Interpolation. Introduction and basic concepts. Computer User Training Course Paul Dando. User Support Section.

Transcription

1 Interpolation Introduction and basic concepts Computer User Training Course 2011 Paul Dando User Support Section 1

2 Contents Introduction Overview Spectral Transformations Grid point Transformations Interpolation Considerations Fortran-callable routines Future plans Practical mipan.info 2

3 Introduction Topic: Interpolation of data (used by MARS, operational dissemination and the Metview graphics package). Documentation: mipan.info 3

4 Interpolation Overview INPUT FIELD GRIB Product Fortran array Transformations INTERPOLATION - Spectral Spectral - Spectral Grid-point - Grid-point Grid-point Change resolution Sub-area extractions Derived fields - e.g. U and V from vorticity and divergence Rotation OUTPUT FIELD GRIB Product Fortran array mipan.info 4

5 Interpolation Overview Input can be a GRIB product or a Fortran array of values Output can be a GRIB product or a Fortran array of values For GRIB products, characteristics are taken from the GRIB header Interpolation library comprises a set of Fortran-callable routines - INTIN to describe input product - INTOUT to describe output product - INTF to perform interpolation of raw data (Fortran arrays) - INTF2 to interpolate GRIB 1 and GRIB 2 fields - INTUVP2 and INTUVU to convert vorticity and divergence to U and V components of wind Fortran routines are part of EMOSLIB mipan.info 5

6 Spectral Transformations Spectral to Spectral With truncation With rotation (very expensive in resources) Spectral to grid-point Latitude-Longitude Regular Gaussian Reduced Gaussian Interpolation coefficient files created (in $PPDIR) Automatic truncation based on output grid resolution 6

7 Spectral to grid-point truncation Truncation before interpolation reduces resources needed and avoids spurious aliased values Grid increment Truncation 2.5 Δ T Δ < 2.5 T Δ < 1.5 T Δ < 0.6 T Δ < 0.4 T Δ < 0.3 T Δ < 0.15 T Δ < 0.09 T2047 Controlled using truncation option in call to INTOUT For MARS retrieval use the resol keyword, e.g. resol=106 7

8 Grid-point Transformations Grid-point to grid-point Regular lat/long to regular lat/long Regular lat/long to regular Gaussian Regular Gaussian to regular lat/long Regular Gaussian to regular Gaussian Reduced Gaussian to regular lat/long Reduced Gaussian to regular Gaussian (Reduced Gaussian to reduced Gaussian) 8

9 Regular Gaussian Grids N48 N lines of latitude between pole and equator Latitude spacing not regular but is symmetric about equator 4 x N equally spaced points at each latitude No latitude points at poles or equator Special treatment at poles 9

10 Reduced Gaussian Grids N48 Lines of latitude same as a regular Gaussian grid Fewer longitude points at latitudes close to poles Local east-west grid length similar for all latitudes 10

11 Interpolation Considerations Grid-point Interpolation schemes - Bilinear interpolation - Nearest-neighbour - 12-point interpolation scheme for rotation Treatment of land-sea masks Treatment of precipitation Geographical sub-areas 11

12 Bilinear Interpolation Default for all parameters except vegetation and soil type fields and Wave 2D spectra Each point of output grid generated from 4 neighbouring points of input grid treated as Cartesian coordinates Weights applied to the 4 input grid points calculated: - by performing a linear fit along each line of latitude - normalising the two partial weights for each point - performing a linear fit in the north-south direction Vegetation and soil type fields and Wave 2D spectra use nearest neighbour 12

13 Rotation from Gaussian Grids Uses a 12-point interpolation scheme Old grid point New grid point Can produce non-physical values for some fields, e.g., cloud cover - Consider using bilinear interpolation for such fields - MARS keyword: interpolation = bilinear 13

14 Land-Sea Masks Land-sea masks represented as values 0 and 1 If land-sea mask of neighbouring point differs from grid-point being generated, weight of input point is modified to reduce effect L 1 S 1 L N L N = L 1 + L 2 + L S 1 L 2 L 3 Land-sea masks are applied by default to surface fields (except MSL and LSM) Behaviour can be changed by calls to INTIN 14

15 Precipitation Rules are applied to prevent spreading of trace amounts Interpolated value for precipitation at a point is set to zero if: - the calculated value is less than a defined threshold - its neighbour with the highest weight had no precipitation Operation performed before any special processing at the poles when interpolating from Gaussian to latitude-longitude grids Polar values for precipitation are always the average of nearest Gaussian line with no threshold check applied Care needed with accumulated fields! For EPS accumulated fields can use double interpolation - E.g. Interpolate from N320 to N160 and then to lat-long 15

16 Geographical Sub-areas Sub-areas can be created for new fields by specifying lat/long boundaries (north/west/south/east) Sub-areas are based on the full global grid - Global regular grids have longitude at 0 West - Lat/long grids have a line of latitude at the equator - Gaussian grids are symmetrical about the equator Boundaries of sub-areas are expanded outwards towards global grid (for rotations, boundaries are preserved) - Can change behaviour in MARS by setting the environment variable MARS_INTERPOLATION_INWARDS Sub-areas not currently supported for reduced Gaussian grids full global grid produced for these 16

17 Geographical sub-areas an example Blue box is the requested subarea of (87N,3W) to (81S,15E) Lat/long boundaries are compared with the global grid Green box is the provided sub-area of (90N,6W) to (84S,18E) 17

18 Fortran functions INTIN, INTOUT and INTF INTIN - Call to describe the input field - No need to call if the input field is in GRIB format - Call several times to describe input data if a Fortran array of real numbers INTOUT - Call to describe the output field - For GRIB input only call to describe features of output field different to those of input - For GRIB input some information is carried over to output field INTF / INTF2 - Call to generate new field from existing by interpolation 18

19 Fortran functions INTUVP2 and INTUVU Used to generate U and V wind components from vorticity and divergence fields Use INTUVP2 if vorticity and divergence are in GRIB format - Output U and V fields are also in GRIB format - Calls to INTIN not needed (input fields are GRIB!) Use INTUVU if vorticity and divergence are in real Fortran arrays - Must call INTIN to describe input field If INTOUT is not called generated U and V fields will have same format as the input vorticity and divergence fields See 19

20 EMOSLIB notes Library: EMOSLIB (located in /usr/local/lib) Single precision REALs ($EMOSLIB on ecgate) xlf myprog.f $EMOSLIB Double precision REALs xlf qrealsize=8 myprog.f -L/usr/local/lib -lemos.r64.d64.i32 (On C1A $EMOSLIB is -lemos.r64.d64.i32) 20

21 Future plans Current interpolation package is not easy to maintain A new interpolation package is being written in C++ - Improve code, maintainability and portability The new package will provide a Library and API - It will be callable from C, C++, Fortran 90, Python (?) - It will include some Unix-style command line tools All current EMOSLIB features will be supported Some new features will be added - Include some vertical interpolation routines (?) - Include routines for single-point interpolation - Handle different grid types Undergoing extensive testing at ECMWF before release 21

22 Interpolation Practical We will investigate some differences between bilinear and 12- point interpolation using a MARS retrieval Copy the example MARS retrieval script from ~trx/paul/interpolation/interp.mars - run the script interactively - examine the contents of the GRIB file cc_bl.grib using grib_ls - get the max, min and average values of the field using grib_get Change the MARS retrieval to add a rotation to -32.5/10.0 (set MARS keyword rotation=-32.5/10.0) and re-run - get the max, min and average values of the field using grib_get Run again with the MARS keyword interpolation=bilinear - get the max, min and average values of the field using grib_get 22