Compression Techniques in Standard Rate X-Tag Firmware 4.4:
An Explanation of Delta Limited Values

When the X-Tag is in data collection mode, high-resolution pressure, temperature, and light levels are measured every two minutes. The X-Tag stores all the high-resolution two-minute measurements in memory. Consequently, if an X-Tag is recovered, the entire two-minute dataset may be extracted providing the user with a wealth of high-resolution data from the full duration of deployment.

Unfortunately, this complete dataset cannot be transmitted because Argos limits the size of transmitted data packets, and the tag has a limited battery life for data transmission. Given these constraints, a subset of data is carefully selected for transmission. The transmitted data subset must go through a series of compressions in order to preserve the data's valuable time-series format. These compression techniques lead to the possibility of "delta limited" depth and temperature values. Delta limited values are only found in the transmitted data subset, and therefore, if an X-Tag is recovered, the extracted archived data will not contain any delta limited values. In spring 2011, the new X-Tag firmware 4.4 was introduced to improve the accuracy of transmitted datasets by decreasing the quantity of delta limited depth values in data reports. The methods for determining delta limited values in firmware version 4.4 will be described.

Understanding Depth Data

Time-series data compression focuses on how depth measurements change between consecutive hours. For example, suppose at 2:00 the tag measures a depth of 50 m, and one hour later at 3:00, the tag measures a depth of 75 m. The "delta value" or change in depth for this hour is 25 m. 

Periodically through the day, full-resolution depths are designated as a reference for delta depth values. The temporal resolution of depth data depends on the deployment duration. For the first four months of deployment, the tag's transmitted dataset contains 15-minute records. Between four and eight months of deployment, the transmitted dataset contains records on 30-minute intervals, overwriting the 15-minute data. Lastly, for tags deployed over eight months, the transmitted dataset contains records on hourly intervals, overwriting the 30-minute data. Independent of the temporal resolution, delta values are always calculated between measurements separated by 60 minutes. As an example, consider the following 15-minute transmitted depth data. In this example for a three-month deployment duration, suppose that the depth measurements during the hour of 2:00 (2:00, 2:15, 2:30, and 2:45) are designated as full-resolution measurements.

Time   Depth
 3:00   change in depth with respect to 2:00
 3:15   change in depth with respect to 2:15
 3:30   change in depth with respect to 2:30
 3:45   change in depth with respect to 2:45

Notice that the delta values are not necessarily calculated with respect to the previous depth, but rather they are calculated with respect to the measurement taken 60 minutes earlier. 

There is a limit to the change in depth that can be accurately represented. The following figure illustrates the allowed delta value range. 

If a fish dives more than 166.8 m or ascends more than 172.1 m in a one-hour period, the depth cannot be accurately represented and is identified as "delta limited". The following examples explain delta limited dives and ascents. 

Delta Limited Dive

Example 1

Suppose at 2:00 an X-Tag measures a depth of 250 m, and one hour later at 3:00, the tag measures a depth of 480 m. This is a dive of 230 m, but only a maximum dive of 166.8 m can be represented in the transmitted dataset. Since the change in depth within one hour is outside the allowed range, the dive is limited to 416.8 m. In the final data report, the depth for 3:00 would be identified as 416.8 m, and it would be marked as a delta limited dive.

Example 2

It may take time for delta limited depths to catch up to the actual depth. The following illustration shows a sequence of depths over four consecutive hours. Black indicates the actual depths, and red indicates the transmitted delta limited depths. For this example of a nine-month deployment duration suppose a full-resolution depth record is designated as a reference at 6:00. Starting with the first time step, the change in depth from 6:00 to 7:00 is outside the allowed range, and therefore, the dive is limited to 416.8 m. Continuing on, the delta depth for 8:00 is calculated relative to the transmitted delta limited depth (416.8 m) at 7:00. Even though the fish only descends 110 m during this one-hour period, the change relative to the delta limited value at 7:00 is outside the allowed range. Consequently, the depth at 8:00 is delta limited to 583.6 m. Lastly, the delta depth for 9:00 is calculated relative to the transmitted delta limited depth (583.6 m) at 8:00. The delta depth relative to the delta limited depth at 8:00 is inside the allowed range, and thus, the depth at 9:00 (610 m) is accurately represented.

Delta Limited Ascent

Suppose at 2:00 an X-Tag measures a depth of 825 m, and one hour later at 3:00, the fish ascends to a depth of 500 m. This is an ascent of 325 m, but only a maximum ascent of 172.1 m can be represented in the transmitted dataset. Since the change in depth in one hour is outside the allowed range, the ascent is limited to 652.9 m. In the final data report, the depth for 3:00 would be identified as 652.9 m, and it would be marked as a delta limited ascent.

 

To summarize, if a depth is identified as a delta limited dive in the final report, then the actual depth of the fish was greater than or equal to the delta limited dive depth.

Actual Depth >= Delta Limited Dive Depth

Similarly, if a depth is identified as a delta limited ascent in the final report, then the actual depth was less than or equal to the delta limited ascent depth.

Actual Depth <= Delta Limited Ascent Depth

Understanding Temperature Data

Time-series data compression focuses on how temperature measurements change between consecutive hours. Similar to depth data, there is a limit to the change in temperature that can be accurately represented. If the temperature changes by more than the allowed amount, the temperature cannot be accurately represented and is identified as "delta limited".

Periodically through the day, full-resolution temperatures are designated as a reference for delta values. Like depth data, the temporal resolution of temperature data depends on the deployment duration. Independent of the temporal resolution, delta values are always calculated between measurements separated by 60 minutes.

If a temperature is identified as a delta limited increase in the final report, then the actual temperature was greater than or equal to the delta limited increase temperature.

Actual Temperature >= Delta Limited Increase Temperature

Similarly, if the temperature measurement is identified as a delta limited decrease in the final report, then the actual temperature was less than or equal to the delta limited decrease temperature.

Actual Temperature <= Delta Limited Decrease Temperature

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