Geo-Position Estimation using Magnetic Anomalies:
Tracking Salmon within the Smallest of the Great Lakes
April 11, 2015 by Marco Flagg
Tracking the migration pattern of pelagic fish with the light and magnetic field intensity observation method of SeaTag is quite easy, automated and accurate on oceanic and even regional migration scales. For these applications magnetic anomalies, the bumpiness of the magnetic field caused by magnetized rock in the earth's crust, can for the most part be smoothed out by averaging data over a few days. Relying on the north-south intensity gradient of the earth's main field as modeled by the International Geomagnetic Reference Field (IGRF) or the World Magnetic Model (WMM), a latitude accuracy of around 30 nautical miles or even better can be obtained in many cases.
However, tracking within the bounds of a much smaller body of water, Lake Ontario in this case, requires a different method. Here, the gradient of the earth's main field is small as compared to the amplitude of the magnetic anomalies. In this and similar cases, the geo-estimation method must be adjusted and use the location information contained in the anomalies, rather than smooth them out. In addition, all other sensor data collected by the tag should be analyzed for clues to the animal's location.
This paper explains a method use to estimate the position track of a salmon tagged by U.S. FWS with SeaTag-MOD S/N 859 in the Niagara River. It should be pointed out here that marine animal tracking based on magnetic anomalies is clearly in its infancy. A Google search such as for 'magnetic anomaly geo-position estimation of fish' does not yield much. Thus, the method described here is just a basic first step. The standard of position estimation sought is merely one of a plausible position track or migratory range. Consequently, the reader is encouraged to experiment and drive this fascinating field forward.
Accuracy Available with SeaTrack Processing
Figure 1 shows the deployment and pop-up positions (two push pins) of tag #859 along with the positions as resolved by SeaTrack (green circles). SeaTrack plots the track based solely on noon time detection through light observations for longitude and observed magnetic field intensity for latitude. The magnetometer readings are compared by SeaTrack to the earth's main magnetic field as modeled by the International Geomagnetic Reference Field (IGRF). The purple arcs in figure 1 are the field strength lines of the International Geomagnetic Reference Field (IGRF) in 1000 nT increments.
Figure 1: Position Estimates (green circles) for tag SN 859 as auto-generated by the SeaTrack software using magnetic (latitude) and light (longitude) observations. SeaTrack compares and plots magnetic observations as they correspond to IGRF field strength predictions. Actual deployment and pop-up locations designated by yellow push-pins. SeaTrack filter settings were 7-day averaging and 'Longitude Confidence' filter cut-off at 0 minutes, i.e. when observed day length between the morning and evening light threshold crossings is shorter than predicted sunrise to sunset duration.
The accuracy available with the method is visible on the map. The overall position error (latitude and longitude combined) was a median of 51 nautical miles under the assumption that the fish in fact stayed between the deployment and pop-up positions. However, there were also three significantly displaced positions, called out on this map. Recalling again that the purple arcs reflect 1000nT increments of magnetic field strength, the latitude error amounts to about 500 nT. This can be accounted for by magnetic anomalies in the area. Anomalies degrade latitude estimation when using the IGRF as a reference, but in this case we will actually use it to tighten the migratory path estimation of the fish.
Overall, the position fixes using SeaTrack showed the fish remaining within Lake Ontario rather than migrating to other lakes, and this is confirmed by the pop-up position. However, the method clearly isn't accurate enough to resolve positions within the confines of Lake Ontario itself.
Using Magnetic Maps to Tighten Position Estimation Accuracy
An opportunity exists to tighten the position estimates by making use of magnetic anomaly maps. Figure 2 shows the Great Lakes region with an overlay of the World Digital Magnetic Anomaly Map (WDMAM). In this color coded and shaded map, magnetic anomalies are visualized as mountain ranges. Purple are positive anomalies with >= 100nT, while dark blue indicates negative anomalies of ⇐ -100nT. However, WDMAM data is at a reference altitude of 5km, where the anomalies are much smaller than at ground level due to their origin in magnetized rock that may be close to the surface. In rough numbers, ground level or sea level anomalies of several hundred nT are common, and in some areas they can reach into the thousands of nT at the sea floor.
