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Evaluation of Sub-Monthly Oceanographic Signal in GRACE “Daily” Swath Series Using Altimetry

Bottom pressure estimates from three different GRACE gravity series (an experimental CSR swath series, ITSG2016, and ITSG2018) and two global ocean models (OMCT and MPIOM) are compared to Jason altimetry sea level anomaly estimates, in order to determine the accuracy of the 10 GRACE and model data at sub-monthly time scales. We find that the GRACE series are capable of explaining 25-75% of the sub-monthly altimetric variability over most of those ocean regions which have high signal strength. All three GRACE series explain more of the sub-monthly variability than the de-aliasing products they were created with do. Upon examination over finer frequency bands, the GRACE series prove superior at explaining that altimetric signal for signals with periods as short as 10 15 days.


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Many Earth-observing satellite missions utilize high-frequency oceanographic models to prevent quickmoving geophysical signals from aliasing into longer-period errors under the effect of a relatively long orbital repeat pattern. Both the Gravity Recovery and Climate Experiment (GRACE) mission (Tapley et al., 2004;Wouters et al., 2014) and the Jason family of radar altimeters (Lambin et al., 2010;Ménard et al., 2003) use such ocean de-aliasing models. For such de-aliasing to be successful, the models must 40 naturally be close to reality, else the errors in using them might be even larger than not de-aliasing at all. Over the past two decades, the sub-monthly global de-aliasing models have improved substantially. Yet they remain imperfect, particularly in hard-to-observe areas such as the distant and deep southern ocean.
In this work, we utilize Jason satellite altimetry data to demonstrate that sub-monthly GRACE data can improve upon the existing GRACE de-aliasing model in several high-signal regions. We then attempt 45 to measure over which frequency bands GRACE is more like altimetry than the existing model is, and thus where and when it might add value over the current de-aliasing model.
The work in this paper was preceded by Bonin and Chambers (2011), called BC11 henceforth. BC11 used older altimetry, model, and GRACE data, but was still able to demonstrate that the then-modern 50 daily ITG-GRACE2010 series could explain 10-30% more of altimetry's variance than the de-aliasing model of the day could, across large bands of the southern ocean and northern Pacific. The theory which both that paper and this one are based upon is straight-forward. If GRACE is observing real submonthly ocean bottom pressure signals, then the variability of the difference between GRACE and altimetry (along the altimetry groundtracks) ought to be smaller than the variability within altimetry 55 alone. Or, put in a more mathematical form, if GRACE is seeing real signal, then: var(Altimetry -GRACE) < var(Altimetry) (1) In this case, the percent of altimetry's variance explained by GRACE will be greater than zero. 60 Similarly, if GRACE is more accurate than the de-aliasing model, then a double-difference of the variances will show that: var(Altimetry -GRACE) < var(Altimetry -Model) (2) 65 Or in terms of relative percent variance explained: pervar(Alt. explained by GRACE) -pervar(Alt. explained by Model) > 0 We do not expect this method of comparison to work well in places with strong mesoscale variability, 70 which neither GRACE nor the models resolve well, nor where altimetry is measuring ocean height changes induced primarily by temperature or salinity anomalies, which GRACE cannot see at all. However, as we determined in BC11, this restricts us only from regions with strong currents, such as along the western boundaries of the continents and the center of the Antarctic Circumpolar Current, leaving most of the ocean accessible to this analysis. 75 Our ultimate goals in this work are two-fold. First, we wish to demonstrate conclusively that the 80 modern "daily" GRACE series we consider are truly measuring real sub-monthly signal, and that not all of that signal is coming from their apriori ocean de-aliasing models. Second, unlike in BC11, we wish to place more specific bounds on which frequency bands GRACE is able to measure better than its dealiasing model does. The ultimate goal which we aspire to in future work is to create a combined submonthly ocean de-aliasing model, where the highest frequencies and shortest wavelengths remain 85 purely model-based, but the longer frequencies and larger spatial scales are blended with those pieces of information from GRACE which are statistically likely to be more accurate.

