## 1. Introduction

Together with satellite-based ocean observations, Argo floats represent part of the “oceanographic revolution” by providing researchers with an unprecedented amount of information (Argo Science Team 2001).^{1} However, despite the relatively low cost of the Argo-based observing system component, the costs of construction and deployment still pose limitations on the total number of floats that will be deployed in the foreseeable future. The current status of the Argo observing system in the Indian Ocean is shown in Fig. 1. At the time of writing this manuscript (March 2004) the number of floats deployed in the Indian Ocean (∼210) represents about 46% of the planned final deployment of 450 floats in 2005.

To maximize the use of data provided by the limited number of floats available, it is necessary to design an optimal sampling strategy. The Indian Ocean is particularly challenging to monitor as its dominant time scales cover intraseasonal [Madden–Julian oscillations (MJOs)], seasonal (monsoon), interannual (Indian Ocean “dipole”), and climate change time scales, ranging from weeks to centuries. This paper focuses on the two time scales of intreaseasonal and seasonal variability and associated sampling strategies for Argo floats. Intraseasonal variability in the tropical Indian Ocean and the associated deep convection in the overlying atmosphere are related to the onset and the intensity of the Asian and Australian monsoons and are also suspected to influence the timing and strength of the El Niño–Southern Oscillation (ENSO) (Webster et al. 1998). The seasonal reversal of cross-equatorial mass and heat transport in the Indian Ocean is the most dominant and coherent component of monsoon-related variability in the tropical Indian Ocean (Schott and McCreary 2001).

The rationale for the actual 10-day temporal and 3° × 3° spatial sampling scheme of Argo floats has been outlined in the design and implementation plan of Argo (Argo Science Team 1998). The purpose of the Argo array with a 10-day sampling cycle is to provide global coverage of the upper ocean on broad spatial scales, *O*(1000 km), and on time scales of months and longer. The focus is on observing the physical state of the ocean (*T,* *S,* and reference-level velocity) on a regular basis anywhere in the world, enabling the measurement of heat and freshwater storage in the global air–sea–land climate system, both of which are dominated by oceanic variability (Argo Science Team 2001). The use of Argo floats as Lagrangian tracers is of secondary importance. Ultimately, the implementation of and any changes to the current Argo network represent a balancing of the scientific requirements, for example, measuring high-frequency signals such as intraseasonal variability, with the physical and technical issues such as potentially faster depletion of floats due to more frequent sampling. The latter is associated with affordability in terms of the costs of implementation.

The purpose of this paper is to provide some guidance on the design of the Argo-based component of an Indian Ocean observing system. The particular aim is to provide a quantitative assessment of the impact of spatial and temporal sampling strategies on Argo floats, taking into account different noise levels at different depths caused by, for example, tides, internal waves, and other unresolved processes. More specifically, we address the following issues.

Are typical horizontal velocities at parking depths and at the surface small enough so that Argo floats can be regarded as quasi-stationary over their anticipated lifetime of about 3 yr?

What are the required temporal and spatial sampling intervals for capturing seasonal and longer-term variability?

Using Argo floats, can we simultaneously measure intraseasonal and longer-term variability in the Indian Ocean?

Are there areas in the Indian Ocean that need to be more frequently sampled than other areas?

The paper is organized as follows. After a short introduction to the model and method used in this study, a sequential approach is taken by increasing the complexity of subsampling from a complete dataset, the latter being represented here by model output. First, the impact of temporal sampling is investigated before spatial sampling is explored. Finally, we examine signal-to-noise ratios of combined temporal, spatial, and noise-added sampling strategies.

## 2. Method

### a. Model configuration

Model results presented in this study are based on a global version of the Modular Ocean Model (Pacanowski 1995). We only provide a short summary of the model here, as the model has been validated on intraseasonal and seasonal time scales elsewhere. For further details of the model the reader is referred to Schiller and Godfrey (2003). The model has a standard zonal resolution of 2° and an enhanced meridional resolution of 0.5° within 8° latitude of the equator. The meridional resolution gradually increases to 1.5° toward the Poles. There are 25 levels in the vertical, 7 of which are in the top 100 m. The model ocean is driven by 3-day averages of National Centers for Environmental Prediction (NCEP) wind stress data (Kalnay et al. 1996) blended with monthly mean Florida State University (FSU) wind data (Legler et al. 1989; Stricherz et al. 1992). This approach was chosen since experience has shown that our model produces a more realistic long-term ocean circulation with FSU rather than NCEP monthly mean winds.

An important feature of the general circulation model is a hybrid mixed layer model (Chen et al. 1994). Vertical mixing and vertical friction are parameterized by a one-dimensional mixing scheme. The minimum mixed layer depth is determined by the vertical grid resolution near the surface, that is, 15 m. Below the first model level, the total mixed layer depth consists of the bulk mixed-layer component plus the depth range where the gradient Richardson number causes strong vertical mixing; both are independent of the model grid.

Surface fluxes, apart from incoming shortwave radiation, are calculated by coupling the OGCM to an atmospheric boundary layer model (ABLM) (Kleeman and Power 1995). The use of an ABLM, while still reasonably simple to interpret, takes proper account of surface turbulent heat and freshwater fluxes during the period investigated. The net surface heat flux is diagnosed from the ABLM. We used the simulated evaporation (latent heat) together with precipitation from the satellite-based Carbon Dioxide Information Analysis Center (CDIAC) Microwave Sounding Unit (MSU) precipitation dataset to calculate freshwater fluxes (dataset available online at http://ingrid.ldeo.columbia.edu/ SOURCES/CDIAC/msu/).

After a spinup for 20 yr the model reached a steady state in the upper parts of the ocean. The model was subsequently integrated for the period from January 1982 to May 1994 (the end of the CDIAC MSU precipitation dataset).

### b. Sampling method

Twelve years of 3-day averages of potential temperature from the global ocean model have been used in this analysis. The study area is the Indian Ocean north of 25°S and west of 120°E. The model data are subsampled at different temporal and spatial intervals down to a maximum depth of 2000 m to simulate the behavior of the real Argo float array. The current default sampling strategy is parking Argo floats at 2000-m depth and profiling to the surface (taking measurements) every 10 days. However, this sampling frequency might not allow for a bias-free sampling of intraseasonal variability in the Indian Ocean. To allow Argo floats to measure this important frequency band in the Indian Ocean, the Argo Science Team discusses a somewhat modified sampling strategy in the Indian Ocean by parking Argo floats at 500-m depth, sampling to the surface every 5 days (three cycles), which is followed by parking at 2000 m and sampling to the surface every 20 days (Argo Science Team 2003). The impacts of this sampling strategy on seasonal and intraseasonal signal-to-noise ratios are investigated as part of this study (either separately with 6- and 21-day sampling intervals or combined as a 24-day sampling interval).

