However, the earth’s magnetic field intensity is another environmental property that can be used to estimate latitude, which for the most part has been largely overlooked in aquatic biotelemetry. Klimley and Mangan [4] first proposed that an electronic tag could infer the latitude at which a fish was swimming based upon the measurement of the intensity of the earth’s magnetic field. They argued these estimates could be more accurate at certain times of the years (i.e., the equinoxes) and areas on the earth (i.e., near the equator). Furthermore, even during the solstices and in temperate and polar latitudes when and where day length changes along a north south gradient, there are both environmental and biological factors that can reduce the accuracy of latitude estimates based on irradiance.
To appreciate the potential of this environmental feature in geolocation positioning, one must have an understanding of the earth’s geomagnetic field. The earth has a dipole magnetic field, which varies from 0.26 gauss (26,000 nT) at the equator to 0.66 gauss (66,000 nT) at the magnetic poles (Fig. 1). These are separated geographically from the north and south geographic poles, around which the earth rotates. This field is produced by the dynamo movement of molten iron in the outer core 2900 km from the earth’s surface [5]. The distant subterranean origin of the main field accounts for its smooth and predictable structure near the surface and supports accurate latitude estimation. In addition, tiny particles of magnetite, a bipolar ferrous compound, embedded within the basaltic crust of the earth, usually a few km from the surface, generate a magnetic field. This added component distorts the main field with proximity to the magnetized body, but only exceptional anomalies distort the earth’s main field by >1% of the field strength at the equator.
The earth’s total field intensity is the sum of three orthogonal vectors, often described with a vertical, north–south, and east–west component. The intensity of the total field is measured throughout the year at magnetic observatories located over the entire surface of the earth. A series of spherical harmonics are used to determine Gauss coefficients to fit the thousands of magnetic measurements by the worldwide magnetic survey to a spherical dipole. The best fit is an inclined dipole with its axis passing through the center of the earth between north and south geomagnetic poles. This technique has been used to produce the International Geographical Reference Field (IGRF) [7] and the World Magnetic Model (WMM) [6] that map the earth’s total field intensity in three dimensions. While IGRF and WMM model the main field only, the Enhanced Magnetic Model (EMM) [7, 8] also incorporates crustal magnetic anomalies with a minimal geographical extent of 56 km [9]. The modeled magnetic field can be visualized as a globe covered by isoclines, lines indicating similar magnetic strengths, looping around the earth. This feature, whose intensity varies largely along a north–south axis, is a prime candidate for estimating latitude. In this commentary, we describe how geomagnetic intensity can be used to estimate latitude, discuss its strengths and weaknesses for use in aquatic biotelemetry, and argue for its use along with irradiance measurements, sea surface temperature (SST) and other available gradients such as magnetic field inclination for estimating the latitude of a fish carrying an archival tag.
In order to estimate latitude based on magnetic field intensity, it is necessary to first estimate the longitude of the tag. This is determined using irradiance measurements. This technique has already been described in detail within the scientific literature [1]. However, latitude can now also be determined based on the measurement of the average magnetic field intensity. Magnetic field intensity can be measured using a 3-axis magnetometer aboard an archival tag. The intensities recorded on the three axes must be summed to provide an overall measurement of total field intensity. The component measurements can be made when the tag holder is at any depth because the strength of the main magnetic field varies only slightly as a function of depth. The difference in the intensity of field between that present at surface and at a depth of 2000 m, the typical maximum operating depth of most tags, is only roughly 0.1% of the magnitude of the earth’s main field at the surface. This discrepancy is dwarfed by other sources of error such as the uncertainty of WMM measurements, which is roughly 0.3% of the strength of main field [8]. The measurement of the intensity of the earth’s main field must then be paired with an estimate of longitude, derived from the daily series of irradiance measurements. These values are stored in memory aboard the tag and are available for removal upon recovery of the tag. If a fish carrying the tag swims at the surface, and the tag’s antenna is out of water, the measurements can be transmitted via a radio frequency from a platform transmitting terminal (PTT) to the ARGOS satellite, given that it passes overhead when the fish (and tag) is at the sea surface. Archival tags that release from the fish and float to the surface can also transmit their stored information to the satellite. Given the longitude of the tagged animal, the latitude can be determined based upon the measurement of total field intensity. Software is available from the United State Geological Survey that will provide a user with total field intensity, given a longitude and latitude of any point on earth. An algorithm can be used to find the estimated latitude through an iterative examination, searching for the matching intensity along a series of modeled intensities along the estimated line of longitude until a match is found between measured and the modeled field intensity. The process is illustrated on a map of the earth’s main field (Fig. 3). A meridian is drawn on the WMM map at the estimated longitude to isoclines with the measured geomagnetic intensity.
We demonstrate how the method works with an archival tag equipped with a magnetometer, irradiance, and temperature sensors on a tag drifting at the surface. It is our intention to provide error estimates independent of behavior, which varies with species, and thus our estimates would be of greater general value to the general tagging community working on a diversity of aquatic species. The drifting tag can be used to compare the positioning methods under a boundary condition of maximum accuracy. A tag on an animal would experience constantly changing depths and variable water conditions, and this would result in error estimates for the different methods unique to a particular species. An animal swimming at depth would experience greater magnetic anomalies in certain regions such as the Galapagos Islands or the Gulf of California, and this would add to (positive anomaly) or subtract from (negative anomaly) the total field, shifting the geoposition estimate to either a higher or lower latitude. The accuracy of the irradiance-based estimates of apparent noon or day length will be reduced due to an animal’s behavior such as diving and the changing environmental conditions encountered that do not affect a drifter. For example, the deeper an animal goes and the greater the attenuation of irradiance, the later the threshold defining dawn will occur in the morning, and the earlier threshold defining dusk will happen in the evening.
