Statistics

Data Management System: Statistics and computation

 

The GTN-P DMS enable to upload data in a great variety of dimensions in terms of variables, data types, frequencies, profiles. Datasets are processed either on-the-fly or by running scripts.

 

Overall statistics (for each uploaded time serie):

Variable Unit Comments
AVG Temp (°C) Mean of all measurements over the  full period
MIN Temp (°C) Lowest measured value over the full period
MAX Temp (°C) Highest measured value over the full period
StDev   Standard deviation over all measurements and the full period
Variance   Variance over all measurements and the full period
Data   Number of single data in the dataset
Null   Number of null values (fields lacking values)
Start   First day of the measurement period
End   Last day of the measurement period

 

Thermal State of Permafrost:

Statistics are computed for all ground temperature datasets and at each sensor's depths.

 

Annual aggregations of temperature profiles measurements (if frequency < annual).

Variable Unit Comment
AVG (°C) Mean temperature for each depth and year
MIN (°C) Minimum temperature for each depth and year
MAX (°C) Maximum temperature for each depth and year
Data count    

 

 

ZAA depth (Zeros Annual Amplitude)

Variable Unit Comment
Tolerance (+/-°C) Temperature variation tolerance in order to set the ZAA depth
ZAA depth for each year, positive down (m) Applicable only if  the profile reach the ZAA, if  measurements over one depth > 2 month within a year ?
ZAA temperature (°C) (°C) Interpolated temperature found at ZAA
ZAA_deta (m) Delta of the computed ZAA depths over the all time serie
ZAA depth trends (m/year) linear regression. Applicable only if  the the ZAA depth as been found over more than a year

 

Methodical approach:

Zero annual amplitude (ZAA) is the depth in which the difference between the maximum and minimum temperatures for a given year is zero (or 0 ± some tolerance τ, 0.15°C in our case).
Thus given a function δ(x) = |temperature_max(x) - temperature_min(x)| for depth x, we want the smallest x such that δ(x) ≤ τ.
First, starting from x = 0, we walk down the borehole to find the first measured depth x_n such that δ(xn) ≤ τ. 
If such a depth does not exist, then we exit as error, as we have insufficient data to compute the ZAA.
 
Otherwise, the ZAA must exist between xn-1 and xn.  As the measured depths are discrete, we interpolate the function δ to obtain a continuous function.  We chose spline (i.e. piecewise continuous at 2nd derivative) interpolation to ensure smoothness and to have the measured values coincide with the interpolated values.  When there are data for four or more depths, we apply cubic spline.  If there are three depths, we apply quadratic spline, since at least four points are necessary for a cubic spline.  Similarly, if there are two depths, we fit to a line.  If there are fewer than two depths, it is obviously not possible to calculate the ZAA.
 
Once the interpolated function is defined, we take 0.1 m steps from xn-1 down to xn to identify and return the first depth whose temperature is within the tolerance.

The ZAA is computed from the annual MIN, MAX profiles when measurements reach the ZAA depth (0.15°C of tolerance).

Linear regression a spline curve is created to find the ZAA depth at the choosen tolerance (0.15°C).  

The statistical dispersion of the data, only enable a full representativeness of the trends after a period of 30 years with 2 months maximum consecutive gaps from at least monthly time series.

None of our data, so far, are eligible to this quality standard. However the International Permafrost Association's Action Group on Data quality assesses the quality parametres of the permafrost community.

 

  • Linear Interpolation of permafrost temperature profiles

  • In order to produce orthogonal matrix of data:  Reducing the data of each eligible boreholes to 5 depths in the following concept:

  • 0 m, Annual Min.,Max., Average temperature

  • 1 m, Annual Min.,Max., Average temperature

  • 2 m, Annual Min.,Max., Average temperature

  • 5 m, Annual Min.,Max., Average temperature

  • 10 m, Annual Min.,Max., Average temperature

 

Methodical approach:

Every value gets a „flag_depth“ either borehole (1) reaching 10m, (2) reaching 5m, (3) reaching 2m, (4) reaching 1m, (5) reaching less than 1m.

Every value gets a „flag_frequency“ either (1) min. max. and average available or (2) only average available (due to existing raw data).

-     

Active Layer Thawing:

Statistics are computed for all active layer thickness grids and transects

Variable Unit Comment
AVG (cm) over the grid for each date of measurements
MIN (cm) over the grid for each date of measurements
MAX (cm) over the grid for each date of measurements
Stdev (cm) over the grid for each date of measurements
Variance (cm2) over the grid for each date of measurements
Annual rate of thawing (cm/day) Applicable only if more than 3 measurements a year
Annual end-of-season thawing trend (cm/year) Applicable only if more than 2 years of mesurements

 

Methodical approach: The statistical dispersion of the data, only enable a certain representativeness of the trends after a period of 30 years with 2 years maximum of consecutive gap. None of our data, so far, are eligible to this quality standard. However the International Permafrost Association's Action Group on Data quality assesses the quality parametres of the permafrost community.

 

 

Read more:

Functions within the data management system to compute statistics