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The procedures followed in this work are largely those laid out in BC11. In broad form: 1.) Ocean bottom pressure data from GRACE and sea-level anomaly data from Jason-1 and Jason-2 are collected and processed in the standard manner. Bottom pressure estimates from the ocean de-aliasing models used with GRACE are also prepared. Details on this step are given in the following section. 95 2.) Since the altimetry data exists only in those places and times which Jason overflies, the GRACE and model data are masked to cover only those same groundtracks. On days where either GRACE or altimetry data does not exist, no data of any type is utilized. All data types are averaged into daily files at 3° resolution. The altimetry and model data are smoothed using a 300km Gaussian spatial filter, in order to better match them with the native GRACE resolution.

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This also reduces the impacts of eddies and other short-wavelength phenomena.
3.) All data types are band-pass filtered, to recover information within three frequency regimes: signals with periods shorter than 10 days, between 10 and 20 days, and between 20 and 30 days. Gaussian temporal windows are used to segment these regimes so as to avoid incorporating unwanted frequencies due to side-lobes. In addition to these three 105 frequency bands, the sub-monthly variability is considered as a whole, as in BC11.
4.) The differences between GRACE and altimetry, and also between the models and altimetry, are computed over each frequency band. The variances of each differenced series are measured. The percentage of altimetry's variance which is explained by GRACE or the models is computed for each frequency band. A double-difference estimate of this 110 percent variance explained (Eq. 3) demonstrates visually and statistically which GRACE or model estimate explains more of the altimetry signal in the various areas and frequency bands.
In addition to the updated GRACE, model, and altimetry data series, the main difference between this work's techniques and those in BC11 is the use of more frequency bands, so that the type of sub-115 monthly variability can be more closely analyzed. The 10-day altimetry orbital repeat period necessitates the use of larger (3°) grid cells, such that sufficient data is retained within most grids over the shortest frequency band. 120 3 Data Products

Jason Altimetry
The estimates of sea level anomaly considered here come from the most modern Jason-1 and Jason-2 Geophysical Data Records (GDR) available at this time. We use Jason- 1 GDR version E from 2002-125 2008, and Jason-2 GDR version D from 2009. These products are freely available from PODAAC and NOAA (see Data Availability). All standard corrections are applied, including the inverted barometer correction. However, the non-tidal ocean de-aliasing model contained within the dynamic atmospheric correction (DAC) is not removed, as that is what we are attempting to observe. 130 The GDR files were chosen because, unlike more extensively processed products, they are not spatially or temporally smoothed and do not automatically contain the DAC correction. However, because the only GDR files available are two different versions (D and E), at least one known background model difference exists between Jason-1 and Jason-2: the mean sea surface model is not identical, causing an artificial jump between the two series. The supplemental material provides a discussion of this issue 135 and our resolution of it. Fortunately, because our ultimate results are double-differenced statistics where the altimetric signal is treated identically in each of the differenced portions, any errors caused by the change in model will be zero to the first order.

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While most Gravity Recovery and Climate Experiment (GRACE) series have been released at monthly intervals in spherical harmonic form with a maximum spatial resolution of 300-500 km, over the past decade there have been several attempts at resolving the GRACE data into higher temporal frequencies.
We consider three different modern GRACE "daily" series here. 145 The main GRACE series used in this paper, called "CSR swath" throughout, is an experimental mascon (mass-concentration) product created at the Center for Space Research (CSR) at the University of Texas at Austin (Save et al., 2018). The CSR GRACE swath solutions used here are an extension of the CSR RL05 GRACE monthly mascon solutions (Save et al., 2016) but computed daily for those mascons 150 observed by a particular day's ground track. Though the full extent of this data is not currently available for public release, a subset consisting of only the ocean grid cells between 66°S and 66°N has been created and released (see Data Availability). This will allow for replication of this paper's techniques, as desired. 