Still, the map provides an overview and indicates that a fish migrating the length of Lake Michigan for example would encounter alternating regions of negative and positive anomalies between Chicago and Green Bay.
Figure 2: Great Lakes region with WDMAM overlay. Magnetic anomalies produce position errors when using IGRF as the reference, but can potentially be used to resolve migration on a much smaller scale.
Calibration Accuracy of SeaTag-MOD
In lakes and in general to track migrations on scales of tens to hundreds of miles, the optional high-precision calibration option for SeaTag-MOD is recommended. The standard calibration of SeaTag-MOD establishes sensor gain and offset for each of the three axes, and compensates for the tags own magnetic field. The high-precision also establishes the angle of non-orthogonality between the three sensors and the temperature coefficient. The process includes a verification phase with an acceptance cut-off of 200nT for the average of the individual readings. Table 1 and figure 3 show the calibration results for tag SN859.
Due to dynamic effects, individual readings may exhibit errors of several hundred nT. Thus averaged readings with averaging periods of one hour or more (15 samples or more) are recommended for any position estimation purposes. While the residual error for 15-sample averages here is just 23nT, an allowance should be made for measurement errors not captured in our short term verification including drift, slight re-magnetization of the tag itself, inaccuracy of the gain and temperature coefficients etc. There is no hard number available for such errors at this time, but a conservative assumption might be an error of averaged readings of +/- 200 nT.
||INDIVUDAL READINGS||1h AVERAGE (15 SAMPLES)|
|Residual Error of Absolutes (nT)||105.78||22.63|
|Standard Deviation (nT)||141.10||27.76|
Table 1: Residual error and standard deviation of tag SN859 after high-precision calibration. The '1h average' is based on 15 consecutive samples, with the assumption of a 4-minute sample rate, the standard for the SeaTag-MOD magnetic data collection for position estimation purposes.
Figure 3: Individual magnetometer readings of SeaTag-MOD can show spikes up to several hundred nT even after precision calibration due to dynamic effects (the three sensors are read sequentially, but the tag may rotate some in that sample interval). Thus, individual readings should not be used in position estimates. Averaging over 15 samples, equivalent to one hour of standard data acquisition while on-fish, significantly reduces the error.
Step 1: Find adequate magnetic anomaly survey data
The WDMAM is useful for an overview but does not provide sufficient resolution for most underwater tracking purposes. So, the first step is to locate higher resolution magnetic anomaly data. Magnetic fields from anomalies drop of rapidly with the distance from the anomaly (1/r^3), and so the best data will be from marine surveys (i.e. at sea level) or from low altitude flights. For tag #859, a Google search located a magnetic anomaly map from the Canadian government covering western Lake Ontario and Lake Erie . The same series also covers much of the other Great Lakes.
Figure 4: Magnetic anomaly map of western Lake Ontario. Tag (D)eployment, (P)op-Up position and probable area of migration are marked. Original data is from aeromagnetic surveys at 300m altitude. This low altitude provides a good spatial resolution. Notice the negative anomaly reaching around -400nT at Niagara, and the large positive anomaly reaching about +500nT near Toronto. At lake level, these anomalies will be stronger.
This project included a basic marine magnetometer survey that verifies the magnetometer map and provides an example of the anomalies that may be encountered by the tag. For this project, we mounted the sensor of a Geometrics G856 proton magnetometer on a pole extending about 2m from the bow of a (low-magnetic) aluminum hull boat. Figure 5 shows the equipment, the track and the resulting magnetometer plot. Compare to figure 4, and notice the quick strengthening of the magnetic field after the boat leaves the jetty and heads east. It is approaching the strong positive anomaly east of Point Breeze, and the magnetic field strength increases by 200nT. Further, the overall field is at about +200nT, corresponding to the anomaly map.
