth’s radius, and φ is the latitude. Our alias error estimate uses fewer samples per box, thus providing an upper limit to the scale of the aliasing error.

Fig. 3.
Fig. 3.

Aquarius measurement swath pattern showing the number of samples in 28 days on 1° grid.

Citation: Journal of Atmospheric and Oceanic Technology 29, 9; 10.1175/JTECH-D-11-00055.1

Table 2.

Root-mean-square of the aliased high-frequency variability (α) and monthly salinity error by latitude bands. Current best estimate (CBE) salinity errors are based on various error sources and are obtained from Table 2 in Lagerloef et al. (2008). Considering aliasing error as another uncorrelated noise, we combine α with CBE to estimate overall uncertainty and whether it exceeds allocation error. The number of samples per 1° grid cell is based on a 28-day period. Each latitude band contains the same number of such 1° boxes (see text to compare with Table 2 in Lagerloef et al. 2008).

Table 2.

In addition to spatial variations, the sampling pattern is also irregular in time. That is, at a particular geolocation, there can be measurements that are several hours apart followed by a gap of 2 to 6 days. We will explore the effect of uneven sampling in the following sections.

b. Numerical estimates of aliasing error

The impact of HF variability on monthly SSS estimates based on the Aquarius measurement swath pattern was computed according to Eq. (1) and is shown in Fig. 4. The average value of α is about 0.02 psu. Typical values of α in the open ocean are <0.02 psu, where SSS variability is weak in general. In contrast, several coastal, tropical, and western boundary current regions yield the highest values of α (>0.1 with a maximum ~0.9 psu). Tropical salinity could be particularly influenced by strong high-frequency forcing regimes (e.g., heavy rain) that can induce large spikes in SSS. For example, buoy records (Cronin and McPhaden 1999) showed salinity series with rapid and large fluctuations between a baseline and fresher values following precipitation events. In such cases, monthly-averaged SSS values inferred from relatively sparse Aquarius measurements can be affected by unresolved rapid variability.

Fig. 4.
Fig. 4.

Values of parameter α, defined in Eq. (1), showing the impact of rapid variability on monthly salinity estimates computed from HYCOM solution as the RMS difference between “true” monthly averages (based on daily series) and aliased monthly averages (based on Aquarius sampling pattern). Note that in several coastal and tropical regions aliasing error α > 0.1 psu. For comparison, typical expected error for Aquarius surface salinity is 0.2 psu.

Citation: Journal of Atmospheric and Oceanic Technology 29, 9; 10.1175/JTECH-D-11-00055.1

The aliased high-frequency SSS variability can be interpreted as another source of error in the total error budget. Assuming that instrument and various geophysical errors are not correlated, a globally averaged root-mean-square error for monthly gridded salinity analysis is estimated as 0.2 psu (Lagerloef et al. 2008). Combining a global mean aliasing noise of 0.02 psu with 0.2 psu in a root-sum-square sense yields a new value of the total global budget equal to psu. The resulting change is negligible, suggesting that aliasing noise does not affect the error budget significantly on an average sense. To see the impact of aliasing as a function of latitude, in Table 2 we combine the values of α averaged per each latitude band with corresponding current best estimate (CBE) errors provided in Table 2 of Lagerloef et al. (2008). The largest aliasing noise is found in the tropics, mainly due to coastal regions with strong high-frequency forcing regimes. Aliasing noise is typically decreasing toward higher latitudes, where the sample density is increasing and HF variations in SSS are weaker in general. None of the bands analyzed show combined errors that exceed the respective allocation errors provided by Lagerloef et al., indicating that average aliasing is not significant to the overall error budget in the presence of other instrument and geophysical errors. However, regional values show that aliasing could be very important locally, where local values can exceed 0.1 psu, reaching their maximum value of 0.9 psu (see Fig. 4).