A caveat of the analysis presented in this study relates to the 3-day mean model output. A direct comparison of the present 10-day sampling with the proposed 5-day near-surface sampling cycle is hampered by the comparably coarse temporal resolution of the model output. Due to the 3-day-averaged model output fields the 5- and 10-day cycles have to be approximated by 6- and 9-day cycles, respectively. This smaller temporal window and the associated averaging over 3 days is likely to reveal significantly smaller differences in the simulated 6- and 9-day sampling periods than what might be expected from exact 5- and 10-day cycles. Consequently, we focus on the evaluation of the proposed new sampling strategy and its appropriateness for sampling both intraseasonal and seasonal time scales rather than a detailed comparison of the present and proposed sampling cycles. However, whenever appropriate, we show and discuss model results from the present and proposed sampling strategies together. This approach allows us to at least identify the tendency of changes one might expect when changing sampling cycles. In the subsequent paragraphs of this section we describe the procedure to determine signal-to-noise ratios in the Indian Ocean from model data. We define noise as the higher frequency part of the real signal, which is not simulated by the model, represented by time scales smaller than 3 days (the model's sampling interval). First, it is assumed that the statistical properties of the complete model represent the full, noise-free signal. This assumption is met by the fact that this model has proven to realistically simulate both intraseasonal (Schiller and Godfrey 2003) as well as seasonal to longer-term variability in the upper ocean (Schiller et al. 2000), although the amplitudes of the former are typically only half of the observed ones. Next, data are sampled in time and/or space from the complete dataset for some typical Argo sampling intervals, as shown in Table 1. Both the complete and subsampled datasets are subsequently high-pass filtered and low-pass filtered with a cutoff period of 93 days, separating the two time scales of interest in this paper, that is, intraseasonal and seasonal to longer-term variability. Note that our complete model run did not show any significant trend in time in the study area. Consequently, drift elimination was not necessary.

Figure 2 illustrates the method and shows time series of equatorial potential temperature at 160-m depth from the model and an acoustic Doppler current profiler (ADCP) mooring (Reppin et al. 1999). Comparison of the complete time series in Fig. 2a reveals that despite a warm bias of 2.5°C the model simulates the low-frequency variance reasonably well, although simulated individual events can be quite different from the observations. The underestimation of the high frequency variability might be due to both model deficits and errors in the forcing fields. Subsampling of both datasets on the 6-day time scale (expt 6D) essentially produces the same amplitudes and phases (Figs. 2b–e). Accordingly, the differences are small for both simulated and observed time series of subsampled data (Figs. 2f,g). Note, however, that the observed differences show larger fluctuations than the model results.

*T*

_{mod}represents the complete model data and

*T*

_{sub}represents the subsampled dataset, which has been linearly interpolated to the original model grid in space and time. To simulate the impact of unresolved small-scale signals, eddies, and tides (e.g., internal wave breaking) on the sampling strategy, in some cases we have added normally distributed random “white” noise with amplitudes defined by multiplying the random noise (standard deviations between zero and one) with error estimates derived from the

*World Ocean Atlas*(

*WOA*) (Levitus and Boyer 1994). For further details, see section 3d. We note that this approach might represent a simplification as the higher-frequency variations not represented in the model are likely to have serial autocorrelation in time and space. The effects of subsampling a signal with nonzero autocorrelation will be different from subsampling white noise. A detailed investigation of this phenomenon is beyond the scope of this study.

How can we define an “acceptable” SNR, that is, one that still provides useful physical information despite reduced information content due to temporal and spatial sampling plus noise caused by unresolved processes? To answer this question we investigate the spectra of a subsampled time series with different SNRs (expt 6DXN, further details of which are discussed in section 3). Figure 3 shows power spectra of subsampled data with the following SNRs (in parentheses: intraseasonal SNRs for periods <93 days, seasonal and longer-term SNRs for periods >93 days): left column (0.7, 4.2), middle column (0.4, 2.1), right column (0.2, 1.0). It is evident from these results that, as the SNRs are reduced (noise levels increase), both the intraseasonal and seasonal spectra show increasing gaps with the original spectra (Figs. 3a–c). The associated coherence spectra (Figs. 3d–f ) indicate that almost all information contained in the seasonal and longer periods still contain statistically significant information at the 95% confidence level, despite a decrease in SNR from 4.2 to 1.0. The situation is quite different with the intraseasonal signal. Here, only the first spectrum with SNR = 0.7 provides some statistically significant information, and even that is limited to periods longer than 30 days (Fig. 3d). The two intraseasonal signals with reduced SNR are increasingly less significant (Figs. 3e,f ). The associated phase differences (Figs. 3g–i) indicate the degree to which shared spectral peaks between original and subsampled time series are in phase. The phase differences are generally small for seasonal and longer periods (but increase), whereas shorter periods in the intraseasonal signal show strongly growing phase differences with decreasing SNRs. The above results seem to suggest that an SNR around one still provides statistically significant and useful information about Argo-sampled data in the ocean. We note that the SNRs discussed here have been calculated for a single point in the equatorial Indian Ocean (spatially interpolated onto original model grid). We also note that the effect of changing SNRs on spectral coherence and phase by adding white noise is likely to be slightly different from the effect of changing SNRs by changing temporal and spatial subsampling frequencies. Therefore, results presented in Fig. 3 are only indicative of the relationship between statistical significance and SNRs but cannot be generalized. We have performed cross-spectral analyses in other areas of the model ocean and found very similar results. Nevertheless, one has to keep in mind that the above conclusions are derived from subjective judgment, as expressed through the empirical choices of, for example, the significance level and the (unknown) noise amplitudes.

## 3. Results

Before investigating the impact of temporal and spatial sampling on signal-to-noise ratios we need to verify whether the synthetic floats derived from the model can be regarded as stationary over the periods of interest. Otherwise, horizontal advection could cause an additional bias in the subsampling of data and needs to be taken into account in the analysis procedure. Figure 4 represents an attempt to simulate Lagrangian trajectories of present and proposed sampling strategies as closely as possible with the available model output. Figures 4a and 4b represent an approximation to the current sampling strategy of a 10-day cycle with parking at 2000‐m depth (simulated: 9-day cycle with 8½ days at 2000 m and ½ day at surface). Figures 4c and 4d represent an approximation to the proposed 20-day sampling cycle with one profile taken from 2000 m to the surface and three subsequent profiles taken from 500-m depth to the surface (simulated: 24-day cycle with 5½ days at 2000 m and ½ day at surface; followed by three cycles of 5½ days at 500 m, ½ day at surface). To reduce the complexity of the calculation the Lagrangian integration does not take into account the time it takes for floats to ascend/descend from their parking depths to the surface and vice versa (real floats typically need 4–6 h to rise from 2000 m to the surface). The integration period of the Lagrangian floats covers 3 yr, which is the anticipated average lifetime of present Argo floats. As expected, the results reveal larger displacements of floats in the boundary and equatorial current regions (Figs. 4a,c) and smaller displacements in the northern Arabian Sea, Bay of Bengal, and south of 20°S. To assess if the associated advection velocities are small enough such that the floats can still be regarded as quasi-stationary we compare the simulated results with phase propagation velocities of typical intraseasonal and seasonal phenomena in the Indian Ocean. The simulated average advection velocities are 0.5 ± 0.3 cm s^{−1} standard deviation for the simulated 9-day sampling scenario and about twice as large for the higher frequency 24-day sampling scenario (1.2 ± 0.5 cm s^{−1}). These velocities are much smaller than observed propagation speeds of intraseasonal signals, which span a range from 2.75 to 10 m s^{−1} (Shinoda et al. 1998; Kessler and Kleeman 2000). Errors in the simulated propagation velocities of Argo floats are caused by the combined effects of underestimated high-frequency advection velocities (due to errors in surface forcing and model dynamics) and errors due to the simplified kinematics used here for calculating the trajectories of Argo floats. Nevertheless, even a doubling of the simulated float velocities represents only about 1% of the propagation speed of observed intraseasonal signals. However, the situation is different on seasonal time scales. Here, the simulated float velocities in the subtropical Indian Ocean correspond to about 10% of the propagation velocities of observed seasonal Rossby waves (10–15 cm s^{−1}), as discussed by Masumoto and Meyers (1998). Based on this comparison of intraseasonal and seasonal wave and advection velocities it seems to be reasonable to assume that the floats are quasistationary on intraseasonal time scales. However, this statement is less valid for seasonal, decadal, and longer period signals, particularly in strong boundary currents such as the Somali Current. These results and possible limitations in the interpretation of seasonal signals need to be kept in mind when performing analyses in the subsequent sections. It is also interesting to note that, according to Figs. 4b and 4d, neither float deployment created a significant divergence in spatial coverage after a 3-yr deployment despite strong advection in some areas.

