Info  

 
While addressing a suboptimal performance issue for interpolation from the octahedral reduced Gaussian grid introduced with IFS cycle 41r2 to regular latitudelongitude grids, a problem was discovered with the method used to calculate the longitudinal points in the source grid. In some specific cases, this problem leads to an incorrect computation of interpolation weights and hence to incorrect interpolated values at some points of the output grid. The problem affects all versions of EMOSLIB prior to version 4.3.0. The problem is also present in fields retrieved with versions of MARS (including the WebAPI) that use any EMOSLIB version prior to version 4.3.0, Metview versions prior to 4.6.1 and for disseminated products from IFS cycle 41r1 and earlier. This page provides information about the problem and the specific cases where differences can occur. 
Table of Content Zone  


Description of the problem
The problem originates in the calculation of the longitude values of the source grid in EMOSLIB routines IRDIWE and IGDIWE. These routines use an integer value of the longitudinal grid increment (the 'stride') which, in some cases, results in a truncated value of the increment. This can result in an error in the computation of the longitude values for points in the source grid.
 The error occurs at specific latitude lines, j, with Nj longitude points whenever the grid spacing Dj=360/Nj has a remainder smaller than 10 microdegrees (1/100000 of a degree).
 The error accumulates linearly from 0° to 360° along the line of latitude.
 The error is minimal at grid points to the east and maximal at those to the west of the 0° meridian.
 The error is larger the greater the number of longitude points (Nj) along the line of latitude.
When the input grid is an original reduced Gaussian ("Ngrids"):
 the error occurs at bands of consecutive lines of latitude that have the same Nj.
 generally, the error is largest away from the equator (at about 20° N and 20° S for the N640 grid).
When the input grid is an octahedral reduced Gaussian ("Ogrids"):
 the error can occur at almost all lines of latitude because the Nj changes continuously
 the error is largest close to the equator where the resolution is highest.
In situations where the error occurs, the incorrect computation of the longitude values leads to two issues:
 The longitude points in the source grid are computed incorrectly. This leads to an incorrect computation of interpolation weights and hence to incorrect values at some points of the output grid.
 The nearest grid points used for the interpolation may be incorrectly identified due to a numerical 'shift' of the input grid cell.
The error is most evident for parameters where the gradient of the field is large and where a change in the nearest grid points or the interpolation weights used thus has a larger effect.
The error also affects the identification of points used for the landsea mask processing of surface fields.
Which interpolations are affected ?
The problem affects interpolations from:
 input original reduced Gaussian grid point fields to output regular Gaussian or regular latitudelongitude grids (without rotation)
 input octahedral reduced Gaussian grid point fields to output regular Gaussian or regular latitudelongitude grids (without rotation).
Which interpolations are not affected ?
 Interpolations to rotated latitudelongitude grids are unaffected
 Transformations from spherical harmonic components to grid point fields are unaffected.
 Interpolations of wave (WAM, ENSWAM etc) fields are unaffected.
For which cases is the problem fixed ?
The problem is fixed in EMOSLIB version 4.3.0 and newer for the following cases:
 interpolations from original reduced or octahedral reduced Gaussian grids to global, unrotated regular Gaussian grids (gridType=regular_gg);
 interpolations from original reduced or octahedral reduced Gaussian grids to global, unrotated latitudelongitude grids (gridType=regular_ll).
For the Disseminated products from IFS cycle 41r2, the problem is also fixed for interpolations to subareas of regular latitudelongitude grids
In addition, the problem is fixed for interpolations from original reduced or octahedral reduced Gaussian grids to subareas of unrotated regular Gaussian grids or regular latlon grids at EMOSLIB 4.3.7.
For which cases does the problem still exist ?
The problem has not been fixed for the following cases::
 interpolations from subareas of regular Gaussian grids or unrotated regular latitudelongitude grids;
 interpolations from global "staggered" regular latlon grids (i.e., global grids that are not centred on 0° latitude and 0° longitude).
In which software versions is the problem fixed ?
The problem is fixed in EMOSLIB version 4.3.7 and newer. This is used by:
 MARS client updated on 9 February 2016
 Metview version 4.6.4 and newer
 Disseminated products for IFS cycle 41r2 (implemented 8 March 2016)
Can results obtained with EMOSLIB 4.3.x be compared with the old version ?
Users can check results with the previous versions of MARS by using 'mars t p'. This version of MARS uses EMOSLIB 4.2.2 which does not include the bug fix.
Warning 

The 'mars t p' version is provided for testing purposes only. It should not be used as a long term replacement for the default 'mars' version. Please let ECMWF know if you need to use 'mars t p'. 
Examples
Mean sealevel pressure
The plots show the differences between the new interpolation method implemented in EMOSLIB version 4.3.0 and the old method for the interpolation of the mean sealevel pressure from the reduced Gaussian grids to a 0.5°x0.5° regular latitudelongitude grid for the period 114 December 2015.
For this field the differences are:
 between 49.26 Pa and 37.76 Pa for interpolation from an the N640 original reduced Gaussian grid to a 0.5°x0.5° regular latitudelongitude grid
 between 169.26 Pa and 146.26 Pa for interpolation from an the O1280 octahedral reduced Gaussian grid to a 0.5°x0.5° regular latitudelongitude grid
The plots in the upper panels show differences at the global level while those in the lower panels show the same fields plotted over the Europe area in a polar stereographic projection.
Section  


2 metre temperature
The plots show the differences between the new interpolation method implemented in EMOSLIB version 4.3.0 and the old method for the interpolation of the 2m temperature from the reduced Gaussian grids to a 0.5°x0.5° regular latitudelongitude grid for the period 114 December 2015.
For this field the differences are:
 between 8.21 K and 4.79 K for interpolation from an the N640 original reduced Gaussian grid to a 0.5°x0.5° regular latitudelongitude grid
 between 3.62 K and 4.44 K for interpolation from an the O1280 octahedral reduced Gaussian grid to a 0.5°x0.5° regular latitudelongitude grid
Section  

