An Ocean Tidal Inverse Model For Antarctic Ice Shelves: Application to Amery Ice Shelf We are interested in the influence of the ocean with the Antarctic ice shelves. While many ocean processes affect shelf ice, here we just consider the effect of ocean tides. When we look at specifics of the model, we will use the Amery Ice Shelf that Helen just told told us about, as the example. Laurie Padman Helen A. Fricker Richard Coleman

Why Study Tides? Remove tide signals from satellite (InSAR, altimetry) and in situ (GPS, gravity, tilt) data Tides influence: Ice shelf basal melting and refreezing Iceberg calving and subsequent drift Ocean mixing (water mass modification) and sea ice distribution Here is a partial list of what we want to get from an Antarctic tidal model. Point 1 considers tides as “noise” in our attempts to study longer-period processes such as ice shelf response to seasonal forcing and climate variability. This will be the main focus of this talk. Point 2 considers the active influence of tides on other aspects of the ocean-ice system. Helen discussed some of these effects in the previous talk. (Read through list). Most of these influences depend on the tidal currents rather than tide heights. To keep things simple, we don’t consider these processes any more in this talk.

Standard Deviation of Tide Height Amery CADA00.10 Let’s look now at the size of tides around Antarctica. This helps us decide whether we need to worry about tides in a particular place. Lucky for me, we usually do. Based on our latest model run, we find that a typical standard deviation is about 60 cm, the yellow here. The RMS can, however, be as high as 1.8 m in the Weddell Sea under the Filchner-Ronne Ice Shelf (point out). The typical tidal range, peak-to-peak, is about twice this value, and the maximum range is about 4 times this value. So, under the Ronne Ice Shelf, spring tidal range can exceed 7 m. The Amery Ice Shelf that Helen spoke about last is over here (indicate) in East Antarctica. The RMS tide in the Amery varies from about 60 cm to 80 cm, so it is fairly typical of Antarctic tides. Again, applying our rough relationships, these values imply peak-to-peak tides of between about 1.5 and 3 meters. RMS Tide Height (cm) Hmax  4*RMS

Assimilation: formalized hybrid Tide Model Choices Empirical: data analyses Dynamical: momentum equations Assimilation: formalized hybrid Assimilation nudges dynamical solution towards better fit with data There are several ways to model tides. In empirical models, we measure the tide height at a point, then analyze the time series. This gives us a model so that tides can be predicted at that point at times outside the measurement interval. In a dynamical model, we rely on the equations of motion and specified forcing to give us the tides at any point in our model grid. Empirical models can be very accurate but are only valid at the point where the data are measured. Tidal data records are sparse, especially in the Antarctic. Dynamical models can provide great spatial resolution, but fail when the model physics are simplified for computational reasons, or boundary conditions are not perfect. So, the assimilation model, combining both options, is what we use here. The basic idea is to use data to nudge a dynamical model towards a better fit with the data. The technique is formalized by choosing logical criteria for minimizing the misfit, taking into account the sources of expected errors.

The Inverse Model (CADA) Circum-Antarctic, 86o-58oS, ~10 km grid spacing Oregon State Tidal Inversion Software (G. Egbert) “Bathymetry” includes water column thickness under major ice shelves The resulting inverse model is called CADA, for Circum-Antarctic Data Assimilation. (Read through slide) Model performance depends on finding sufficient data to assimilate. We discuss these on the next slide.

Potential Data Sources  TOPEX/Poseidon radar altimetry  Tide gauges (coastal, benthic) (~30)  GPS on ice shelves (1 only)  Gravimeter (Ross: ~10) ERS-1 & ERS-2 radar altimetry Future laser altimetry (GLAS on ICESat) So, the data sources that we have identified for the Antarctic region are: (work through list) A tick means we are already using these data. TOPEX/Poseidon only goes to about 66oS and so misses most of the Antarctic. There are about 30 tide gauges that we’ve found. GPS data are particularly valuable if the record length is greater than about 30 days. At present we only have one such record on the ice shelves, but expect to get many more in the next couple of years, especially on the Amery. There are about 10 gravimeter records from the Ross Ice Shelf and one near the Rutford Ice Stream entering the Ronne Ice Shelf. ERS goes to about 82oS and so overcomes some of the restrictions of TOPEX/Poseidon. However, it is noisier, the orbit is not designed with tides in mind, and it is difficult to interpret when sea ice is present. But, we will look at how ERS data may help in future. Finally, we expect to get useful heights from the Geoscience Laser Altimeter System after the ICESat launch in late 2001. These values will be much more accurate than ERS over the shelf ice.