### a. Temporal sampling

As is evident from Figs. 2f and 2g and as might be expected from the Nyquist frequency criteria (Jenkins and Watts 1968, Nyquist frequency ∼25 days for MJO), subsampling in time seems to have a smaller impact on the seasonal than on the intraseasonal time scale. This feature is further investigated in the next two figures. Figure 5 displays statistical information about seasonal variability of potential temperature at 100-m depth, based on a 21-day sampling interval (expt 21D). Seasonal variability (Fig. 5a) is generally high in the areas dominated by the monsoons in the far northern Indian Ocean and also around 12°S, an area known for Rossby wave activity (Masumoto and Meyers 1998). The subsampled data (Fig. 5b) hardly show any weakening of the variability and it is mostly concentrated along the equator and the low-latitude boundaries of the ocean. Accordingly, signal-to-noise ratios are largest in the off-equatorial region (SNR > 10) and smallest along the equator (SNR < 10).

Because the floats sample near the Nyquist frequency of intraseasonal variability, SNR is much more sensitive to changes in temporal subsampling at 6, 9, and 21 days (expts 6D, 9D, 21D). Figure 6a shows the variability of the complete data due to intraseasonal variability, which is clearly concentrated around the equatorial Indian Ocean. The three columns in Fig. 6 show the same statistical information as in Fig. 5 but for intraseasonal variability and three different temporal sampling intervals. It is obvious that a decrease in sampling frequency from 6 to 21 days has quite a remarkable impact on the variability (Figs. 6b–d), the rms errors (Figs. 6e–g), and ultimately on the SNRs (Figs. 6h–j). Whereas SNRs are equal to or larger than 3 in the 6-day case, these ratios locally deteriorate to just above one for the 21-day case, indicating that intraseasonal information derived from Argo floats and sampling errors are of about the same size. On the other hand, the 9-day sampling case reveals that SNRs are still slightly larger than one, suggesting that in the case of noise-free ocean data the current 10-day sampling strategy might be adequate (at 100-m depth level).

Figure 7 reveals the meridional structure of the subsampling in the upper 500 m along 80°E. Both the seasonal and intraseasonal signals show largest variability in subsurface areas at 0° and at 8°N (plus an additional maximum of the seasonal variability at 12°S, Fig. 7a). This picture changes only marginally for the 6-day sampling of the seasonal time scale in Fig. 7b, but a decrease in variability is noticeable in the intraseasonal data, in particular along the axis of the Equatorial Undercurrent (Fig. 7c). The associated SNRs are still large for the seasonal cycle (∼40 along the equator and much larger elsewhere) but as small as one for the intraseasonal case (Fig. 7d).

The previous discussion focused on the upper ocean above 500 m. In the following paragraph we extend our investigation down to the depth level of 2000 m, in accordance with the proposed sampling strategy outlined in section 2b. Figure 8 shows equatorial averages (5°S–5°N) of statistical parameters. Note the split axis at 500 m; the upper part uses the 6-day subsampled dataset (expt 6D); the lower part uses a 21-day subsampled dataset (expt 21D). These two sampling periods are close to the proposed sampling periods of 5 and 20 days, respectively. Equatorial variability has a maximum at about 130 m (∼2°C), which is also where both seasonal and intraseasonal variability peak. Note that there is virtually no difference between the complete dataset (black line) and the seasonal signal, but variability is already slightly reduced on intraseasonal time scales, even with this relatively high sampling frequency. Although rms errors are reasonably small over the whole water column (<0.15°C) the associated SNRs depict a clear difference between seasonal and intraseasonal signal. The former is between 100 and 70 over the whole water column (Fig. 8d), whereas the SNR of the intraseasonal signal ranges from 3 to 2 in the upper 500 m of the ocean and is about 0.6 in the depth range below 500 m. The small intraseasonal SNR at depths deeper than 500 m is probably not a dynamically important factor, as intraseasonal variability relevant to monsoon activity is confined to the upper few hundred meters of the ocean. The basin-averaged profiles are similar in shape to the equatorial averages but generally display somewhat smaller variability in the thermocline, smaller rms errors, and larger SNRs (not shown). Figure 8d also shows results from the 9-day sampling (expt 9D, thin lines). As expected, associated SNRs in the upper 500 m are smaller than those from 6-day sampling but larger than SNRs of the 21-day sampling below 500 m. Particularly, the differences in the upper level might represent an underestimate due to the proximity and averaging of the 6- and 9-day model data compared to 5- and 10-day sampling in the real ocean.

### b. Spatial sampling

Current plans for the Argo array in the Indian Ocean aim for about 450 floats in the Indian Ocean north of 50°S by 2005, with a full coverage of the tropical Indian Ocean at the horizontal standard Argo sampling density (1 float in each 300-km square). We try to simulate the proposed float density by spatially subsampling model data (“Argo floats”), as depicted in Fig. 9. It shows the full model grid (Δ*x* = 200 km, Δ*y* = 50–100 km, ∼2500 floats) and two spatially subsampled versions of it (experiments with label “X”: Δ*x* = 600 km, Δ*y* = 150– 300 km, ∼300 floats; experiments with label “XX”: Δ*x* = 1200 km, Δ*y* = 300–600 km, ∼80 floats; see Table 1). Experiments X are likely to be closest to the final number of floats in the Indian Ocean. We therefore discuss these cases in more detail and refer to experiments with coarser spatial sampling (XX) when appropriate.

Figure 10 shows horizontal averages of spatially subsampled equatorial variability, rms errors, and SNRs for both seasonal and intraseasonal potential temperature. To reconstruct the time series at grid points between floats subsampled data were linearly interpolated in space onto the original grid prior to performing analyses. The subsampled seasonal variability is almost as large as in the complete dataset (2.1°C, Fig. 10a), whereas subsampled intraseasonal variability in the upper 300 m is slightly smaller than in the complete dataset (maximum 0.26° versus 0.32°C, Fig. 10b). These values are very similar to the temporal sampling of the upper 500 m discussed in Fig. 8. Note, however, that the associated rms errors are slightly larger in the spatial sampling case; in particular the seasonal rms error in the thermocline (0.42°C) is now larger than the intraseasonal rms error (0.12°C), contrary to the temporal sampling in Fig. 8. As a result, both SNR profiles are much closer in the spatial sampling (expt 3DX, Fig. 10d) compared to temporal sampling (expt 6D, Fig 8d). We also note that equatorial (and basin scale, not shown) mixed-layer dynamics seem to be most affected by spatial subsampling, as it reveals the smallest SNRs over the whole water column for both frequencies (Fig. 10d). In summary, separate spatial and temporal subsampling significantly influence SNRs of seasonal and intraseasonal signals, but SNRs are mostly significantly larger than one (apart from the intraseasonal signal below 500 m in Fig. 8d).