The method by which geolocation is determined may vary between manufacturers. Hence, the method by which this Desert Star’s SeaTag estimates longitude and latitude will be explained below. The explanation is general without some details because the information is proprietary. The tag’s wrap-around solar power panel serves as the irradiance sensor. This 360° design provides near-equal response to illumination independent of tag orientation on the fish, thus improving the reliability of local apparent noon and apparent day length measurements. The magnetometer undergoes extensive factory calibrations to maximize the accuracy and reliability of magnetic field intensity measurements in order to accurately compare these measurements to values predicted by geomagnetic models. The irradiance measurements are based on timing the dawn and dusk illumination threshold crossing of an intensity of 1.4 Lux; a value above maximum expected surface moonlight but well below the nominal sunrise and sunset illumination of 400 Lux at the surface. This assures that for an animal located anywhere in the euphotic zone (light absorption ≤99%), dawn timing occurs before sunrise and dusk timing after sunset. Twilight is the period of the steepest irradiance gradient where measurements are least affected by disturbances such as varying turbidity, weather or animal diving behavior. The tag archives the determined local apparent noon, apparent day length, and a 24-h average magnetic field intensity that are used to estimate geolocation in a single daily observation summary packet. This is transmitted in a single ARGOS packet which maximizes the number of daily positions that will be available even if post pop-up transmissions should be interrupted.
Current measurements transmitted after pop-up by the tag in periodically transmitted engineering packets are compared to model predictions for the ARGSO-identified tag location and used to establish sensor biases for compensation. Sensor stability is verified by comparing sensor bias for the start and end of positions of the track. Conversion to geographical coordinates is accomplished by matching tag measurements to geomagnetic models and astronomical equations. If processed through CLS Track&Loc, these are improved based on information from sea surface temperature, bathymetry and coastal maps. The irradiance-based local apparent noon is converted to longitude, while latitude is identified by matching the observed and bias-compensated magnetic field intensity to the intensity at a point on the established line of longitude using the WMM geomagnetic model. The accuracy of the irradiance measurements for a given day, and thus the longitude component, is evaluated by comparing the apparent length of day, after bias compensation, to the length of day predicted for the magnetometer-identified latitude. If the observed day is much shorter than the predicted day, then the measurement of apparent noon may be unreliable due to turbidity, diving behavior, weather, or shading. Conversely, a matching or somewhat long apparent day indicates reliable longitude because the steep light gradient at dawn and dusk provides an upper bound to the observable day length and will only be observed if shading events have not unduly influenced the dawn or dusk irradiance measurements [10].
The tag was shed from a tiger shark (Galeocerdo cuvier) off the coast of Florida after traveling to the vicinity of Nova Scotia and back [11]. The buoyant tag drifted northwestward across the northern Atlantic Ocean from its release site from the shark on December 26, 2012, north of Grand Bahama Island off the southeastern coast of Florida for a period of 10 months until October 25, 2013, when the PTT was last detected off the coast Newfoundland, Canada. The PTT transmitted periodically to ARGOS over this period providing reference positions with a median error of 6.1 km. At this time, the solar cells charging the tag became covered with fouling organisms, and the tag did not generate enough power to transmit through the PTT to the ARGOS satellite. Shown in Fig. 2 are three tracks, which were computed using different positioning methods of the tag after it popped off the shark and was drifting for 10 months at the surface. The first track is composed of geolocations using magnetic measurements to estimate latitude (see red circles), the second track consists of geolocations using irradiance measurements for estimating latitude (yellow hexagons), and the third track is comprised of Doppler-derived ARGOS positions (white triangles and lines). Note that there was sufficient power received by its solar panel and stored in the tag for its logic circuit to continue to record and log irradiance and geomagnetic measurements in its memory until December 14, 2014, when the tag was recovered on a beach in South Wales, UK.
The geomagnetic geolocations for the drifting tag were determined with the use of a map of geomagnetic isoclines (Fig. 3). For example, analysis of the irradiance measurements indicated that the tag drifted across a longitude of 65°W during June 15, 2013 (see yellow rectangle in Fig. 2). The measurement of magnetic intensity by the tag for this day was 48,790 nT. A north–south trending line from the poles 65°N and 65°S through the 65°W meridian would intersect the isocline for 48,790 nT off the northeastern coast of North America at a latitude of 37.6°N. For geomagnetic estimates of latitude, there are generally two locations (solutions) for each north–south line. In most cases, they are widely separated, and one can be eliminated because it is considerably farther from the release location or not consistent with previous daily observations. In this case, the drifter was more likely to be at 37.6°N than 85°S, which is on the Antarctic Peninsula (see dashed red lines in Fig. 3). This estimate could further be validated, if the tag was also to provide an estimate of latitude based on day length and sea surface temperature.