GrazeZone

Plotting the Graze Zone in Your Area

The graze zone brackets the predicted northern and southern limits of the edge of totality, as described in the “Where are the eclipse ‘graze zones’” at http://occultations.org/eclipse2017/. Any of the interactive Google Maps for the eclipse can be used to get a general idea of where the path limits are, to an accuracy of about a kilometer; they are not more accurate than that because all of them plot the limits for sea level (the path shifts about 500 ft. south, measured perpendicular to the path, for each 1000 ft. of elevation above sea level) and most of them do not take into account the lunar topography. Especially at the southern limit, with the deep valleys between the high Leibnitz Mountains near the lunar south pole, the lunar corrections can be quite large.

Unfortunately, there’s no easy way to generate the graze zone plots accurately from one Web site, although once the graze zone “offset” values are determined for a given area, this interactive map by Derek Breit  can be used to generate detailed plots across a region, as I’ve done for St. Louis here . As described in that .pdf document, the offsets used for most of the St. Louis-area maps given on the last page are  -56.347 and -57.347, but slightly different values should be used for accurate positioning for the lower Mississippi and Missouri River flood plains. Those offset values are distances in kilometers from the predicted central line, of the (Earth and lunar terrain-corrected) edges of the kilometer-wide graze zone. The procedure for determining the offset values is given below, for the southern limit in the Kansas City area.

Xavier Jubier Interactive Map. We start with Jubier’s excellent Google Map web site . If you left- click on any location on the map, it will give you a box of detailed information about the eclipse for that site, including the latitude and longitude of the location in the upper left corner, and the times and circumstances of the eclipse contacts. But most important, if you click on the small mountain symbol in the right of the two small boxes, 2nd from the last in the column of boxes on the left side (it is just above and left of the initial “O” in “OKLAHOMA’), the mountain turns dark blue and the box is shaded light blue, as shown on Map 1 below. That enables calculation of the contact times taking into account the extensive LRO terrain data of the Moon, and also using for those calculations, the height of the selected location above sea level.

Map 1. The small terrain box on the left side, near the “O” in OKLAHOMA, is enabled.

An example of the contact times box is shown on Map 2 below; note that the elevation above sea level of the site is given below the longitude now. That shows that terrain (both lunar and terrestrial) have been taken into account, and the “lunar limb corrected” duration of totality is given in the upper right part of the box. I selected a series of points along north-south S Crysler Ave., left-clicking at different locations (the process is faster if you select the “Map” option in the upper right, rather than the default “Satellite” that takes time to show the aerial imagery) until I found a location with a limb-corrected non-zero duration of totality that was less than 1.5s. With a value of 1.2s, this is certainly good enough, locating the “true” predicted southern limit to within about 20 meters. You need to note the location relative to features shown on the map; even cars can be used, since the same images are used on all interactive Google maps, but in this case, I just noted that the point was a short distance south of S Crysler Ave.’s intersection with East 43rd St S. Note that the red line shown on the map marking the southern limit, between the shaded and unshaded areas, is NOT corrected, so it should be ignored.

Map 2. The terrain-corrected southern limit is found, with a corrected totality of only 1.2s.

If we move only 15 meters farther south, the data changes, as shown on Map 3. The corrected duration of totality is zero; there is no true totality, with some small beads remaining visible for about 19 seconds, during what Jubier calls “beaded totality”. The phenomena become quite complex and the limb correction time calculation fails; Jubier gives values of +41.6s or -41.6s in the last (LC) column when this happens. This situation persists for a few hundred meters farther south, before the 2nd and 3rd contact lines are dropped and Jubier than considers the eclipse only partial.

Map 3. Only about 15m farther south and no true totality, only “beaded totality”, is found.

Now that Jubier’s corrected s. limit point has been found, it is necessary to find the same point on Derek Breit’s interactive map (link given above). That is done on Map 4 below. The value of Breit’s map is that two dark gray lines, parallel to the central line, can be plotted at different distances, with the final goal of defining the “graze zone”, as done with the maps of the St. Louis area. The gray lines (called A and B) are drawn by specifying values in the two boxes just above the map, then clicking on the gray buttons that say “click here”. Successive values are used until one (or in this case, both) of the gray lines pass through the point (on S Crysler Ave. just s. of East 43rd St S) found above with Jubier’s map; note that the value is 56.352. The value is positive for locations south of center. This convention may seem odd, but it’s IOTA’s “right-hand” rule, also used for asteroidal occultation paths that can go in any direction; the rule is, if you stand at the center and face in the direction that the shadow is moving (towards the east, in this case), then the positive values are on your right. The offset values for the northern graze zone for St. Louis are negative. Another feature of Breit’s map is that, if you left-click on a point, its elevation above sea level will be displayed. You can move about the map, finding the elevation at different points, perhaps selecting hills or rivers, to see how different the elevations are for other areas. As long as it’s within 50 meters (160 feet) of the point found on Jubier’s map, then the gray lines remain valid.

Map 4. Jubier’s s. limit point from Map 2 is found on Breit’s map with offset of 56.652.

Next, the graze zone is specified on Map 5. Since the southern edge of the graze zone is 300m outside the limit, its offset is 56.352 + 0.300 = 56.652. Then the northern edge value is just 1.0 km less, or 55.652. I’ve clicked on the (corrected) s. limit point from Jubier’s map to show its elevation of 314 meters. That is one of the highest values in the graze zone across the Kansas City region, but all the other points in the part of the graze zone shown have an elevation greater than 280 meters, so the graze zone as plotted is accurate enough. By sheer coincidence, the southern edge of the graze zone is almost coincident with the blue uncorrected southern limit line, which should be ignored.

Map 5 shows the graze zone accurately over this area southeast of Kansas City.

Next, we want to plot the path over a wider area; this has been done on Map 6 simply by zooming out, and re-centering the map towards the west, to show the path across the whole downtown Kansas City area. The elevation point is still at Jubier’s corrected s. limit point. Since the elevations are greater than 270 meters over most of the area, the graze zone plot is alright. There are some low areas, as in the Missouri River flood plain, and near the Kansas and Blue Rivers, where the elevation is around 240m, but at the low scale of Map 6, this won’t matter. But if medium-scale maps showing the path across Kansas City are generated, like those for St. Louis, then separate maps with different offsets should be used for the low areas. If we use 240m for the elevation, which is fine for all of the low areas, the difference from the 315m elevation for the used offsets is 75m. Since the offset differences are half the elevation difference, that would be 0.038 km. For the lower elevations, the path is farther north, so subtract 0.038 from the offsets, to find offsets for the low areas of 56.614 and 55.614.

Map 6 showing the southern-limit graze zone across Kansas City.

David Dunham, dunham@starpower.net