We note that the basin averages of experiment 3DX are very similar in shape and amplitude to their equatorial averages but with broader peaks in variability and rms values around 150-m depth and almost identical SNRs (not shown). In contrast, experiment 3DXX produced slightly reduced intraseasonal and seasonal variability and a pronounced increase in rms error (particularly above 200 m in the seasonal signal: rms = 0.9°C), reducing both the seasonal SNR by about a factor of 3 and the intraseasonal SNR by about a factor of 2 over the whole water column compared to experiment 3DX (not shown).

### c. Mixed temporal–spatial sampling

We now move a step closer to a more realistic sampling strategy by combining temporal and spatial subsampling. Figures 11 and 12 show analyses of basin-scale and equatorial regions for a measurement system that would probe the ocean every 6 days between 0 and 500 m, every 21 days between 500 and 2000 m, and a spatial sampling scale of 150–600 km, all of which are similar to the proposed sampling cycle (expts 6DX, 21DX). Differences in reproducing the “observed” seasonal and intraseasonal variability are visible in Figs. 11a,b and 12a,b, with the most pronounced differences to be found in the intraseasonal signal (Δ*T* = 0.1°C) of the equatorial thermocline. Maximum rms errors for the seasonal signal are almost identical in both equatorial and basin-scale averages (0.45°C, Figs. 11c and 12c) and largest for the intraseasonal signal in the equatorial average (0.2°C, Fig. 12c). Comparison of the two SNRs reveals a very similar pattern due to the fact that stronger signals (along the equator) are usually associated with larger errors, thus “compensating” each other in the SNR. Close examination and comparison with SNRs discussed for temporal sampling (Fig. 8d) and for spatial sampling (Fig. 10d) reveal that in all but one case the SNRs of the combined temporal and spatial sampling (Figs. 11d and 12d) are equal to or less than those of the individual sampling strategies. Consequently, a degradation of information through combined temporal and spatial subsampling almost always reduces SNRs to values smaller than the smallest individual ratios. This result also applies to the 9-day sampling (expt 9DX), which is shown as thin lines in Fig. 12d. In summary, we note that apart from the dynamically less relevant intraseasonal signal below 500 m (cf. Fig. 8d) all signals in the mixed temporal–spatial sampling case have SNRs equal to or larger than one (Figs. 11d, 12d).

### d. Impact of white noise on signal-to-noise ratios

*World Ocean Atlas*(Levitus and Boyer 1994) as a starting point for our investigation of the impact of noise on sampling strategies. The vertical error profile of potential temperature in the Indian Ocean based on the

*WOA*is displayed in Fig. 13a, represented by values along the vertical dashed line where the abscissa equals one. Values range from 1.2°C near the surface to less than 0.1°C at 2000-m depth. Instead of assuming a fixed error we define a fixed vertical shape for the error curve, which allows us to explore the impact of variable error amplitudes on Argo sampling strategies:

*T̃*

_{sub}

*T*

_{sub}

*αn*

*t,*

*x*

*α*being the amplification factor between 0 and 3 (the abscissa in Fig. 13a) and

*n*(

*t,*

*x*) being the noise, which is assumed to have a Gaussian probability density function that is statistically uncorrelated with the spatially and temporally subsampled signal

*T*

_{sub}. This approach enables us to investigate the impact of a wider error spectrum on the sampling strategy, making it more likely that the real error is encapsulated by the empirical error range.

The observed (Reppin et al. 1999) and simulated time series at 0°, 81°E, (160-m depth) in combination with Eq. (2) provide a quantitative estimate of *α* at one point in the ocean. Taking the square of Eq. (2) and solving for the error *αn*(*t,* *x*) gives an estimate of the temperature error of the model. The error has been calculated for high-pass-filtered data, assuming that the signals to be resolved reside with the longer time scales. The calculated error estimates for high-pass-filtered data with cutoff frequencies at 1, 3, and 6 months are 0.4°, 0.5°, and 0.6°C, respectively. If one inserts these numbers in Fig. 13a at the 160-m depth level the associated *α* values can be read from the abscissa. These numbers are *α* ≈ 0.4, 0.7, and 0.9, confirming that a value of *α* = 1 (error based on *WOA*) is a reasonable estimate of an error factor associated with intraseasonal and longer-term time scales.

Before evaluating the impact of noise on subsampled data and their SNRs, we assess the impact of noise on the complete dataset. These SNRs will subsequently serve as reference for the case of subsampled noisy data. Figure 13 shows SNRs for the basin and equatorial region. Small errors expectedly create large SNRs, with decreasing SNRs toward larger error values. Largest seasonal and intraseasonal SNRs occur in the thermocline of the model (indicative of strong signals) with the equatorial signals being stronger than the basin averages. For a “typical” error profile provided by the *WOA* (*α* = 1), seasonal SNRs in both basin and equatorial domains range from 2 to 7 (Figs. 13b,c). In contrast, the basin-scale intraseasonal signal (Fig. 13d) is much more sensitive to the noise level, as indicated by small SNRs between 0.05 and 0.3 (*α* = 1). However, intraseasonal SNRs at the *α* range inferred from the model-to-observation comparison (0.4 ≤ *α* ≤ 0.9) are still as large as one. It is interesting to note that the intraseasonal signal in the equatorial domain produces slightly larger SNRs than on the basin scale, indicating the stronger intraseasonal amplitude along the equator that is less subject to noise. We also note that for *α* = 0 SNRs in Figs. 13b–d are infinite.

Figure 14 depicts SNRs for the more realistic case of temporally and spatially subsampled data with added noise (expts 6DXN, 21DXN); the thin dashed lines show SNR = 1 of the 9-day sampling (expt 9DXN). The subsampling is identical to experiments 6DX, 21DX, and 9DX (section 3c). Again, we split the vertical axes to accommodate a more realistic sampling strategy of frequent sampling (6 days) in the upper 500 m and less frequent sampling between 500 and 2000 m (21 days). For *α* = 0 the SNRs of Figs. 11 and 12 are reproduced. For the more reliable range of seasonal errors of 1 ≤ *α* ≤ 2, basin-averaged SNRs of the subsampled data (Fig. 14a) are only marginally smaller than the noise-loaded complete data (Fig. 13a) but are somewhat smaller in the equatorial averages (maximum value of SNR ≈ 4 compared to SNR ≈ 7 in the complete model). Similar to the noise-free experiments in Figs. 8, 11, and 12, the 9-day sampling cycle produces somewhat smaller (larger) SNRs in the upper (deeper) ocean than the 6-day (21 day) sampling.

The intraseasonal SNRs for basin and equatorial averages (Figs. 14c,d) range from 0.08 to 0.35 and from 0.6 to 1.1, respectively. Comparison between complete and subsampled noise-loaded data (Figs. 13c,d and 14c,d) reveals the surprising result that, at least for the central range of *α* values, SNRs of the subsampled cases are somewhat larger than for the complete dataset (but differences are usually small, apart from the deep equatorial ocean). This increase in SNR might be associated with smaller spatial features being removed from the complete model dataset when linearly interpolating the subsampled data to the original model grid. This process can cause smoother signals than those existing in the complete model and, consequently, can create slightly larger SNRs in the subsampled than in the complete model. We also note that the 9-day intraseasonal sampling produces SNRs very similar to the 6-day cycle (at least for SNR = 1 and with the exception of the deep equatorial ocean). As mentioned previously, we ascribe the lack of any distinct differences between 6- and 9-day sampling to the comparably coarse temporal resolution and averaging of model data.