To assess the effect of uneven temporal sampling, we repeat the analysis in Fig. 4 using an idealized case with a regular sampling interval and compare the results with those based on Aquarius’ actual sampling scenarios. On average, over the globe, the satellite completes about eight measurements per month per 1° grid cell, which corresponds to a sampling interval of ~3.5 day, or twice within a 7-day repeat cycle. Figure 5 shows the values of α computed based on aliased series that are sampled every 3.5 days. If one uses eight evenly sampled measurements per month to compute monthly mean value, the impact of rapid variability on monthly SSS is considerably weaker. The global average value of such error is about 0.01 psu, with many ocean regions yielding errors <0.005 psu, indicating that irregular time sampling can result in higher aliasing noise.

Fig. 5.
Fig. 5.

As in Fig. 4, but with aliased monthly averages computed based on regular sampling every 3.5 days.

Citation: Journal of Atmospheric and Oceanic Technology 29, 9; 10.1175/JTECH-D-11-00055.1

The extent to which the true SSS can be contaminated by unresolved HF signals can be examined by calculating the percentage of variance due to aliasing at different frequencies. Aliased power r is computed at each grid point according to Eq. (2) at periods of 2, 4, 6, and 12 months and averaged over the globe. The strongest impact of aliasing is found at the highest frequencies, with values of r being 45% on average. The impact of aliasing diminishes toward longer periods, with global aliased energy corresponding to 23%, 17%, and 2% at 4-, 6-, and 12-month periods, respectively. This suggests that Aquarius’ temporal sampling is adequate to resolve low-frequency climate signals with confidence, as far as potential aliasing errors are concerned. This estimate also represents an upper bound because it excludes the spectral content of the other instrument and geophysical error sources.

c. In situ estimates of aliasing error

To estimate α based on in situ measurements, we average the data into monthly means using daily true series and aliased series using Aquarius sampling intervals at the location of each mooring. The resulting monthly means are shown in Fig. 6, where the black lines are monthly T series and the red dots are monthly A series. The departure of the aliased values from the “truth” forms the values of αm and their root-mean-square is defined as the aliasing error α. To examine the amount of aliased energy at different time scales, we compute the spectra Φ(T) and Φ(A) based on the true and aliased monthly values and then compute the ratio r according to Eq. (2). The values of α and r at each mooring station are given in Table 1.

Fig. 6.
Fig. 6.

Aliasing effects based on in situ data: True (black line) and aliased (red dots) monthly averages computed based on Aquarius sampling intervals and their annual cycles (blue) obtained using corresponding series. The annual cycle is estimated as A cos[2πw0(tt0) + φ], where A and φ are annual amplitude and phase, w0 is the annual frequency, t is time, and t0 is the point the phase was calculated from.

Citation: Journal of Atmospheric and Oceanic Technology 29, 9; 10.1175/JTECH-D-11-00055.1

The largest impact of aliasing is found in the Indian Ocean (station 8 in northern Bay of Bengal), where the values of α can exceed 0.1 psu. These regions are characterized by strong HF variability (σD = 0.26 psu; Table 1), which is induced by strong HF precipitation and river discharge (Sharma et al. 2010). At most of the stations the effect of aliasing is the strongest at shorter time periods (see r2mo in Table 1), where aliasing can account for 6%–38% of the observed variance. As the period increases toward 4 months, the effects of aliasing typically diminish and range from 1% to 16%. Longer time scales are less affected by aliasing. Typically, spectra contamination does not extend beyond the semiannual cycle and aliasing noise at periods >6 months accounts for less than 5% of the observed variance. In particular, the annual cycle based on aliased values fits the true annual cycle very well (Fig. 6). Moreover, the effect of aliasing on annual variance is weak regardless of its amplitude. See, for example, stations 8 and 9 in the Indian Ocean, where the annual cycle is a major signal and accounts for >50% of the total variability, overwhelming any effects from HF fluctuations. Also notice stations with weak annual cycles (e.g., station 5 in the tropical Pacific), where aliasing energy is still negligible at annual periods.

