HMI_Logo HMI Pipelines
Ring Diagrams

Ring-Diagrams Pipeline Specifications

Introduction

The fundamental scientific data products to be produced from ring-diagram analysis, in accordance with the HMI Science Plan, are full-disc and synoptic maps of horizontal velocity and sound-speed profiles from the surface to a depth of 30 Mm. In addition to these it is possible that we may be able to produce high-resolution maps to the same depths and deep-focus maps extending to 200 Mm. The distinction between full-disc and synoptic maps is not clear in the Science Plan; since the analysis normally relies on mapping onto some co-rotating surface coordinate system in any case, it may only be a matter of organization or continuity of the data. Continuous analysis of the full disc is necessary in any case to prepare the synoptic maps. Likewise the distinction between full-disc and synoptic maps on the one hand and high-resolution on the other is not made specific in the Science Plan.

We regard the full-disc and synoptic data products as ones produced over the entire available grid of time and spatial coordinates at a fixed resolution, and the high-resolution products as any products of higher spatial resolution produced either irregularly or only in the vicinity of designated areas and times, such as NOAA active regions and selected comparison quiet sun regions. We refer to the pipelines producing these products as the synoptic and target pipelines, respectively. The pipeline producing the contemplated deep-focus products, if implemented distinctly from the synoptic pipeline, will be referred to as the deep-focus pipeline.

Synoptic Pipeline

Region Sampling

The synoptic data products for transverse velocities are to be sampled at a spatial scale corresponding to 2°.5 heliographic (~30 Mm), with analysis regions of diameter 5°, extending out to μ = 0.986, about 80° from disc center. At this distance the area of foreshortened HMI pixels is comparable to that of the limit at which we are able to extract useful ring-diagram fits from full-disc MDI data at one-third the resolution. The minimum temporal sampling period will correspond to 5 degrees of Carrington rotation (1/72 of a synodic rotation, ~545 min), i.e. the time for a sampled region to rotate through its diameter as viewed by the observer.

In order to invert for velocities and thermal structures below the immediate sub-surface layers, it is necessary to sample larger areas for longer times in order to measure higher order modes. Therefore we will also produce data products on 7°.5 and 15° sampling grids, with the regions having diameters twice the grid spacing and temporal sampling correspondingly decreased to the region-crossing times, 1/24 and 1/12 of a synodic rotation, respectively (~1635 min and ~54.5 hr, respectively).

Target Locations

Because we expect to be able to do ring diagram analysis so close to the limb with HMI resolution, the annual effect of the change in the observer heliographic latitude must be considered. It will allow us to reach, at some times of year, 5° diameter regions centered at latitudes as high as 85° in each hemisphere, and the extreme accessible longitudinal extent at each latitude will vary over the course of the year. Also, with our ability to reach to high latitudes, the longitude spacing of the analysis grid should be adjusted to retain a similar heliometric spatial sampling. We plan to have the longitude spacing in the 2°.5 grid be 2°.5 at latitudes between ±40°.0, 5°.0 at latitudes between 42°.5 and 65°.0 in each hemisphere, 7°.5 at latitudes between 67°.5 and 72°.5 in each hemisphere, and 10°.0 at latitudes ±75°.0 and above. With these spacings, the number of possible grid points on each Carrington map, and each full-disc map at the 2°.5 spacing, will be 3007. Of these, 2481 will always be accessible. 242 will be accessible at some times in both hemispheres (i.e. inaccesible in one hemisphere only part of the year), and 142 will be accessible in only one hemisphere part of the year. (The distinction between the latter two classes might be thought of as accessible except in “winter”, and only accessible in “summer&rdwuo;.) How finally to divide the regions of accessibility by the latitude of disc center needs to be established, but for now we propose dividing the year into quadrants with the boundaries at B0 = 0.0, ± 3°.625, and ±7°.25. Thus, the northern hemisphere classes, for example, would be those accessible all year, those accessible except when B0 < -3°.625 (~8 months), and those only accessible when B0 ≥ 3°.625 (~4 months).