### e. Impact of large-scale smoothing and asynchronous profiling

The ability of Argo floats to measure seasonal, 1000-km-scale heat and freshwater anomalies could be degraded due to aliasing caused by intraseasonal and higher-frequency variability such as large-scale waves. We have incorporated these features in a final set of experiments by calculating large-scale averages of the data before adding noise and subsequent asynchronous sampling of the data in time. A spatial filter was applied to the original model data with a zonal length scale of 1000 km and a meridional length scale between 250 km along the equator and 500 km in midlatitudes. The asynchronous sampling was performed such that neighboring Argo floats sampled the ocean at separate times but with each Argo float still sampling at the prescribed temporal sampling frequency.

Figure 15 shows SNRs of the large-scale averaged potential temperature fields with noise added from the *WOA* (expt 3DNL). Comparison with Fig. 13 reveals that the basin-scale and equatorial SNRs of seasonal variability are almost identical to the SNRs based on the unsmoothed horizontal fields (Figs. 13b,c and 15a,b). The intraseasonal SNRs (Figs. 15c,d) show some improvements over the unsmoothed SNRs (Figs. 13d,e), which is mostly visible on the basin scale (∼30%). The large-scale averaged and asynchronously subsampled case with additional noise (expts 6DXNL, 21DXNL; Figs. 16a,b) shows some improvement in SNRs over the similar case (expts 6DXN, 21DXN; Figs. 14a,b) on seasonal time scales, in particular at thermocline depths where SNRs increase by 20%–30%. At deeper levels the SNRs are almost identical. On intraseasonal time scales large-scale averaging and asynchronous sampling only have a marginal impact on SNRs (Figs. 14c,d; Figs. 16c,d). The largest improvements can be found in the deeper ocean where SNRs increase by up to 20%, but these improvements seem to be confined to nonequatorial areas, and SNRs are typically still less than one. The 9-day sampling interval in the top 500 m of the ocean (expt 9DXNL, thin lines in Fig. 14) reveals similarly small changes in intraseasonal and seasonal SNRs.

The small changes in SNRs associated with large-scale averaging and asynchronously sampling of data in time relative to experiments 6DXN and 21DXN might be associated with the model's coarse resolution (the large scale is the characteristic scale resolved by the model such that additional spatial smoothing has only little impact on statistical properties). The 3-day averages in surface forcing fields applied to the model might also have created less large-scale wave activity than could have been expected from higher-frequency forcing, thus underestimating the impact of asynchronous sampling on SNRs in the experiments.

## 4. Discussion and conclusions

Observing system simulation experiments have been performed with an OGCM to assess the feasibility of sampling strategies in the Indian Ocean. It has been shown that some useful information about sampling with Argo floats can be derived from a state-of-the-art ocean model, particularly lending support for the proposed mixed mission of Argo floats in the Indian Ocean, sampling both intraseasonal and seasonal to longer-term time scales.

Assuming a lower limit of one for an “acceptable” signal-to-noise ratio and combining results from temporal and spatial sampling, it has been shown that the extent to which seasonal variability can be measured by Argo profilers is predominantly determined by spatial sampling and to a lesser extent by temporal sampling (Figs. 8a, 10b, 12c). In contrast, intraseasonal variability is determined about equally by spatial and temporal sampling (Figs. 8b, 10b, 12b).

Maximum rms errors in seasonal sampling are almost completely determined by the spatial rms error (<0.05° versus 0.4°C), whereas rms errors of intraseasonal variability contribute about equally (0.1°C) to the mixed temporal–spatial rms error (Figs. 8c, 10c, 12c). Within reasonable temporal and spatial sampling intervals, in most regions of the upper Indian Ocean seasonal SNRs exceed values of 50, whereas intraseasonal SNRs are generally smaller and within one order of magnitude (0.5–5).

More realistic sampling scenarios with white noise added to subsampled data expectedly further reduce SNRs. Within a reasonable range of error estimates, SNRs of seasonal variability are still equal to or larger than one (Figs. 14a,b). However, SNRs of intraseasonal variability are much more sensitive to noise and typically cover a range of 0.1–1.

To reduce degradation of Argo-based observations of large-scale intraseasonal and seasonal climate signals due to higher-frequency variability and large-scale wave propagation, observations have to be spatially smoothed. This procedure (plus asynchronous profiling in time) was applied to a series of sampling experiments. The results reveal some increases in SNRs, which were typically of the order of 10%–30%, but most of the resulting intraseasonal SNRs remain smaller than one (for proposed sampling intervals between 5 and 10 days in the top 500 m and 20 days for the deeper ocean; Figs. 15 and 16).

To capture monsoon-related ocean variability on intraseasonal to seasonal time scales in the Indian Ocean the results presented in this study suggest the following.

Spatial sampling of the ocean is of crucial importance. Argo floats need to be seeded such that they resolve the spatial scales of interest. Along the equator this suggests scales of about 500 km zonally and 100 km meridionally (Figs. 9, 10). Higher spatial sampling is also required along the western boundary current (not resolved by this model).

Due to the comparably coarse 3-day mean temporal resolution of the model output (see section 2) the present study does not provide a decisive conclusion about the relative merits of a 5-day (6 days in model) over a 10-day (9 days in model) sampling cycle regarding the measurement of intraseasonal variability in the upper ocean. The noise-free results suggest that there is some notable gain in intraseasonal SNRs when sampling the ocean with a 5-day cycle (Figs. 8, 11, 12), whereas the situation is less clear from noise-loaded experiments (Figs. 14, 16). Experiments with higher temporal resolution (at least daily) are required before any final recommendations can be made regarding the relative merit of a 5-day sampling cycle over a 10-day sampling cycle. However, assessment of the noise-loaded simulated 6-day cycle (Figs. 13–16) against its signal-to-noise ratios suggests that the minimum sampling interval in the real ocean for capturing intraseasonal variability should be at least 5 days. High-frequency temporal sampling of the order of 5 days becomes particularly important in dynamically active regions of the Indian Ocean, such as the equatorial and western boundary current regimes (Figs. 5, 6), and is required to maintain an acceptable signal-to-noise ratio on intraseasonal time scales. A similar sampling interval is required in the dynamically more quiescent regions of the Indian Ocean that is due to a higher sensitivity of the SNR to noise (cf. Figs. 14c,d). Even with a 5-day sampling interval only part of the intraseasonal spectrum might be captured (depending on the noise amplitude of processes that remain unresolved by the sampling).

Although this study focused on the characteristics of subsampled potential temperature, it is interesting to note that the corresponding SNRs of salinity [with basin-averaged annual mean standard errors taken from Levitus et al. (1994)] are quantitatively very similar to the SNRs of potential temperature (not shown). However, SNRs of salinity at the upper levels of the ocean depict some differences to potential temperature, in particular in the thermocline. Here, for a given error factor *α,* SNRs of potential temperature show a considerable maximum at about 150 m (e.g., Fig. 14), whereas salinity SNRs show a steady increase from 500 m to the bottom of the mixed layer. Combining the results of potential temperature and salinity suggests that the strongest “noise resistant” seasonal and intraseasonal signals can be found in the thermocline. On the other hand, a combined temperature–salinity field with a reasonable noise level (*α* ≈ 1) is unlikely to properly capture intraseasonal variability in the deep ocean on a basin scale, even with a 5-day sampling interval. However, as intraseasonal SNRs in the equatorial deep ocean are *O*(1), one would hope that some useful intraseasonal information can be derived from Argo data gathered there.