155 The CSR swath series is a near-daily solution, with the world divided into 40962 equal-area geodesic mascon blocks with an average distance of 120 km across. Equivalent water layer (cm) anomalies are computed for each daily orbital pass by estimating the mass change observed in a narrow swath around the GRACE groundtrack. These passes are then accumulated over consecutive days to give an estimate Deleted: ¶ While computing the sea level anomaly values, we stumbled across one surprise difficulty which we would like to make particular note of, for the benefit of other Jason GDR data users. When we went to 230 reference the Jason-2 data to the Jason-1 data, we determined that there is a large, geographically-correlated bias between the most modern data releases of the two missions (Fig. 1a). To provide a historical backdrop, Jason-1 produced solo data from January 2002 through July 2008, at which point it was joined by Jason-2. The two 235 satellites flew in the same orbit, one shortly behind the other, until the start of 2009, at which point Jason-1 was moved into an interleaved complementary orbit. The last of the Jason-1 data was captured in March 2012, after which Jason-2 flew alone for four years. In February of 2016 (after GRACE finished) Jason-3 was 240 added in an identical orbit for eight months, until Jason-2 was moved to the complimentary orbit through its demise in May 2017. The common way of aligning the two missions is to take the data during the overlap periods and compute a bias from that. Historically these mission biases have pointed out several complex 245 error types, but those are now understood, so that the Jason-1 GDR-D to Jason-2 GDR-D biases were constant across the ocean. When we compute the Jason-2 GDR-D to Jason-3 GDR-D biases ( The change of MSS model results in two types of differences during the Jason-1 to Jason-2 leveling process. First, the newer GDR-E 265 MSS model has a finer resolution and is averaged over differing years, which will result in slightly different values in some areas. We are currently assuming that any such differences will be small and will tend to cancel out when looking at data over the entire globe. The second, much more concerning issue is that of the mean 270 bias. The MSS model used in GDR-E is referenced to a center date of 2003, while the GDR-D is referenced to a center date of 2001and no bias correction has been applied (or provided) to align the two averages to an identical time stamp. In areas where the sea surface height is experiencing a trend, this will introduce an artificial 275 jump between the two averages. Averages made from even identical input data would be offset from each other by a time-constant, but spatially-variable, bias of approximately the size shown in Figure 1a. ¶ ¶ To correct for this properly, one would ideally need to reprocess 280 both (or all three) sets of Jason data with a consistent MSS model. This being a lengthy process, however, we used the following approximate technique instead. We computed the average overlap bias (Fig. 1a) along the ground-tracks, then smoothed it with a 100km Gaussian smoother to remove very short-wavelength 285 features, and used the value of that at each point as the Jason-2 bias correction. We note that it is very important to compute the value at each point, as there would be a ±4 cm spread in water heights otherwise, depending on where in the ocean you are looking. Using ... [1] of the global mass anomaly at shorter temporal resolution. The mass estimate of each mascon is only 290 directly updated when GRACE satellites overfly the mascons within 250 km from the center of the mascon. The mascons at high latitudes are observed every 1-2 days while a few mascons near the equator are observed only once every 4-5 days depending on how the groundtracks lay out over time.
Typical ocean mascons at mid-latitudes are observed once every 2-4 days. A statistical combination of older data and newer neighboring data fills in the gaps. The global mascon solutions and regularization 295 are purely driven by GRACE without any influence from external models. The only external information used to inform the constraints is the land/ocean boundary mask. All the other information for constraints comes from expected signals in GRACE for that month from regularized spherical harmonic solutions (Save et. al. 2016) and the GRACE groundtrack. Since the daily constraints are derived from the respective monthly expected signals from GRACE, the regularization also allows for 300 adjustment of unexpected signals that are captured in the monthly solutions. The only submontly signals that will get constrained to zero in the swath solutions are the signals that may have a zero mean over 30 days throughout the mission but do have sub-monthly variability. The implementation of the swath estimation assumes that such locations are very rare. Thus, the time-variable regularization process used does not bias or attenuate future regional signals based on statistics from models or past GRACE 305 months, but is intentionally designed to encourage no land/ocean correlation in order to reduce leakage. Further details of the data processing for producing the daily GRACE swath solutions will be available in Save et. al. 2019 (in-preparation/in-review).
During processing, the sub-monthly release-5 GRACE de-aliasing model ("AOD5", see next section) 310 was removed as one of the standard apriori background models. The GRACE swath series thus estimates the ocean mass change relative to this AOD5 model. We have restored the daily average of the non-tidal ocean model, such that the results shown here are the updated combination. (A model of ocean tides was similarly removed during GRACE processing, but was not restored.) The CSR swath series has also had a GIA model removed (A et al., 2013), though at sub-monthly scale that is 315 noncritical. No geocenter information is included, because GRACE cannot measure it. We chose not to insert an external geocenter estimate, since geocenter series with daily output are rare, and the accuracy on the weekly and sub-weekly scale is highly uncertain and likely to be poor (for example: Männel and Rothacher, 2017) . Interpolating linearly between monthly geocenter values would not add information to the sub-monthly frequencies we are interested in. Similarly, the GRACE C20 signal was not replaced 320 and thus assumed to be correct.