The values of α based on in situ data are in general agreement with those based on the HYCOM solution (Table 1). At several stations, αH tends to be smaller than αD, showing that in these regions the impact of rapid variability on monthly salinity can be even higher than that estimated by the model. Some differences could be attributed to the presence in the data of short-scale spatial structures, which are partially removed in the HYCOM fields by the spatial averaging onto a 1° grid. Small spatial scales can be associated with tropical fronts, including the meridional front near the equatorial upwelling zone (Delcroix et al. 2005) and the sharp zonal SSS front at the eastern edge of the Pacific warm pool (Eldin et al. 1997). To illustrate the impact of short-scale spatial structures on temporal variability, we compared the values of the standard deviation that we computed based on and 1° HYCOM fields at the location of the mooring sites (Table 1). At most stations, spatial averaging results in a decrease in σ by 30%–50%, illustrating the importance of rapid SSS variability induced by fronts and eddies. At some stations (1 and 8) rapid variability computed based on in situ data still exceeds that computed based on full high-resolution HYCOM fields, suggesting that HYCOM can underestimate the amount of rapid SSS variability, at least at these mooring locations.

Not all of the differences between the values of α based on HYCOM and in situ series are necessarily associated with short-scale spatial structures. Other contributing factors can be the difference in the length of the records, the absence of a common time period, and the interpolation of the model-based estimates onto mooring locations. In addition, realism of the model estimates could be limited by uncertainties in atmospheric forcing, assimilation techniques and errors in the model physics. Nevertheless, the comparison between the values of α points to similar conclusions, with both estimates suggesting that locally aliasing noise is ranging from 0.02 to 0.11 psu.

6. Conclusions

Based on daily time series from a global, eddy-resolving HYCOM solution, which is constrained to a variety of ocean datasets, rapid variations in SSS can be significant and vary from place to place, contributing about 20% to the total variability on average and exceeding 50% in some ocean regions. Enhanced HF variability tends to occur in coastal, tropical, western boundary current and Arctic regions and can be attributed to local forcing regimes (e.g., precipitation) and upper-ocean processes (e.g., turbulent mixing, instabilities, advection). We examine the potential aliasing effects of such HF fluctuations on SSS monthly estimates derived from the satellite mission Aquarius/SAC-D, using the satellite sampling scenarios. The sampling pattern is spatially complex with fewer samples in the tropics and increasing sampling density toward the poles. Sampling intervals are also irregular in time, which tends to increase the amount of aliased variance compared to evenly sampled measurements.

Our analysis of the HYCOM daily series suggests that aliased signals can induce errors in monthly mean salinity estimates of ~0.02 psu on average and >0.1 psu in the regions with enhanced HF variability. When aliasing noise is included as an additional source of uncertainty in the Aquarius error budget, both globally averaged errors and errors averaged per 10° latitude band do not exceed allocation errors as discussed in Lagerloef et al. (2008). Thus, for averaged values over large spatial scales, aliased variance does not seem to be a major concern in the presence of other instrument and geophysical errors. Aliasing noise can, however, have a significant local impact in many ocean regions with strong HF fluctuations in SSS.

The HYCOM-based estimates of aliasing error are in general agreement with those based on the few in situ data analyzed; comparisons with observations suggest that at some stations HYCOM can underestimate the effect. The data, all collected at mooring stations in the tropical oceans, show that at periods <2 months, from 6% to 38% of the observed variance can be due to aliasing, indicating that spectral analyses of Aquarius data at periods <2 months should take into account the sample aliasing as well as the spectral content of the other error sources.

It should be noted that, although the results presented here are based on daily series, an attempt has been made to examine the effect of fluctuations at periods <2 days. Our analysis of hourly records at the same tropical stations (not shown) indicates that the amount of aliased variance could be underestimated on average by a factor of ⅓ if using daily instead of hourly values. In addition, the variance at periods <2 days might also be “seen” at longer periods (e.g., 5% of additional variance is present at the annual frequency if using hourly values). Although some of these stations might be in places with strong precipitation, which can induce more hourly variability, estimates of the aliasing error using daily HYCOM fields might be biased low in general.

Finally we note that the amount of observed variance due to aliasing gradually diminishes toward longer periods. Modeled and observed variability at periods >6 months shows almost no distortion by aliasing noise. In particular, both model and data indicate that the annual cycle is unaffected by aliasing, as well as variations at longer periods at mooring stations (not shown). This suggests that the Aquarius sampling is more than adequate to observe annual and interannual SSS variations, which are important climate scales of wide oceanographic interest.