There are two potential problems with the statistical analysis performed in this study. One is the size and structure of the noise compared with the modeled intraseasonal signal. This makes the spatiotemporal formulation of the noise critical. It is treated here as “white” noise, although other more complex formulations such a scale-dependent noise levels are imaginable. The second issue is the analysis method that would be used to detect intraseasonal signals in Argo data. If specific phenomena are sought, such as MJOs and these have characteristic spatiotemporal patterns, then one might want to ensure that more statistically powerful analysis techniques would be applied to Argo data to clarify these. Such techniques were not discussed here, as we tried to discuss sampling strategies for spectral bands with intraseasonal and seasonal time scales but not sampling strategies for specific phenomena within these spectral bands.

As all conclusions drawn from this study are based on a single model, results have to be treated with caution. For instance, a caveat associated with the model is its slight underestimation of intraseasonal variability (Schiller and Godfrey 2003), despite some reasonably good agreement (depicted in Fig. 2). This result has two implications: first, in the real ocean intraseasonal signals and associated SNRs are likely to be larger than simulated in this study and, second, deficits of the model are likely to be associated with its limited horizontal and vertical resolution, errors in model parameterization or physics, and errors in surface forcing fields. An option to overcome limitations caused by individual models would be to perform multimodel observing system simulation experiments, especially with eddy-resolving models, based on a coordinated effort.

## Acknowledgments

Support from Helen Phillips, Jim Mansbridge, and Russell Fiedler with the preparation of the figures is greatly appreciated. John Parslow and two anonymous reviewers provided constructive criticism and suggestions that helped to improve the manuscript. Most of the figures were prepared with the public domain software package FERRET from PMEL. This work was partly funded by CSIRO and a grant from the Royal Australian Navy in support of an ocean forecasting partnership project for the Australian region (http://www.marine.csiro.au/bluelink/).

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Simulated (solid line) and observed (dashed line; Reppin et al. 1999) time series of potential temperature at 0°, 81°E at 160‐m depth: (a) 3-day averages of observed and simulated time series; (left column) low-pass-filtered seasonal components of (b) complete and (d) 6-day subsampled data (expt 6D) and (f) their differences. (right column) As for left column but for high-pass-filtered intraseasonal components. Prior to filtering, observations were averaged to 3-day mean values to make them consistent with model data. Note that the observational time series commenced in Jul 1993 and the model simulation finished in May 1994. The model shows a warm bias of about 2.5°C

Citation: Journal of Atmospheric and Oceanic Technology 21, 10; 10.1175/1520-0426(2004)021<1598:DRFAAF>2.0.CO;2

Simulated (solid line) and observed (dashed line; Reppin et al. 1999) time series of potential temperature at 0°, 81°E at 160‐m depth: (a) 3-day averages of observed and simulated time series; (left column) low-pass-filtered seasonal components of (b) complete and (d) 6-day subsampled data (expt 6D) and (f) their differences. (right column) As for left column but for high-pass-filtered intraseasonal components. Prior to filtering, observations were averaged to 3-day mean values to make them consistent with model data. Note that the observational time series commenced in Jul 1993 and the model simulation finished in May 1994. The model shows a warm bias of about 2.5°C

Citation: Journal of Atmospheric and Oceanic Technology 21, 10; 10.1175/1520-0426(2004)021<1598:DRFAAF>2.0.CO;2

Simulated (solid line) and observed (dashed line; Reppin et al. 1999) time series of potential temperature at 0°, 81°E at 160‐m depth: (a) 3-day averages of observed and simulated time series; (left column) low-pass-filtered seasonal components of (b) complete and (d) 6-day subsampled data (expt 6D) and (f) their differences. (right column) As for left column but for high-pass-filtered intraseasonal components. Prior to filtering, observations were averaged to 3-day mean values to make them consistent with model data. Note that the observational time series commenced in Jul 1993 and the model simulation finished in May 1994. The model shows a warm bias of about 2.5°C

Citation: Journal of Atmospheric and Oceanic Technology 21, 10; 10.1175/1520-0426(2004)021<1598:DRFAAF>2.0.CO;2

Cross-spectral analysis of time series of potential temperature at 0°, 81°E at 160-m depth: (a)–(c) high-pass-filtered (*T* < 93 days) and low-pass-filtered (*T* > 93 days) power spectral densities of the complete dataset and the subsampled dataset (expt 6DXN), separated by vertical dotted line. Solid line: complete model; dashed line: temporally and spatially subsampled model data. The three columns are based on an error factor *α* = 0.5, 1.0, 2.0, respectively (see section 3d). Increases in noise amplitudes added to the subsampled data result in decreasing SNRs, as indicated by numbers at upper-left corners in (a)–(c). (d)–(f) The associated coherences together with the 95% significance levels. (g)–(i) The corresponding phases. For further details see text

Cross-spectral analysis of time series of potential temperature at 0°, 81°E at 160-m depth: (a)–(c) high-pass-filtered (*T* < 93 days) and low-pass-filtered (*T* > 93 days) power spectral densities of the complete dataset and the subsampled dataset (expt 6DXN), separated by vertical dotted line. Solid line: complete model; dashed line: temporally and spatially subsampled model data. The three columns are based on an error factor *α* = 0.5, 1.0, 2.0, respectively (see section 3d). Increases in noise amplitudes added to the subsampled data result in decreasing SNRs, as indicated by numbers at upper-left corners in (a)–(c). (d)–(f) The associated coherences together with the 95% significance levels. (g)–(i) The corresponding phases. For further details see text

Cross-spectral analysis of time series of potential temperature at 0°, 81°E at 160-m depth: (a)–(c) high-pass-filtered (*T* < 93 days) and low-pass-filtered (*T* > 93 days) power spectral densities of the complete dataset and the subsampled dataset (expt 6DXN), separated by vertical dotted line. Solid line: complete model; dashed line: temporally and spatially subsampled model data. The three columns are based on an error factor *α* = 0.5, 1.0, 2.0, respectively (see section 3d). Increases in noise amplitudes added to the subsampled data result in decreasing SNRs, as indicated by numbers at upper-left corners in (a)–(c). (d)–(f) The associated coherences together with the 95% significance levels. (g)–(i) The corresponding phases. For further details see text

(a), (c) Trajectories plus (b), (d) initial (black) and final points (red) of simulated Lagrangian floats integrated over a 3-yr period (Jan 1991–Dec 1993); (a), (b) 9-day sampling cycle with 8½ days of drifting at 2000 m plus 12 h at the surface; (c), (d) 24-day sampling cycle with 5½ days of drifting at 2000 m plus 12 h at the surface and three subsequent drifting cycles at 500-m depth (5.5 days), each followed by 12 h at the surface. The number of simulated Argo floats (290) represents about 65% of the anticipated total number of floats (450) in the Indian Ocean by 2005. Average distances traveled plus standard deviation (km) are given for each experiment. Spatial distribution of initial points as in Fig. 9b