Figure 5: Marine magnetic anomaly survey at Point Breeze
A second magnetometer survey run was done on the Niagara River, from about 1km south of the American power station, to the mouth of the river. Figure 6 shows the survey plot for a south-north run. There are strong anomalies near the power station in the south and near the mouth of the river. These are man-made objects such as bridges and underwater cables (not further analyzed). Generally, the field is at about -500nT to -250nT relative to IGRF, and again reflecting the anomaly map in figure 4.
Figure 6: Marine magnetic anomaly survey of the Niagara River from about 1km south of the U.S power station to the mouth of the river
Step 2: Compare (Sanity Check) Tag Readings at Deployment and Pop-Up Locations to Anomaly Map
Assuring that the magnetometer readings are reasonable in the context of IGRF and the anomaly information should be done next. Use NOAA's on-line geo-magnetic calculator  to compute the predicted total magnetic field intensity for the deployment and pop-up locations and dates. Then, compare to the closest available 'magnetic field magnitude daily avg (nT)' from the daily summary (SDPT_MODDAILY) packets. For the deployment location, it's important here to use the data from the tags first full day at liberty so that the data is no influenced by magnetic readings taken while the tag was still on a boat, in a vehicle or in a building. Anomalies are offsets of a local reading vs. the predicted IGRF value for the location. So, compare the offsets you get to the anomaly map to make sure they make sense. Be aware here that measurements at ground level anomalies will have a higher amplitude than in an aeromagnetic survey due to closer proximity to the body of magnetized rock. As there are many unknown variables (rock magnetization intensity, depth of the magnetic body underground, size of the body) these comparisons will generally be imprecise and perhaps incorporate some experience values.
For tag #859, the observed magnetic field at the deployment location was -128nT relative to IGRF, while for the pop-up date it was +465nT relative to IGRF. Given that the anomaly map shows greater negative and positive anomalies in the vicinity of these two locations respectively, these appear to be reasonable observations.
Step 3: Plot the Observed Magnetic Profile
Figure 7 was computed from tag #859 magnetic observations in the daily summary packets (SDPT_MODDAILY) and the sensor snapshot packets (SDPT_MODSN2). The IGRF predicted value for the center point between the deployment and pop-up locations was subtracted from the magnetic field daily averages reported in the SDPT_MODDAILY packets (red curve). The original data for the blue curve are the X, Y and Z components of the magnetic field as reported in the SDPT_MODSN2 packets. These packets do not state the total field value which was computed as √(X^2+Y^2+Z^2). Next, a 1-hour running average was formed, and the IGRF predicted magnetic field intensity was subtracted.
The graph is divided into two halves. From the start until 7/14, the field averages +76nT. There are oscillation to +500nT, but the measurements then return to the lower baseline. Starting on 7/15 and continuing to the end, the baseline shifts up and the field averages +477nT. Referring to the anomaly map, the deployment location is in an area of lower field strength and so the tagged fish may have stayed close to the deployment location or possibly moved east along the southern shore of Lake Ontario in the area of similar field strength. The higher field strength in the second half is consistent with the fish approaching the large positive anomaly.
Clearly visible in this graph is a rising trend, starting with slight negative anomaly values and ending with +500nT anomaly readings. There are however strong fluctuation such as between 7/6 and 7/9 where the anomaly readings drop from +500nT to 0nT and then rise again.
Figure 7: Tag magnetic field strength measurements show multiple anomalies
Step 4: Compare Results to the Anomaly Map
The graph is divided into two halves. From the start until 7/14, the field averages +76nT. There are oscillation to +500nT, but the measurements then return to the lower baseline. Starting on 7/15 and continuing to the end, the baseline shifts up and the field averages +477nT. Referring to the anomaly map, the deployment location is in an area of lower field strength and so the tagged fish may have stayed close to the deployment location or possibly moved east along the southern shore of Lake Ontario in the area of similar field strength. The higher field strength in the second half is consistent with the fish approaching the large positive anomaly to the northwest near Toronto.