The result is a smoothly-varying series with the ability to pinpoint signals very well spatially (Fig. 1a). The CSR swath technique (like most other mascon methods) has the ability to separate ocean and land signals reasonably well, thus decreasing leakage from land and ice-covered areas into the ocean. The 325 swath series also tends not to show the classic north-south "stripe" errors which are customary with GRACE spherical harmonic solutions. The practical combination of temporal and spatial accuracy can be examined by looking at the average signal at each time over relatively small areas of the world. Consider the average across the Argentine ocean basin, off the coast of Brazil (Fig. 1b). While it is likely that many of the spikes seen there are error-driven, there are significant sub-monthly-scale 330 features picked up which are hoped to be real (for example: Hughes et al., 2007). The GRACE swath 6 solutions show higher amplitude in the sub-monthly frequencies that are not observed by the background AOD5 model in that region. Studies are ongoing to identify the period(s) of these sub-335 monthly signals and are a topic of discussion in Save et. al. 2019 (in preparation/review).
We also consider a pair of additional GRACE series, ITSG2016 and ITSG2018, created by the Technische Universität Graz (TU Graz, see Data Availability). The older of the two, ITSG2016 (Mayer-Gürr et al., 2016), is being superceded by the newer ITSG2018 Kvas and 340 Mayer-Gürr, 2019). Both series are created in spherical harmonic form to maximum degree/order 40, using Kalman filtering. In order to resolve the daily global gravity field, the solutions are stabilized using a stochastic model derived from geophysical models, along with apriori land/ocean masks (Kurtenbach et al., 2012). ITSG data exists even when GRACE does not augment it, but it tends toward the models used, so we omit all days when the CSR swath data denotes a gap. The two ITSG versions 345 differ in the background models used and the details in how instrumental processing steps were handled (see the above websites for details). Significantly, ITSG2016 uses the release 5 ocean de-aliasing model (AOD5), while ITSG2018 uses the newer release 6 version (AOD6, see next section).

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It is critically important for the production of monthly GRACE gravity products that sub-monthly changes within the ocean which could cause gravitational anomalies are estimated and removed from the GRACE data before processing. Doing so prevents sub-monthly signals from aliasing into the monthly estimates. Even the higher-frequency GRACE series remove these modelled estimates from 355 their input before processing the gravity fields, and then restore them later. This means the CSR swath and ITSG solutions considered here actually solve for the residual gravitational signal between the reality and the ocean model. In this paper, we look for evidence that GRACE can see not merely the reproduced apriori model, but additional high-frequency ocean signal beyond that. 360 We will consider the oceanic bottom pressure signals ("GAD" products) of the two most recent GRACE Atmosphere and Ocean De-aliasing (AOD) models, AOD release 5 (Dobslaw et al., 2013;Flechtner et al., 2014) and AOD release 6 (Dobslaw et al., 2017). These ocean bottom pressure products are the output of high-resolution baroclinic ocean models and do not predict the influence of tides. 365 AOD5's ocean bottom pressure estimates come from the Ocean Model for Circulation and Tides (OMCT) (Thomas, 2002), a baroclinic ocean model which estimates the state along 1° horizontal grids with 20 vertical layers and time-steps of 20 minutes. OMCT is forced every six hours with the European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric pressures, wind stresses, temperatures, and freshwater fluxes. Its bottom pressure output is made available for GRACE 370 processing every six hours with spatial resolution given by maximum spherical harmonic degree/order 100 (~200km). The CSR swath and ITSG2016 GRACE series were both made using AOD5. The innate spatial resolution of this model is 1° along the horizontal with 40 vertical layers, and timesteps are given as 90 minutes. It is similarly forced by ECMWF atmospheric pressures, wind stresses, temperatures, and freshwater fluxes, but outputs every 3 hours rather than every 6 and to a maximum spherical harmonic degree/order of 180 (~111km). 390 As a comparison, we also briefly consider the high-frequency ocean component of the de-aliasing product used with the Jason altimetry data. A run of the barotropic, non-linear, finite-element model Mog2D (Carrère and Lyard, 2003;Lynch and Gray, 1979) is used for this, representing the impacts of the ECMWF winds and pressure fields at frequencies with periods below 20 days (note: this is different 395 than the ~30-day months used elsewhere in this paper). The full Dynamic Atmospheric Correction (DAC) product is unfortunately released as a combination of Mog2D with the larger inverted barometer model, which contains significant sub-20-day signal as well and thus cannot be easily separated (see Data Availability). However, a separated subset of the high-frequency Mog2D altimetry de-aliasing ocean model is available, only along the Jason groundtracks, within the GDR records themselves, which 400 is what we use here.