(a), (c) Trajectories plus (b), (d) initial (black) and final points (red) of simulated Lagrangian floats integrated over a 3-yr period (Jan 1991–Dec 1993); (a), (b) 9-day sampling cycle with 8½ days of drifting at 2000 m plus 12 h at the surface; (c), (d) 24-day sampling cycle with 5½ days of drifting at 2000 m plus 12 h at the surface and three subsequent drifting cycles at 500-m depth (5.5 days), each followed by 12 h at the surface. The number of simulated Argo floats (290) represents about 65% of the anticipated total number of floats (450) in the Indian Ocean by 2005. Average distances traveled plus standard deviation (km) are given for each experiment. Spatial distribution of initial points as in Fig. 9b

(a), (c) Trajectories plus (b), (d) initial (black) and final points (red) of simulated Lagrangian floats integrated over a 3-yr period (Jan 1991–Dec 1993); (a), (b) 9-day sampling cycle with 8½ days of drifting at 2000 m plus 12 h at the surface; (c), (d) 24-day sampling cycle with 5½ days of drifting at 2000 m plus 12 h at the surface and three subsequent drifting cycles at 500-m depth (5.5 days), each followed by 12 h at the surface. The number of simulated Argo floats (290) represents about 65% of the anticipated total number of floats (450) in the Indian Ocean by 2005. Average distances traveled plus standard deviation (km) are given for each experiment. Spatial distribution of initial points as in Fig. 9b

Seasonal variability of potential temperature at 100-m depth: (a) standard deviation of complete dataset (°C), (b) standard deviation (°C), (c) rms (°C), and (d) signal-to-noise ratio for 21-day sampling interval (expt 21D)

Seasonal variability of potential temperature at 100-m depth: (a) standard deviation of complete dataset (°C), (b) standard deviation (°C), (c) rms (°C), and (d) signal-to-noise ratio for 21-day sampling interval (expt 21D)

Seasonal variability of potential temperature at 100-m depth: (a) standard deviation of complete dataset (°C), (b) standard deviation (°C), (c) rms (°C), and (d) signal-to-noise ratio for 21-day sampling interval (expt 21D)

Intraseasonal variability of potential temperature at 100-m depth. (a) Standard deviation of complete dataset. (left column) Standard deviation, rms, and signal-to-noise ratio for 6-day sampling interval (expt 6D). (middle, right columns) As for left column but for 9- and 21-day sampling intervals (expts 9D, 21D)

Intraseasonal variability of potential temperature at 100-m depth. (a) Standard deviation of complete dataset. (left column) Standard deviation, rms, and signal-to-noise ratio for 6-day sampling interval (expt 6D). (middle, right columns) As for left column but for 9- and 21-day sampling intervals (expts 9D, 21D)

Intraseasonal variability of potential temperature at 100-m depth. (a) Standard deviation of complete dataset. (left column) Standard deviation, rms, and signal-to-noise ratio for 6-day sampling interval (expt 6D). (middle, right columns) As for left column but for 9- and 21-day sampling intervals (expts 9D, 21D)

Intraseasonal (color) and seasonal (isolines) variability of potential temperature at 80°E: (a) standard deviation of complete dataset and (b) standard deviation, (c) rms, and (d) signal-to-noise ratio for 6-day sampling interval (expt 6D)

Intraseasonal (color) and seasonal (isolines) variability of potential temperature at 80°E: (a) standard deviation of complete dataset and (b) standard deviation, (c) rms, and (d) signal-to-noise ratio for 6-day sampling interval (expt 6D)

Intraseasonal (color) and seasonal (isolines) variability of potential temperature at 80°E: (a) standard deviation of complete dataset and (b) standard deviation, (c) rms, and (d) signal-to-noise ratio for 6-day sampling interval (expt 6D)

Equatorial averages (5°S–5°N) of temporal sampling of potential temperature with 6-day sampling (expt 6D, 0–500 m) and 21-day sampling (expt 21D, 500–2000 m): Standard deviation of (a) seasonal (dashed line) and (b) intraseasonal variability (dash–dotted line). Solid lines in (a), (b) show complete dataset; (c) rms errors of seasonal and intraseasonal variability; (d) corresponding signal-to-noise ratios. Thin dashed and dashed–dotted lines in (d) show 9-day sampling (expt 9D) of seasonal and intraseasonal variability, respectively. Scales have been chosen to accommodate all subsequent plots

Equatorial averages (5°S–5°N) of temporal sampling of potential temperature with 6-day sampling (expt 6D, 0–500 m) and 21-day sampling (expt 21D, 500–2000 m): Standard deviation of (a) seasonal (dashed line) and (b) intraseasonal variability (dash–dotted line). Solid lines in (a), (b) show complete dataset; (c) rms errors of seasonal and intraseasonal variability; (d) corresponding signal-to-noise ratios. Thin dashed and dashed–dotted lines in (d) show 9-day sampling (expt 9D) of seasonal and intraseasonal variability, respectively. Scales have been chosen to accommodate all subsequent plots

Equatorial averages (5°S–5°N) of temporal sampling of potential temperature with 6-day sampling (expt 6D, 0–500 m) and 21-day sampling (expt 21D, 500–2000 m): Standard deviation of (a) seasonal (dashed line) and (b) intraseasonal variability (dash–dotted line). Solid lines in (a), (b) show complete dataset; (c) rms errors of seasonal and intraseasonal variability; (d) corresponding signal-to-noise ratios. Thin dashed and dashed–dotted lines in (d) show 9-day sampling (expt 9D) of seasonal and intraseasonal variability, respectively. Scales have been chosen to accommodate all subsequent plots

Spatial sampling strategies with Argo floats in the Indian Ocean: (a) Δ*x* = 200 km, Δ*y* = 50–100 km, ∼2500 floats; (b) Δ*x* = 600 km, Δ*y* = 150–300 km, ∼300 floats; (c) Δ*x* = 1200 km, Δ*y* = 300–600 km, ∼80 floats. Distances are approximations only

Spatial sampling strategies with Argo floats in the Indian Ocean: (a) Δ*x* = 200 km, Δ*y* = 50–100 km, ∼2500 floats; (b) Δ*x* = 600 km, Δ*y* = 150–300 km, ∼300 floats; (c) Δ*x* = 1200 km, Δ*y* = 300–600 km, ∼80 floats. Distances are approximations only

Spatial sampling strategies with Argo floats in the Indian Ocean: (a) Δ*x* = 200 km, Δ*y* = 50–100 km, ∼2500 floats; (b) Δ*x* = 600 km, Δ*y* = 150–300 km, ∼300 floats; (c) Δ*x* = 1200 km, Δ*y* = 300–600 km, ∼80 floats. Distances are approximations only

Equatorial averages (5°S–5°N) of spatial sampling of potential temperature (expt 3DX, Δ*x* = 600 km, Δ*y* = 150–300 km, 3-day means). Notation as in Fig. 8

Equatorial averages (5°S–5°N) of spatial sampling of potential temperature (expt 3DX, Δ*x* = 600 km, Δ*y* = 150–300 km, 3-day means). Notation as in Fig. 8

Equatorial averages (5°S–5°N) of spatial sampling of potential temperature (expt 3DX, Δ*x* = 600 km, Δ*y* = 150–300 km, 3-day means). Notation as in Fig. 8

Basin-averaged properties of combined spatial and temporal sampling of potential temperature with 6- (expt 6DX, 0–500 m) and 21-day sampling (expt 21DX, 500–2000 m). Notation as in Fig. 8. Thin dashed and dashed–dotted lines in (d) show 9-day sampling (expt 9DX) of seasonal and intraseasonal variability, respectively