Dynamics-only With Assimilation Amery Ice Shelf Dynamics-only With Assimilation * * Now let’s look at the effect of assimilating the data we presently have. Here we compare pre- and post-assimilation models for the Amery, using just the amplitude and phase of one tidal constituent, the main semidiurnal tide, M2. The three red squares are assimilated tide height stations: Beaver Lake (here); a 30-day GPS record collected early this year (here), and Davis Station (here). Notice that, with assimilation, the amplitude for M2 in the southern Amery decreases from about 40 cm, red shading, to about 30 cm, orange shades. Phase also changes with assimilation. The contours on each plot show the same 3 phase lines 10 degrees apart. With assimilation, the change in phase for most of the Amery is about 5-10 degrees. Next we’ll look at the different model predictions for the point marked with an asterisk down here in the southern Amery. M2 Amplitude (cm)

Model Comparisons, Southern Amery Forward Assimilation Difference Here we shown 15 days of predictions for the point on the previous slide. Blue is the dynamic model. Red is after data assimilation. Green is the difference between the two models. The typical difference is 10-to-20 cm. We can’t tell at this time if the new solution really is better, since the only data from the southern Amery are short, 1-to-2 day GPS records. The longer GPS records that we expect to get from the Amery this coming austral summer will help with model validation and in new assimilation runs. GLAS, the Laser Altimeter System on ICESat, can measure elevation to about 5 cm, which is much less than the difference between these two models. If we want to fully utilize the GLAS measurements for studies of seasonal and long-term changes, we need to spend more time on validating and improving our models. For the Amery, planned GPS measurements will help further constrain the inverse model. For most major ice shelves, however, the best hope for model improvements lies with satellites. Since the best tide-resolving satellite, TOPEX/Poseidon, does not get south of 66oS, we look at what might be learned from the ERS satellites. This can also give us an idea about what GLAS might tell us.

Satellite Aliasing Problem TOPEX/Poseidon: ERS 35-day (Skip if time is short) Let’s first look at one of the significant problems with satellite data. Satellites give great areal coverage, especially down near their turning latitudes. Satellites don’t do a very good job of resolving in time, however. The high frequencies of tides, 1 and 2 cycles per day. are aliased into resolvable low frequencies. On this plot the x-axis is about 4 years long, and the y-axis is about plus-or-minus 1 m. The fuzzy gray line is a predicted hourly time series of tide height from one point on the Amery Ice Shelf. The red line shows how this time series looks when sampled by the 35-day phases of ERS. The blue line shows the time series if it was sampled by TOPEX/Poseidon. The site is actually too far south to be seen by this satellite, but the idea is to show how different satellite orbit choices perform. The TOPEX/Poseidon orbit was specifically chosen to alias major tidal constituents to relatively high resolvable frequencies of about 60-90 days. So, as we see, the whole range of tidal amplitudes is sensed by the fictitious TOPEX/Poseidon sampling in a few hundred days. However, with ERS, it is difficult or impossible, even with several years of data, to record the whole character of the tide. This means that ERS data cannot be used to make empirical maps of most tidal coefficients. GLAS will have the same problem, although its higher accuracy and the presence of a shorter near repeat sub-cycle (25 days), will help. But the ERS and GLAS data can be used to judge model performance, and to nudge an assimilation model towards a better solution. In the next couple of months we will assimilate ERS data from the open ocean, during periods when the ocean is free of sea ice. We also have ERS data over the ice shelves, however, and in the next slide we show our first steps to test the use of the ERS data in this way.

ERS Altimeter Tide Measurements G1 (near ice front) t2.4 days CADA00.10 We have just started looking at ERS data over the Amery. Remember that the tides on the Amery are fairly typical of Antarctic tides, roughly 2.5 meters peak to peak. We look only at crossover differences, that is the difference in height sensed during ascending and descending orbits at a single location a few days apart. This reduces the influence of actual non-tidal changes in surface elevation. Here is a plot of differences for a flat site near the Amery ice front, actually the drill site in which over 100 m of marine ice was found on the bottom of the core. The x-axis is the measured difference, and the y-axis is the model prediction for the same pass times. We know from GPS data that the model works okay, to about 10-20 cm, so we discard clearly bad points before calculating the linear regression. The points we keep are in yellow, discarded points are in gray. The red line shows exact equivalence between the measurements and the model. The green line shows the linear regression fit. In spite of the noise in each point, this figure shows that ERS data do show tides over the Amery. In this particular site, the uncertainty in the models is less than the noise on individual altimeter points and so the data don’t really help. However, the ice shelves of the Weddell Sea, and the Siple Coast in the Ross embayment, have larger signals and larger uncertainties, and so ERS might be helpful in those areas. ERS data over ice are noisy, and each measurement is only good to about 50 cm. However, there are a lot of ERS data over the shelves, and it may be that individual constituents can be further tuned by use of ERS data in our assimilation model. We are exploring this possibility, but don’t yet know how it will turn out. Hmodel=8+0.8*HERS

Summary Optimistic outlook for tide prediction with data assimilation Useful data for model upgrades include: Satellite altimetry (ERS, GLAS) Better open-ocean bathymetry grid Ice shelf grounding lines (InSAR) Ice shelf GPS Sub-ice water column thickness (ground- based radar) In summary, we expect tidal model skill to get much better over the next couple of years. Our understanding of some of the missing energy sinks in dynamical models is improving rapidly and can be included in future dynamical models that are used as the prior solution in the inverse models. Additional satellite radar and laser altimetry will improve the assimilation model. Improvements will be made in the model domain through SAR interferometry measurements of ice grounding lines, and the increasing data base of Antarctic ocean bathymetry. We’d like to encourage people to collect GPS records whenever they can, especially on the large shelves and in regions such as Pine Island Bay, where no such records exist at all. Records should be at least 30 days long if possible, but shorter high quality records are still valuable. The last item, new under-ice water column thickness, would be extremely useful but we do not know of any plans to do this for any of the major shelves. If people do plan to acquire such data, we’d like to know. Thank you.