Sub-monthly Results
As an example of the statistics we will be computing, we show the point-by-point standard deviation of 405 the full sub-monthly signal from CSR swath, altimetry, and the difference of CSRswath-altimetry in Fig. 2. This plot, like all others, is computed only over dates when all data types exist, between April 2002 to January 2016. Notice how the altimetry sea level anomaly product shows a very large (>5 cm water height) variability within the major current systems. GRACE does not see these signals, either because they are short-wavelength signals (for example, eddies) beneath the ~300-km resolution of 410 GRACE, or because they are sea surface height changes which do not correspond to a mass change (for example, those caused by a change in temperature, not pressure). Additionally, there are several areas of high, short-wavelength ocean activity, such as the Argentine gyre southeast of Brazil, where GRACE registers only a reduced fraction of the full signal, for the aforementioned reasons. 415 It may appear at first glimpse that GRACE does not measure sufficient altimetric signal to allow our technique to work, but that is a trick of the eye. Fig. 3a shows the percent of altimetry's sub-monthly variability explained by the GRACE swath series. This Percent Variance Explained (P.V.E.) is closely related to the normalization of Fig. 2c found by dividing through by Fig. 2b, and can be computed as: 420 where obviously signals other than GRACE can be inserted in its place. We see that there are large sections of ocean, particularly the southern ocean, where the CSR swath series explains 25-75% or more of altimetry's sub-monthly variability. It does not explain the variability within the equatorial region simply because there is so little signal there (see Fig. 2) that the signal-to-noise ratio gets very low. The 430 altimetric P.V.E. by ITSG2016 and ITSG2018, and by the de-aliasing models GAD5 and GAD6, are shown in direct comparison in Fig. 3. In each case, the largest P.V.E.s occur in about the same areas as in the CSR swath series, with only the relative amplitude changing. Generally, with the exception of the northern Atlantic, the three high-frequency GRACE series show a higher P.V.E. compared to altimetry than either of the GRACE de-aliasing models. 435 Table 1 lists the areal percentage of the ocean between 66°S and 66°N in which each series explains at least 25% of altimetry's variance. The first data column shows this statistic for all grid cells, while the last two columns consider only those non-coastal cells where the CSR swath series measures an RMS of at least 2 or 3 cm water height (masks outlined in Fig. 2a). All three of the GRACE series show a large 440 negative P.V.E. (<-25%) near 90°E, 5°N (Fig. 3a, b, c). This solid-Earth signal is the impact of the Andaman-Sumatra earthquake from 2004, which had a large gravitational effect both during and after the event. For statistical purposes, we have removed the most affected grids from our analysis in all of the following tables. 445 The double-difference plots (Fig. 4) obtained by subtracting one map in Fig. 3 from another via Eq. 3, can better show us which data series most closely matches altimetry in the sub-monthly realm. The percentage of negative non-coastal ocean area between 66°S and 66°N is listed in Table 2. These percentages measure the area where each alternative series explains more of altimetry's variance than the CSR swath series does -or, in other words, places where the alternative series is more likely than 450 CSR swath to be correct. The statistics are again given for all grid cells as well as for the low-signal and high-signal areas separately. They again omit the earthquake area as well as coastal regions which might contain ice or hydrological leakage effects.
