09 Spatial homogenity tests

Spatial homogeneity test

General

The test described here is applicable to quality and quantity parameters with a spatial character, like rainfall, temperature, evaporation, etc., but sampled at a number of stations (point measurements).
To investigate the reliability of point observations at a station, called the test station, the observations are compared with weighted averages of the rainfall at neighbour stations. The weights are inversely proportional to some power of the distance between the test station and the neighbouring stations. Now the test is considering the difference between the observed and estimated value at the test station. If the absolute difference between observation and estimate exceeds specific limits (absolute and relative), the observation will be flagged (but not deleted!) to stress the need for further investigation.

Series codes

The test series can be selected by selecting a series in the series list box and pressing the Select button.

Radius of Area influence

A radius of influence must be entered in km's. Series with the selected parameters located within this area will be presented in the spreadsheet. From every quadrant the two stations closest to the test station will be selected. Changing the values <On/Off> form 0 to 1 a station can be selected.

Search

By pressing the Search button, series within the entered search radius with the selected parameters will be searched for and presented in the spreadsheet.

Test procedure

To be specific and to avoid general phrasing the test will be explained for rainfall series, where rainfall may be replaced by any other spatial parameter.
In this chapter the following topics will be discussed:

• selection of neighbour stations
• estimation of point rainfall
• test criterion
• corrections for heterogeneity
• limitations
  Selection of neighbour stations
  Following criteria are used to select the neighbours of the test station:
  1. series with selected data type and the same interval as the one under investigation should be available;
  2. the distance between the test station and a neighbour should be less than a specified maximum correlation distance R_max (km);
  3. maximum amount of neighbours is 8;
  4. per quadrant at maximum 4 stations out of 4 fulfilling criterion 2 can be selected, but criterion 3 remains valid, default are the two stations nearest to the base station.
  The selection on quadrants is applied to obtain a proper spatial distribution of stations around the test station. However, due to prevailing wind conditions or orographical effects spatial heterogeneity may be present. In those cases normalised rather than actual values should be investigated.
  

  Estimation of point rainfall

  The point estimate for the test station based on the observations at N neighbour stations for the same time interval reads:
  
  where:
  P_est (t) = estimated rainfall at the test station at time t
  P_i (t) = measured rainfall at neighbour station i at time t
  D_i = distance between the test station and neighbour station i
  N = number of neighbour stations taken into account
  b = power of distance D, (default b = 2).
  

  Test criterion

  The difference between the observed value, P_obs (t), and the estimated value, P_est (t), is considered to be insignificant if the following conditions are met:
  ¦P_obs (t) - P_est (t)¦ £X_abs , and)
  ¦P_obs (t) - P_est (t)¦ £X_rel *
  with:
  X_abs = admissible absolute difference
  = standard deviation of neighbouring values, see equation (6.4)
  X_rel = multiplier of standard deviation
  
  If the difference is unacceptably high, the recorded value is flagged "+" or "-", depending on whether the observed total is greater or less than the estimate. In case no estimate is available the value will be flagged with "*". Only the flagged, i.e. the suspicious, data will be printed.
  

  Corrections for heterogeneity

  To correct for sources of heterogeneity, e.g. orographic effects, normalised rather then actual values may be used. This implies that in the equations (6.1) through (6.4) the observations at the neighbour stations are multiplied by the ratio of the test station normal and the neighbour station normal:
  P_ci = (N_test /N_i ).P_i
  where:
  P_ci = for heterogeneity corrected value at neighbour station i
  N_test = normal of test station
  N_i = normal of neighbour station i
  The station normals are read from a station-normal file or are given as a function of the altitude of a station.
  The station normal as a function of the station altitude is of the following form:
  N_i = a₁ + b₁ . H_{S {}} for H_S £H₁
  N_i = a₂ + b₂ . H_{S {}} for H_S > H₁
  

  Limitations

  Following limitations to the use of the spatial validation option apply:
  
• Only series with the same time interval are considered