Basin-averaged properties of combined spatial and temporal sampling of potential temperature with 6- (expt 6DX, 0–500 m) and 21-day sampling (expt 21DX, 500–2000 m). Notation as in Fig. 8. Thin dashed and dashed–dotted lines in (d) show 9-day sampling (expt 9DX) of seasonal and intraseasonal variability, respectively

Basin-averaged properties of combined spatial and temporal sampling of potential temperature with 6- (expt 6DX, 0–500 m) and 21-day sampling (expt 21DX, 500–2000 m). Notation as in Fig. 8. Thin dashed and dashed–dotted lines in (d) show 9-day sampling (expt 9DX) of seasonal and intraseasonal variability, respectively

Equatorial averages (5°S–5°N) of combined spatial and temporal of potential temperature with 6-day sampling (expt 6DX, 0–500 m) and 21-day sampling (expt 21DX, 500–2000 m). Notation as in Fig. 8. Thin dashed and dashed– dotted lines in (d) show 9-day sampling (expt 9DX) of seasonal and intraseasonal variability, respectively

Equatorial averages (5°S–5°N) of combined spatial and temporal of potential temperature with 6-day sampling (expt 6DX, 0–500 m) and 21-day sampling (expt 21DX, 500–2000 m). Notation as in Fig. 8. Thin dashed and dashed– dotted lines in (d) show 9-day sampling (expt 9DX) of seasonal and intraseasonal variability, respectively

Equatorial averages (5°S–5°N) of combined spatial and temporal of potential temperature with 6-day sampling (expt 6DX, 0–500 m) and 21-day sampling (expt 21DX, 500–2000 m). Notation as in Fig. 8. Thin dashed and dashed– dotted lines in (d) show 9-day sampling (expt 9DX) of seasonal and intraseasonal variability, respectively

Impact of white noise on signal-to-noise ratio of complete dataset: (a) error estimates of potential temperature (°C) in the Indian Ocean based on the *WOA* (Levitus and Boyer 1994). The abscissa represents the multiplicative factor *α* of the error curve; the dotted line represents the *WOA* error estimate. (b), (d) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on complete model. (c), (e) As for (b) and (d) but for equatorial region 5°S–5°N. Contour lines plotted in (b) and (c) are 0.5, 1, 2, 3, 4, 5, 10, 50, and in (d) and (e) are 0.05, 0.1, 0.3, 0.5, 1, 2

Impact of white noise on signal-to-noise ratio of complete dataset: (a) error estimates of potential temperature (°C) in the Indian Ocean based on the *WOA* (Levitus and Boyer 1994). The abscissa represents the multiplicative factor *α* of the error curve; the dotted line represents the *WOA* error estimate. (b), (d) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on complete model. (c), (e) As for (b) and (d) but for equatorial region 5°S–5°N. Contour lines plotted in (b) and (c) are 0.5, 1, 2, 3, 4, 5, 10, 50, and in (d) and (e) are 0.05, 0.1, 0.3, 0.5, 1, 2

Impact of white noise on signal-to-noise ratio of complete dataset: (a) error estimates of potential temperature (°C) in the Indian Ocean based on the *WOA* (Levitus and Boyer 1994). The abscissa represents the multiplicative factor *α* of the error curve; the dotted line represents the *WOA* error estimate. (b), (d) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on complete model. (c), (e) As for (b) and (d) but for equatorial region 5°S–5°N. Contour lines plotted in (b) and (c) are 0.5, 1, 2, 3, 4, 5, 10, 50, and in (d) and (e) are 0.05, 0.1, 0.3, 0.5, 1, 2

Impact of white noise on signal-to-noise ratio of subsampled potential temperature. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expts 6DXN (0–500 m) and 21DXN (500– 2000 m). (b), (d) Same as for (a) and (c), but for equatorial region 5°S–5°N. Contour lines plotted in (a) and (b) are 0.5, 1, 2, 3, 4, 5, 10, 50, and in (c) and (d) are 0.05, 0.1, 0.3, 0.5, 1, 2. Dashed lines show SNR = 1 of the 9-day sampling experiment (expt 9DXN)

Impact of white noise on signal-to-noise ratio of subsampled potential temperature. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expts 6DXN (0–500 m) and 21DXN (500– 2000 m). (b), (d) Same as for (a) and (c), but for equatorial region 5°S–5°N. Contour lines plotted in (a) and (b) are 0.5, 1, 2, 3, 4, 5, 10, 50, and in (c) and (d) are 0.05, 0.1, 0.3, 0.5, 1, 2. Dashed lines show SNR = 1 of the 9-day sampling experiment (expt 9DXN)

Impact of white noise on signal-to-noise ratio of subsampled potential temperature. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expts 6DXN (0–500 m) and 21DXN (500– 2000 m). (b), (d) Same as for (a) and (c), but for equatorial region 5°S–5°N. Contour lines plotted in (a) and (b) are 0.5, 1, 2, 3, 4, 5, 10, 50, and in (c) and (d) are 0.05, 0.1, 0.3, 0.5, 1, 2. Dashed lines show SNR = 1 of the 9-day sampling experiment (expt 9DXN)

Impact of large-scale smoothing and white noise on signal-to-noise ratio of complete dataset. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expt 3DNL. (b), (d) same as for (a) and (c) but for equatorial region 5°S– 5°N. Notations and contour intervals as in Figs. 13b–d

Impact of large-scale smoothing and white noise on signal-to-noise ratio of complete dataset. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expt 3DNL. (b), (d) same as for (a) and (c) but for equatorial region 5°S– 5°N. Notations and contour intervals as in Figs. 13b–d

Impact of large-scale smoothing and white noise on signal-to-noise ratio of complete dataset. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expt 3DNL. (b), (d) same as for (a) and (c) but for equatorial region 5°S– 5°N. Notations and contour intervals as in Figs. 13b–d

Combined impact of large-scale smoothing and white noise on signal-to-noise ratio of asynchronously sampled potential temperature. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expts 6DXNL (0–500 m) and 21DXNL (500–2000 m); (b), (d) as for (a) and (c) but for equatorial region 5°S–5°N. Notations and contour intervals as in Fig. 14. Dashed lines show SNR = 1 of the 9-day sampling experiment (expt 9DXNL)

Combined impact of large-scale smoothing and white noise on signal-to-noise ratio of asynchronously sampled potential temperature. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expts 6DXNL (0–500 m) and 21DXNL (500–2000 m); (b), (d) as for (a) and (c) but for equatorial region 5°S–5°N. Notations and contour intervals as in Fig. 14. Dashed lines show SNR = 1 of the 9-day sampling experiment (expt 9DXNL)

Combined impact of large-scale smoothing and white noise on signal-to-noise ratio of asynchronously sampled potential temperature. (a), (c) Basin-averaged signal-to-noise ratios of seasonal and intraseasonal variability based on expts 6DXNL (0–500 m) and 21DXNL (500–2000 m); (b), (d) as for (a) and (c) but for equatorial region 5°S–5°N. Notations and contour intervals as in Fig. 14. Dashed lines show SNR = 1 of the 9-day sampling experiment (expt 9DXNL)

Summary of sampling experiments

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Argo Science Team: D. Roemmich, O. Boebel, Y. Desaubies, H. Freeland, K. Kim, B. King, P.-Y. LeTraon, R. Molinari, W. B. Owens, S. Riser, U. Send, K. Takeuchi, and S. Wijffels