We use the CSR swath series as our main comparison series here. We immediately note that the CSR 455 swath series is, in nearly all higher-lattitude locations, better than the AOD5 model upon which it was founded. Fig. 4a is clear proof that the CSR swath series is not merely regurgitating the apriori ocean model provided to it, but is altering it in a manner which makes it more like altimetry -a manner very likely to be an improvement. 460 By comparing Fig. 4b to 4a, we see that in most places, the newer AOD6 model improves upon AOD5, making the differences between it and the GRACE CSR swath series smaller. However, this is surprisingly not true within one region, near 210°E, 60°S. In the bright-pink-colored region there, the AOD6 model is found to be both different from the CSR swath series and measurably worse based on the altimetric P.V.E. To confirm that this difference was not caused by an error in the altimetry 465 product, we also ran the same analysis on the high-frequency ocean de-aliasing model used by Jason altimetry (Fig. 4c). We found that the CSR swath series is roughly equivalent to the Jason ocean dealiasing model in that spot. This implies that GRACE, AOD5, and the Jason de-aliasing model all Deleted: 5 estimate one signal, which additionally matches with the altimetry data, while the AOD6 model predicts something very different. Presumably the AOD6 model is wrong, though precisely why was not 480 immediately clear.
We examined whether an error over a limited time period was causing the AOD6 discrepancy, but found that the same patch of poorly-matched data occurred for all years from 2003-2016. Fig. 5b shows the regionally-averaged sub-monthly time series of AOD5, AOD6, and CSR swath over a single year, 485 compared to the sea level anomalies from Jason altimetry. The time-series of all four series are very similar, with altimetry being the most unlike the other three, as might be expected. The correlation between CSR swath and AOD5 time-series is 94.2%, while the correlation between CSR swath and AOD6 is a still-high 91.6%. However, the main difference is not a matter of correlation, but of amplitude: AOD6 is magnified compared to AOD5. The standard deviation of the CSR swath series 490 over 2003-2013 is 3.72 cm, which corresponds well with AOD5's standard deviation of 3.75 cm. The AOD6 time-series has a much higher standard deviation than either: 5.33 cm.
We then ran a spectral analysis of the four time series over the mostly-continuous 2003-2013 timespan (Fig. 5a), using the least-squares-based Lomb-Scargle method to accommodate the remaining gaps in 495 the data. From this we learned that the AOD6 differences are not caused by a change at a single harmonic, but are rather an amplified signal throughout the entire sub-monthly band, particularly at periods below 10-15 days. The root cause of this difference was initially unknown, though the comparison with altimetry strongly suggested that the AOD6 data was in error in this region. This assessment has since been provided to the developers of AOD1B, who hypothesize that the problem 500 may be caused by a deficit in the MPIOM ocean model configuration around Ross Sea. In AOD6, the model treats all ice shelf areas as land, whereas in fact water several hundreds of meters deep is present underneath the floating ice. In the next release 07 of AOD1B, ice shelf areas will be included into the ocean model domain, which is expected to have a positive effect on the simulation of the region's dominant eigenmodes at 3 to 8 day periods, thus hopefully correcting this problem. 505 We also compared the CSR swath series to the two ITSG high-frequency GRACE series ( Fig. 3d and  3e). The older ITSG2016 series is generally less like altimetry than the CSR swath series, particularly in the equatorial and northern oceans. Only 26.8% of the ocean area shows an improvement relative to 510 altimetry, when switching from CSR swath to ITSG2016. The newer ITSG2018 series is decidedly better, with 45.2% of the grids improving over CSR swath, including 73.7% of the area with more than 2 cm RMS GRACE variability. ITSG2018 is likely an improvement over the CSR swath series in the southern ocean, while CSR swath is probably still better in the equatorial and quieter northern parts of the ocean. Larger differences for both ITSG series along some coasts suggest either worse tidal models 515 or (particularly near Greenland) significantly increased leakage from nearby land, in comparison to the CSR swath series. We would also anticipate the arctic and near-Antarctic oceans to be more poorly measured by ITSG2018 than CSR swath because of the large impact of ice leakage in those areas, but that cannot be tested using the non-polar Jason altimetry data. 520 We used a set of Gaussian temporal windows to act as band-pass filters, dividing the above results into three pieces: signals with periods below 10 days, between 10-20 days, and between 20-30 days. To create the band-pass effect, we used three highpass filters, with 10-day, 20-day, and 30-day cutoffs, then 530 subtracted one from the other in subsequent pairings. (For example, the 20-30 day bandpass signal is the 30-day highpass signal minus the 20-day highpass signal.) To provide a baseline, Fig. 6 shows the altimetric P.V.E. by the CSR swath series for each frequency band. For signals with periods of more than 10 days, the CSR swath series perceives at least 25% and often more than 50% of the altimetric variability across most of the southern ocean and the high-signal part of the north Pacific. Conversely, 535 the swath series does a poor job of reproducing the altimetry signal at periods shorter than 10 days. Since most of the altimetric signal in this highest temporal frequency band occurs over small spatial scales along the major currents, it is not surprising that GRACE cannot measure it. Fig. 7 shows the double-difference P.V.E. comparison for the three frequency bands, with statistics 540 given in Table 3. Its left-hand column depicts the CSR swath series minus AOD5 results, demonstrating that the CSR swath series estimates an improved ocean signal across the entire southern ocean in all three frequency bands, but especially for signals with periods longer than 10 days. In the 10-20 day band, the CSR swath series better explains the altimetric signal than its apriori model can in 83.4% of the high-signal (RMS > 2 cm) part of the southern ocean. In the 20-30 day band, that 545 improves to 87.8%.