Acknowledgments

This work was supported by NASA’s Physical Oceanography Program and the Ocean Surface Salinity Project through Contract NNH10CC10C to AER. The authors are grateful to Ashwanth Srinivasan and Michael McDonald for providing HYCOM regridding algorithms. We thank two anonymous reviewers for their help in improving the manuscript. Additional thanks are due to Mark Shiffer for useful discussions on analyzing sampling patterns based on Aquarius geolocation and track data records.

REFERENCES

  • Athié, G., , and Marin F. , 2008: Cross-equatorial structure and temporal modulation of intra-seasonal variability at the surface of the Tropical Atlantic Ocean. J. Geophys. Res., 113, C08020, doi:10.1029/2007JC004332.

    • Search Google Scholar
    • Export Citation
  • Athié, G., , Marin F. , , Treguierd A. , , Bourlès B. , , and Guiavarch C. , 2009: Sensitivity of near-surface tropical instability waves to submonthly wind forcing in the tropical Atlantic. Ocean Model., 30, 241255.

    • Search Google Scholar
    • Export Citation
  • Boyer, T. P., , and Levitus S. , 2002: Harmonic analysis of climatological sea surface salinity. J. Geophys. Res., 107, 8006, doi:10.1029/2001JC000829.

    • Search Google Scholar
    • Export Citation
  • Chassignet, E. P., and Coauthors, 2009: U.S. GODAE: Global Ocean Prediction with the Hybrid Coordinate Ocean Model (HYCOM). Oceanography, 22, 6475.

    • Search Google Scholar
    • Export Citation
  • Cronin, M. F., , and McPhaden M. J. , 1999: Diurnal cycle of rainfall and surface salinity in the western Pacific warm pool. Geophys. Res. Lett., 26, 34653468.

    • Search Google Scholar
    • Export Citation
  • Cummings, J. A., 2005: Operational multivariate ocean data assimilation. Quart. J. Roy. Meteor. Soc., 131C, 35833604.

  • Delcroix, T., , and Henin C. , 1991: Seasonal and interannual variations of sea-surface salinity in the tropical Pacific Ocean. J. Geophys. Res., 96, 22 13522 150.

    • Search Google Scholar
    • Export Citation
  • Delcroix, T., , and McPhaden M. J. , 2002: Interannual sea surface salinity and temperature changes in the western Pacific warm pool during 1992–2000. J. Geophys. Res., 107, 8002, doi:10.1029/2001JC000862.

    • Search Google Scholar
    • Export Citation
  • Delcroix, T., , McPhaden M. J. , , Dessier A. , , and Gouriou Y. , 2005: Time and space scales for sea surface salinity in the tropical oceans. Deep-Sea Res. I, 52, 787813.

    • Search Google Scholar
    • Export Citation
  • Eldin, G., , Rodier M. , , and Radenac M. H. , 1997: Physical and nutrient variability in the upper equatorial Pacific associated with westerly wind forcing and wave activity in October 1994. Deep-Sea Res. I, 44, 17831800.

    • Search Google Scholar
    • Export Citation
  • Font, J., and Coauthors, 2010: SMOS: The challenging sea surface salinity measurement from space. Proc. IEEE, 98, 649665.

  • Fox, D. N., , Teague W. J. , , Barron C. N. , , Carnes M. R. , , and Lee C. M. , 2002: The Modular Ocean Data Assimilation System (MODAS). J. Atmos. Oceanic Technol., 19, 240252.

    • Search Google Scholar
    • Export Citation
  • Freitag, H. P., , McCarty M. E. , , Nosse C. , , Lukas R. , , McPhaden M. J. , , and Cronin M. F. , 1999: COARE Seacat data: Calibrations and quality control procedures. NOAA Tech. Memo. ERL PMEL-115, 89 pp.

  • Johnson, E.,, Lagerloef, G. , Gunn, and J. , Bonjean F. , 2002: Surface salinity advection in the tropical oceans compared with atmospheric forcing: a trial balance. J. Geophys. Res., 107, doi:10.1029/2001JC001122.