A plausible area of migration is outlined in white. The fish probably did not venture fully into the strong northern anomaly, as a higher amplitude between the starting point and the center of that anomaly would be expected. To the south, the Niagara Falls block the fish's path in any case, but from a pure magnetic perspective, a transition into Lake Erie is not likely, as it should manifest into two solid 'bump' in the magnetic data if the fish transitioned first south and then north again to reach the pop-up location. A migration along the southern shore to the west is not likely because an extended negative anomaly should be encountered. And, while the fish could have first traced the southern shore to the east and then angled north-east, there are numerous strong anomalies and the graph would probably look more complex.
Step #5: A look at other data
All available data should be inspected for clues to the migratory pattern. The depth curve shows the fish stayed shallow until 7/6, followed by a deep period until 7/29 and a final return to shallow depth. The sonar panel voltage describes very low light levels at the deeper depths, suggesting the water was quite turbid. The Z-axis of acceleration (figure 10) corresponds to tag deflection. Values below 1 G indicate water is flowing over the tag, causing the deflection. Early, around 6/25 to 6/27, there is a strong deflection. This could indicate the fish is still in the river, experiencing strong water flow. After a period of migration, the tag deflection nearly stops on 7/29 and through pop-off. The fish must have been static here, resting or dead. During that same time, the three axes of the magnetic field change little. This means the tag was not rotating through the magnetic field, and supports the static condition identified by the accelerometer data.
Figure 8: Depth Measurements
Figure 9: Solar panel voltage indicates the light level the fish is exposed to. The solar panel reaches full voltage of about 4V with light levels greater than 400 Lux, or 0.4% of full sunlight.
Figure 10: Z-axis acceleration data shows the vertical orientation of the tag. 1 G is antenna straight up, 0G is tag flat, and -1G is antenna straight down. This data can be used to determine if the fish is resting or moving; is in a river or a lake. If water is flowing over the fish, the tag will deflect and Z-axis of acceleration will be <1G. The early tag deflection to 0.25G, about 75 deg from vertical, may indicate the fish is in a river. The tag vertical orientation after 7/29/14 means the fish is resting or dead.
Figure 11: The temperature profile can also provide migratory information. Could the strong temperature rise be related to the fish transitioning from the Niagara River into Lake Ontario?
Figure 12: The three axes of the magnetic field. After 7/29/14, there is little change. This means the tag is near static relative to the magnetic field (not turning). Figure 10 confirms the data of figure 8, indicating the fish is not active.
Summary and Possibilities for Improvement
Magnetic anomalies explain variations of magnetic field readings observed by the tag. While anomalies cause position errors along the latitude axis for standard processing with SeaTrack, they can also be used to estimate a migratory path or area on a much smaller scale. However, as magnetometer surveys are most frequently done by airplane at a greater distance from the magnetized rock, the amplitude as well as the shape of anomalies may look substantially different to the tag. Thus, uncertainty exists and an estimated track or migratory area may only meet a standard of plausibility.
Combining the magnetic data with other observations of the tag is recommended. For example, deepest diving depth can be compared to bathymetry, the Z-axis of the acceleration measurements indicate tag deflection and can show if the fish was moving (or at least water was flowing over the fish) etc.
One significant opportunity for improvement would be to derive compass information from the tags magnetometer and accelerometer data. This could provide the fish's heading. However, the method requires a two-point attachment of the tag so that it is aligned with the longitudinal axis of the fish.
Another option is to program a set of tags to release on specific dates, so that the definitive pop-off positions are available throughout a season. When using SeaTag-MOD in a lake environment with high tag recovery rates, the tags reusability improves the economic viability of this approach.
: Geological Survey of Canada. Map NK-17-M. link
: NOAA Geomagnetic Calculator. link