The middle column of Fig. 7 shows the same thing, but for AOD6. For periods shorter than 10 days, the two series are roughly equivalent. For sub-monthly periods longer than 10 days, the AOD6 series better matches altimetry over northern and equatorial regions, while the CSR swath series proves to be 550 10% or more better than AOD6 in much of the southern ocean. Improvements over its AOD5 predecessor can be seen in all frequency bands. The CSR swath series better explains the 10-20-day altimetric signal than the AOD6 model does in 44.5% of the high-signal southern ocean bins. For the 20-30 day band, CSR swath better explains 58.9% of these bins. Additionally, the small region of poor performance near 210°E, 60°S is confirmed to be a very high frequency issue, mainly visible in the 1-555 10-day band and not visible in the 20-30-day band.
The right-hand column of Fig. 7 is the ITSG2018 comparison. (ITSG2016 was found to be inferior to its successor in all bands, so we do not depict it here.) There are few frequency-based distinctions between the CSR swath and ITSG2018 series. In the southern ocean, ITSG2018 signals with any sub-560 monthly period are more likely than CSR swath signals to be like altimetry (ITSG2018 is better in 65.5%, 85.6%, and 79.4% of the grids by area, for the 0-10, 10-20, and 20-30 day bands respectively). The opposite is true in the lower-signal equatorial and northern oceans (similar percentages of 26.0%, 45.2%, and 44.7%). The large positive (>30%) coastal differences near Alaska, Patagonia, the Antarctic Peninsula, and Greenland again suggest that ITSG2018 does not segregate the land ice leakage as well as the CSR swath series does, while the large negative (<-30%) coastal differences north 570 of Australia hint towards a possibly improved tidal or ocean model. CSR swath series' generally higher equatorial P.V.E. could indicate that series has better reduced the GRACE stripe-like errors compared to ITSG2018 in these regions of relatively low oceanographic signal.

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Using a comparison with Jason altimetry, we have demonstrated that two modern near-daily GRACE series are capable of estimating real sub-monthly oceanographic signal. Both the CSR swath series and ITSG2018 explain a fair proportion of the high-frequency altimetric signal outside of major currents, the equatorial region, and the northern Atlantic; more of it than the apriori ocean models they are based 580 upon can. We found that these near-daily GRACE series are particularly sensitive for signals with periods above about 10 days, and less so as the signal length shortens below that.
At the moment, it appears that the CSR swath series is better able to eliminate land-leakage from ice and hydrology from entering the ocean grids, making it distinctly better than ITSG2018 along the coasts 585 and near the large ice sheets. CSR swath also appears probably better at removing the false north-south stripes commonly created during GRACE processing, allowing the quieter equatorial regions to be better estimated. The ITSG2018 series, on the other hand, appears to better observe the sub-monthly state of the southern ocean, particularly in those areas with large amounts of variability. This might be an impact of the different processing scheme, or it might be due to the use of the newer AOD6 model as 590 an ocean de-aliaser. To test the latter, we plan on eventually reproducing the CSR swath data with AOD6 as an apriori model.
Our analysis here demonstrates that, particularly in the poorly-observed southern ocean, sub-monthly GRACE data can be used to improve our knowledge of the ocean bottom pressure. We hope to use this 595 in the future to validate global ocean models, perhaps even merging the GRACE data with modeled results in order to produce a combined de-aliasing product superior to either source alone.

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All data required to reproduce this work is freely available online in the following locations: •

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• The GRACE CSR Swath data is not generally available for release yet, but a subset consisting of only the ocean grid cells between 66°S and 66°N has been placed at https://doi.org/10.18738/T8/95ITIK.