The spatial grid so defined may be visualized with this sample for one quadrant. Points marked A will be included always, those marked 2 will be included in that hemisphere 8 months of the year (and both hemispheres 4 months), and those marked 1 will be included 4 months of the year. The grid is labeled by the target latitudes and longitudes in tenths of a degree.

lon 000 050 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
      025 075 125 175 225 175 325 375 425 475 525 575 625 675 725 775
lat
850  1       1       1       1       1       1
825  1       1       1       1       1       1       1       1
800  2       1       1       1       1       1       1       1
775  2       2       2       2       1       1       1       1
750  2       2       2       2       2       1       1       1
725  A     A     2     2     2     2     2     1     1     1     1
700  A     A     A     A     2     2     2     2     1     1     1
675  A     A     A     A     A     2     2     2     1     1     1
650  A   A   A   A   A   A   A   A   A   2   2   2   2   1   1   1
625  A   A   A   A   A   A   A   A   A   A   A   2   2   2   1   1
600  A   A   A   A   A   A   A   A   A   A   A   2   2   2   1   1
575  A   A   A   A   A   A   A   A   A   A   A   A   2   2   1   1
550  A   A   A   A   A   A   A   A   A   A   A   A   A   2   1   1
525  A   A   A   A   A   A   A   A   A   A   A   A   A   2   1   1
500  A   A   A   A   A   A   A   A   A   A   A   A   A   2   2   1
475  A   A   A   A   A   A   A   A   A   A   A   A   A   2   2   1
450  A   A   A   A   A   A   A   A   A   A   A   A   A   2   2   1
425  A   A   A   A   A   A   A   A   A   A   A   A   A   A   2   1
400  A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 2 2 1 1
375  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 2 1 1
350  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 2 1 1
325  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 2 1 1
300  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 1 1
275  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 1 1
250  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 2 1
225  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 2 1
200  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 1
175  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 1
150  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 1
125  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2 1
100  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 2
 75  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A
 50  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A
 25  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A
 00  A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A

For the 7°.5 grid, approximately equal spatial sampling suggests that the longitude sampling should be as follows:

 lat lon spacing
 0.0   7.5
 7.5   7.5
15.0   7.5
22.5   7.5
30.0   7.5
37.5  10.0
45.0  10.0
52.5  12.5* (see below)
60.0  15.0
67.5  20.0
75.0  30.0
Similarly the spacings for the 15° grid should be, in each hemisphere,
 0.0  15.0
15.0  15.0
30.0  15.0
45.0  15.0
60.0  30.0
(Strictly speaking, the better spacings in longitude would be 17°.5 at latitude 30.0 and 20°.0 at latitude 45.0, but the comparatively small differences involved in oversampling here do not outweigh the advantage of uniformity.)

The target quadrant grid for the 7°.5 full-disc grids may be visualized as follows:

lon 000 050 100 150 200 250 300 350 400 450 500 550 600 650 700 750
          075 125     225         375     475 525         675 725
lat
750  1
675  A               A               2               1
600  A           A           A           A           2           1
525  A         A        A          A         A        2          1
450  A       A       A       A       A       A       A       2
375  A       A       A       A       A       A       A       2
300  A     A     A     A     A     A     A     A     A     A     1
225  A     A     A     A     A     A     A     A     A     A     1
150  A     A     A     A     A     A     A     A     A     A     1
 75  A     A     A     A     A     A     A     A     A     A
 00  A     A     A     A     A     A     A     A     A     A
(Total of 307, of which 261 always accessible)

Note the suggested spacings of 12°.5 in longitude at latitudes ±52°.5 deg. This is a problem because it is not an integer divisor of 360, thus the selected longitudes would not repeat in each rotation. They should be reduced to 12°, for a cadence of 30 samples per rotation. Also, it is not evident how often the single longitude at latitude ±75° should be resampled. We suggest once every 90° in longitude, since tracking of all regions will presumably be done for about the duration of their disk passage.