    • Search Google Scholar
    • Export Citation
  • Lagerloef, G.,, and Delcroix T. , 2001: Sea surface salinity: A regional case study for the tropical Pacific. Observing the Ocean in the 21st Century, Australian Bureau of Meteorology, 137–148.

    • Search Google Scholar
    • Export Citation
  • Lagerloef, G., , Swift C. T. , , and Le Vine D. M. , 1995: Sea surface salinity: The next remote sensing challenge. J. Oceanogr., 8, 4450.

  • Lagerloef, G., and Coauthors, 2008: The Aquarius/SAC-D mission: Designed to meet the salinity remove-sensing challenge. J. Oceanogr., 21, 6881.

    • Search Google Scholar
    • Export Citation
  • Le Vine, D. M., , and Abraham S. , 2004: Galactic noise and passive microwave remote sensing from space at L-band. IEEE Trans. Geosci. Remote Sens., 42, 119129.

    • Search Google Scholar
    • Export Citation
  • Le Vine, D. M., , Abraham S. , , Wentz F. , , and Lagerloef G. S. E. , 2005: Impact of the sun on remote sensing of sea surface salinity from space. Proc. IEEE Int. Geoscience and Remote Sensing Symp. (IGARSS), Vol. I, Seoul, South Korea, IEEE, 288–291, doi:10.1109/IGARSS.2005.1526164.

  • Le Vine, D. M., , Lagerloef G. S. E. , , Colomb F. R. , , Yeh S. H. , , and Pellerano F. A. , 2007: Aquarius: An instrument to monitor sea surface salinity from space. IEEE Trans. Geosci. Remote Sens., 45, 20402050.

    • Search Google Scholar
    • Export Citation
  • Lukas, R., , and Lindstrom E. , 1991: The mixed layer of the western equatorial Pacific Ocean. J. Geophys. Res., 96, 33433357.

  • McPhaden, M. J., 1995: The TAO array is completed. Bull. Amer. Meteor. Soc., 76, 739741.

  • McPhaden, M. J.,, and Coauthors, 2009: RAMA: The Research Moored Array for African–Asian–Australian Monsoon Analysis and Prediction. Bull. Amer. Meteor. Soc., 90, 459480.

    • Search Google Scholar
    • Export Citation
  • Picaut, J., , Ioualalen M. , , Delcroix T. , , Masia F. , , Murtugudde R. , , and Vialard J. , 2001: The oceanic zone of convergence on the eastern edge of the Pacific warm pool: A synthesis of results and implications for ENSO and biogeochemical phenomena. J. Geophys. Res., 106, 23632386.

    • Search Google Scholar
    • Export Citation
  • Ponte, R. M., , and Lyard F. , 2002: Effects of unresolved high-frequency signals in altimeter records inferred from tide gauge data. J. Atmos. Oceanic Technol., 18, 534539.

    • Search Google Scholar
    • Export Citation
  • Ray, R. D., 1998: Spectral analysis of highly aliased sea-level signals. Geophys. Res. Lett., 103, 24 99125 003.

  • Riser, S. C., , Ren L. , , and Wong A. , 2008: Salinity in ARGO. Oceanography, 21, 5667.

  • Servain, J., , Busalacchi A. , , McPhaden M. , , Moura A. , , Reverdin G. , , Vienna M. , , and Zebiak S. , 1998: A Pilot Research Moored Array in the Tropical Atlantic (PIRATA). Bull. Amer. Meteor. Soc., 79, 20192031.

    • Search Google Scholar
    • Export Citation
  • Schlax, M. G., , and Chelton D. B. , 1994: Aliased tidal errors in TOPEX/Poseidon sea surface height data. J. Geophys. Res., 99, 24 76124 775.

    • Search Google Scholar
    • Export Citation
  • Sharma, R., , Agarwal N. , , Momin I. M. , , Basu S. , , and Agarwal V. K. , 2010: Simulated sea surface salinity variability in the tropical Indian Ocean. J. Climate, 23, 65426554.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., , and Stammer D. , 1995: The global frequency–wavenumber spectrum of oceanic variability estimated from TOPEX/POSEIDON altimetric measurements. J. Geophys. Res., 100, 24 89524 910.

    • Search Google Scholar
    • Export Citation
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