• The Jason de-aliasing DAC model data can be found either as the "HF" section of the GDR files mentioned above, or else in combination with the IB effect at https://www.aviso.altimetry.fr/en/data/products/auxiliaryproducts/atmospheric-corrections/description-atmospheric-corrections.html.

8 Competing Interests
The authors declare that they have no conflicts of interest.

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Jennifer Bonin processed the altimetry, model, and ITSG GRACE data, and computed the band-passed analysis and its statistics. Himanshu Save designed and created the CSR GRACE Swath series, and assisted on the statistical assessment of the results. Jennifer Bonin prepared the manuscript with additions by Himanshu Save.

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Our thanks to Don Chambers for his valuable assistance with the MSS bias investigation. Thanks to Henryk Dobslaw for his helpful review as well as his willingness to look into, explain, and begin correcting the AOD1B RL06 oddity we found. Thank you also to our second anonymous reviewer. This work was funded by an Ocean Surface Topography Science Team NASA grant, for which we are grateful.       While computing the sea level anomaly values, we stumbled across one surprise difficulty which we would like to make particular note of, for the benefit of other Jason GDR data users. When we went to reference the Jason-2 data to the Jason-1 data, we determined that there is a large, geographically-770 correlated bias between the most modern data releases of the two missions (Fig. S1a). To provide a historical backdrop, Jason-1 produced solo data from January 2002 through July 2008, at which point it was joined by Jason-2. The two satellites flew in the same orbit, one shortly behind the other, until the start of 2009, at which point Jason-1 was moved into an interleaved complementary orbit. The last of the Jason-1 data was captured in March 2012, after which Jason-2 flew alone for four years. In 775 February of 2016 (near the end of GRACE) Jason-3 was added in an identical orbit for eight months, until Jason-2 was moved to the complimentary orbit through its demise in May 2017. The common way of aligning the two missions is to take the data during the overlap periods and compute a bias from that. Historically these mission biases have pointed out several complex error types, but those are now understood, so that the Jason-1 GDR-D to Jason-2 GDR-D biases were constant across the ocean. 780 When we compute the Jason-2 GDR-D to Jason-3 GDR-D biases (Fig. S1b), that is still what we see.
However, the transition from Jason-1 GDR-E to Jason-2 GDR-D creates a large, non-uniform bias ( The change of MSS model results in two types of differences during the Jason-1 to Jason-2 leveling process. First, the newer GDR-E MSS model has a finer resolution and is averaged over differing years, which will result in slightly different values in some areas. We are currently assuming that any such differences will be small and will tend to cancel out when looking at data over the entire globe. 795 The second, much more concerning issue is that of the mean bias. The MSS model used in GDR-E is referenced to a center date of 2003, while the GDR-D is referenced to a center date of 2001 -and no bias correction has been applied (or provided) to align the two averages to an identical epoch. In areas where the sea surface height is experiencing a trend, this will introduce an artificial jump between the two averages. Averages made from even identical input data would be offset from each other by a time-800 constant, but spatially-variable, bias of approximately the size shown in Figure 1a.
To correct for this properly, one would ideally need to reprocess both (or all three) sets of Jason data with a consistent MSS model. This being a lengthy process, however, we used the following approximate technique instead. We computed the average overlap bias (Fig. 1a) along the ground-805 tracks, then smoothed it with a 100km Gaussian smoother to remove very short-wavelength features, and used the value of that at each point as the Jason-2 bias correction. We note that it is very important to compute the value at each point, as there would be a ±4 cm spread in water heights otherwise, depending on where in the ocean you are looking. Using the mean bias over this map would result in a constant -0.785 cm correction, which would not be accurate in most places. (As a comparison, we 810 found the Jason-2D to Jason-3D bias to be a larger but very stable -2.871 cm.) Our ultimate results are double-differenced, comparing the statistics of Altimetry minus GRACE to Altimety minus a model. Because of this, the treatment of the MSS model is non-critical. There could be an effect in the percent of altimetry's variance explained by each other series (Fig. 3) but that effect 815 would cancel itself out in the difference in P.V.E. between two comparison series (Fig. 4). For this reason, the rough treatment we have used here is effective. However, any GDR user interested in looking at non-differenced results should be aware of this bias and correct for it by the consistent replacement of the MSS model. 820