The target quadrant grid for the 15° full-disc grids is:

lon 000 050 100 150 200 250 300 350 400 450 500 550 600 650 700 750
lat
600  A                       A                       1
450  A           A           A           A           2
300  A           A           A           A           A
150  A           A           A           A           A
 00  A           A           A           A           A
(Total of 73, of which 65 always accessible)

The duration of tracking of the original cubes, from which the analysis cubes are to be extracted, must be long enough to permit the extraction of all tiles described above. This means that the duration of tracking should extend as far as the outermost longitude tile plus the spacing. For example, for the 15° grid, the regions at low latidudes will be tracked for at least 150 deg in Carrington rotation (twice 60 + 15). The region at latitude +60° will be tracked for 180 degrees in rotation (twice 60 + 30) in the four months that B0 > 3°.625, 120 degrees the rest of the year. The only difficulty is for the regions at 75° latitude in the 7°.5 grid, tracked only at times of extreme B0, for which there is no longitude spacing, as the single tracked region accounts for the full available distance to the limb. We suggest that the region be tracked for 180 degrees of rotation, with a new one initiated every 90 degrees in rotation. (This is equivalent to an effective spacing of 90 deg in longitude.)

Tracking

There are two distinct issues involved in the choice of tracking rate for region analysis. One of these has to do with the identity of the regions being tracked. If the tracking duration is comparable to or greater than the region diameter divided by the difference between the tracking rate and the actual zonal velocity of the region (whatever that means), then the “region” clearly loses its identity. Since different features move at different rates in both latitude and depth, this issue can only be resolved by making the regions sufficiently large and the analysis intervals (tracking durations) sufficiently short. The other issue has to do with the mechanics of fitting ring-diagram parameter models to the power spectra. When a region is grossly mistracked, the wave advection may shift the frequencies of positive and negative wavenumbers for a given order and degree sufficiently to remove them from the fitting interval, or introduce cross-talk with frequency-dependent background terms.

For processing efficiency, and certainly for re-analysis, it is higly desirable that the analysis cubes be extracted from regions tracked across their full disc passage, or at least a sufficient fraction of it to support all of the required tiles. In order to sample the ‘same’ region from such supersets of tracking intervals, it would be necessary to track all regions at the Carrington rate. This will of course introduce ‘spurious’ zonal flows corresponding to the mean differential rotational rate of latitude and depth. The difference between the Carrington rate and the surface Doppler differential rotation rate (the Snodgrass rate currently in standard use) has a maximum value of about 263 m/s at about 50° latitude. (The maximum differential between the Newton & Nunn rate and Carrington rotation is about 176 m/s at about 45° latitude.) The existing ring-fitting code rdfitc has been demonstrated to work even with untracked data (zonal “flows” of up to 2 km/s), so this should not be a problem for it. Concerns about the code rdfitf are being addressed by the analysis of tests on the tracking rate. There are also concerns about the ability of the rdfitf code to fit well when the regions are small enough to isolate the super-granular flows. This should not be a problem for the tile sizes in the Synoptic Pipeline, but may be for the smaller sizes involved in the Target Pipeline. It is arguably a convenience to reference the mean zonal flows as a function of depth and latitude to a uniform rate, just as is done in the surface functional forms of differential rotation. It is certainly helpful in the construction of synoptic analyses to have the data referred to the same co-ordinate system.

Mapping

Target Pipeline

The target data products differ from the synoptic ones primarily in having their locations specified to coincide with regions of interest rather than to lie on a fixed grid. In addition, the temporal sampling may be adjusted to correspond more closely to evolutionary history of features or specific events, and the sizes, tracking rates, and perhaps even shapes of the regions may also be subject to adjustment on a case-by-case basis. All of these issues are to be determined.

Region Sampling

Target Locations

Tracking

Mapping


Valid HTML 4.01 Transitional HMI Ring Diagrams 17 May 2010, 10:50-0700