Suunto Spartan Trainer Wrist HR uses GPS to measure altitude. Under optimal signal conditions, eliminating potential errors typical in calculating GPS position, the GPS altitude reading should give a pretty good indication of your elevation.
To get a more precise reading from GPS altitude, comparable to what you can get from barometric altitude, you need additional sources of data like a gyroscope or Doppler radar to adjust GPS altitude.
Because Suunto Spartan Trainer Wrist HR relies solely on GPS to measure altitude, if the GPS is not set for maximum accuracy, any filtering is subject to error and may result in potentially inaccurate altitude readings.
If you need good elevation readings, ensure your GPS accuracy is set to Best during the recording.
However, even with the best accuracy, GPS altitude should not be considered an absolute position. It is an estimation of your real elevation, and the accuracy of this estimation is heavily dependent on the surrounding conditions.