Replace localization uncertainty properties with one error radius

Replace the localization properties `uncertainty_shape`,
`ra_uncertainty`, `dec_uncertainty`, and `position_angle` with a
single property called `ra_dec_error`.

The original localization uncertainty properties were ill-conceived
in many ways:

1. The names `ra_uncertainty` and `dec_uncertainty` were
   misleading. For example, for ellipses, these fields actually
   represented the lengths of the semi-major and semi-minor axes,
   and not the uncertainty in ra or dec.

2. The names of these properties were inconsistent with other
   schema. Every other uncertainty property exept for these has a
   name ending in `_error`, not `_uncertainty`.

3. The `rectangle` shape was not useful. The most significant
   examples of quadrilateral localization regions are IPN error
   boxes. However, these are parallelograms, not rectangles, so
   the shape would have been under-specified.

We have observed that all current missions in GCN either report
error circles or HEALPix maps. Given that observation, this patch
replaces all of the ill-conceived localization properties with
a single `ra_dec_error` field which is the radius in degrees of
the error circle.

In the future, there might be a mission that requires ellipses.
We won't deal with that now, but in that event we would have a
few different backwards-compatible options. For example, we could:

- Treat the `ra_dec_error` field as the semi-major axis, and add
  optional fields `ra_dec_error_b` and `ra_dec_error_pa` for the
  semi-minor axis and the position angle, respectively; or

- Allow `ra_dec_error` to be either a single scalar, or an array
  of up to three numbers, representing the semi-major axis,
  semi-minor axis, and position angle, respectively.

Fixes #120.

gcn/notices/burstcube/Alert.example.json

@@ -9,9 +9,7 @@
   "id": ["240601000"],
   "ra": 232.0,
   "dec": -53.1,
-  "uncertainty_shape": "circle",
-  "ra_uncertainty": [10],
-  "dec_uncertainty": [10],
+  "ra_dec_error": 10,
   "containment_probability": 0.9,
   "systematic_included": false,
   "healpix_url": "https://heasarc.gsfc.nasa.gov/burstcube/trigger/240601000/current/240601000_locmap.fits",

gcn/notices/burstcube/Test.example.json

@@ -9,9 +9,7 @@
   "id": ["240601000"],
   "ra": 232.0,
   "dec": -53.1,
-  "uncertainty_shape": "circle",
-  "ra_uncertainty": [10],
-  "dec_uncertainty": [10],
+  "ra_dec_error": 10,
   "containment_probability": 0.9,
   "systematic_included": false,
   "healpix_url": "https://heasarc.gsfc.nasa.gov/burstcube/trigger/240601000/current/240601000_locmap.fits",

gcn/notices/core/Localization.example.json

@@ -2,10 +2,7 @@
   "$schema": "https://gcn.nasa.gov/schema/main/gcn/notices/core/Localization.schema.json",
   "ra": 120,
   "dec": 45,
-  "uncertainty_shape": "ellipse",
-  "ra_uncertainty": [-0.1, 0.05],
-  "dec_uncertainity": [-0.2, 0.5],
-  "position_angle": 0,
+  "ra_dec_error": 0.5,
   "containment_probability": 0.95,
   "systematic_included": true,
   "instrument_phi": 90,

gcn/notices/core/Localization.schema.json

@@ -13,25 +13,9 @@
       "type": "number",
       "description": "ICRS declination [deg], utilizes the J2000 epoch and an equatorial coordinate system"
     },
-    "uncertainty_shape": {
-      "enum": ["circle", "ellipse", "rectangle"],
-      "description": "In what manner are the errors in RA and Dec defined - as circular, elliptical, or rectangular shapes",
-      "default": "circle"
-    },
-    "ra_uncertainty": {
-      "type": "array",
-      "maxItems": 2,
-      "description": "Uncertainty in RA [deg] with optional asymmetric errors, measured from the RA in the schema; respective ex: [r], [r1], [l1-, l1+]. For ellipse, ra axis is r1 or semi-major axis."
-    },
-    "dec_uncertainty": {
-      "type": "array",
-      "maxItems": 2,
-      "description": "Uncertainty in Dec [deg] with optional asymmetric errors, measured from the Dec in the schema; respective ex: [r2], [l2-, l2+]. Not reported if circular and Dec axis is r2 or semi-minor axis for ellipse."
-    },
-    "position_angle": {
+    "ra_dec_error": {
       "type": "number",
-      "description": "Anti-clockwise position angle from RA axis [deg]. Used if uncertainty_shape ellipse or rectangle is tilted w.r.t. standard (RA, Dec) coordinate.",
-      "default": 0
+      "description": "Radius [deg] of error circle with the given probability of containing the true, but unknown, position of the source (see containment_probability)"
     },
     "containment_probability": {
       "type": "number",

gcn/notices/icecube/lvk_nu_track_search.example.json

@@ -17,8 +17,7 @@
       "localization": {
         "ra": 17.48,
         "dec": 16.15,
-        "uncertainty_shape": "circle",
-        "ra_uncertainty": [0.43],
+        "ra_dec_error": 0.43,
         "containment_probability": 0.9,
         "systematic_included": false
       },
@@ -30,8 +29,7 @@
       "localization": {
         "ra": 13.82,
         "dec": 18.66,
-        "uncertainty_shape": "circle",
-        "ra_uncertainty": [0.88],
+        "ra_dec_error": 0.88,
         "containment_probability": 0.9,
         "systematic_included": false
       },

gcn/notices/icecube/test/gold_bronze.update.example.json

@@ -7,10 +7,8 @@
   "alert_type": "update",
   "ra": 345.82,
   "dec": 9.01,
-  "uncertainty_shape": "rectangle",
   "position_angle": 0,
-  "ra_uncertainty": [-1.5, 1.4],
-  "dec_uncertainty": [-1.2, 1.3],
+  "ra_dec_error": 1.3,
   "containment_probability": 0.9,
   "systematic_included": false,
   "healpix_url": "https://roc.icecube.wisc.edu/public/",

gcn/notices/icecube/test/gold_bronze_track_alerts.example.json

@@ -6,8 +6,7 @@
   "alert_type": "initial",
   "ra": 345.82,
   "dec": 9.01,
-  "uncertainty_shape": "circle",
-  "ra_uncertainty": [0.51],
+  "ra_dec_error": 0.51,
   "containment_probability": 0.9,
   "systematic_included": false,
   "trigger_time": "2023-04-16T05:22:26.150574Z",

gcn/notices/swift/bat/guano.loc_arc_min.example.json

@@ -10,7 +10,7 @@
   "trigger_time": "2022-12-31T21:46:05.13Z",
   "ra": 336.26,
   "dec": 25.139,
-  "ra_uncertainty": [0.05],
+  "ra_dec_error": 0.05,
   "containment_probability": 0.9,
   "systematic_included": true,
   "rate_snr": 15.8,