Interpolation of forecasted weather

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General description

Interpolation from 0.5 x 0.5 degrees grid to 25 x 25 km regular climate grid.

Forecasted weather data, at daily timesteps, come initially on regular latitude longitude grids in the tables WEATHER_<MODEL>_GRID_RAW. The OPE model is stored on a 0.25x0.25 degrees resolution; the ENS and ENSEXT models on a 0.5x0.5 degrees resolution and the SEAS and ERA model on a 0.75x0.75 degrees resolution. The final target grids are:

  • a regular 0.25 by 0.25 degrees grid used for global crop specific water balance calculations in support of the ASAP system
  • a regular agriculture 25 by 25 km grid in a projected coordinate system for specific regional windows e.g. Europe, used in the crop simulation

To get the daily data on the target grids a downscaling method is applied.

Downscaling

As summarized in section Meteorological data from ECMWF models forecasts for the subsets ENS, ENSEXT, SEAS and ERA are delivered into the MCYFS on coarser grids than the aspired MCYFS target grids of 0.25° or 25 kilometres. That is why scaling methods towards the target grids are applied. Aim is to have forecasts of the ECMWF subsets ENS, ENSEXT, SEAS and ERA that are as comparable and consistent as possible with the deterministic analysis and forecast OPE. The OPE analysis combines the most advanced assimilation system for observed atmospheric data with highest model grid resolution, involving the most accurate model physics, elevation and land use and soil type models. Simple interpolation methods, as inverse distance or spline, do not add information to the data. Differences in elevation, land use, land-sea-pattern are not considered. That is why in MCYFS the temperature and humidity elements, wind and radiation statistical relations between the subsets and the OPE analysis are applied. Each land grid point has its location-specific, time-dependent set of equations per subset.

IDW interpolation
First data are interpolated to a regular 0.25 x 0.25 degrees grid. The spatial resolution of this grid used to be the size (approximately) on which the operational model of ECMWF was running until early 2010. We call this the OPE grid. Note that in the MCYFS database the model HIS appears as separate objects but it actually refers to the analysis part of the OPE model (the first day of the forecast depth). Therefore here only OPE is mentioned. This interpolation is applied for the ENS, ENSEXT, SEAS and ERA models data sets.

For every cell in the target OPE grid, an inverse distance interpolation (also called IDW) for all weather variables is done to the 4 nearest cells of the source grid. As the ENS, ENSEXT, SEAS and ERA source grids completely surrounds the OPE target grid and covers both sea and land, the 4 nearest cells should be roughly in all directions, even for cells at the borders of the OPE target grid. The inverse distance interpolation of for instance precipitation for a single cell can be mathematically written as:


In words, the summed nearest cell precipitations / divided by the distances are divided by the summed inversed distances to give the interpolated precipitation value. Please note that distance works linearly in the used formula. A point twice as far, has half the influence. Furthermore, distances are determined in km by calculating the arc across the globe between the ECMWF model grid cell and the target grid cell and multiplying this arc with the earth’s radius.

Grid specific corrections
Next, down-scaling for these models continues with grid specific corrections because of differences in elevation, land use, land-sea-pattern between the source model (ENS, ENSEXT, SEAS and ERA) and the target model (OPE). Essentially the model data are tuned to the OPE model. Main advantage is that data of the different models can be better compared and more or less consistent time-series are obtained linking reanalysis, SEAS, ENSEXT, ENS all around a common ‘OPE’ reference.

The grid specific equations has been derived by means of linear regression (MOS = Model Output Statistics) with the daily OPE data of at least three recent years as training set.


The MOS routine is used to carry out a linear regression between OPE data and the IDW-interpolated ENS, ENSEXT, SEAS or ERA data for each grid point.

The grid specific correction is done for all elements except rainfall and snow depth as for the latter two no reliable equations could be derived. The coefficients of the equations are available in tables GRID_SEAS_DOWN_ALGORITHMS, GRID_ENS_DOWN_ALGORITHMS, GRID_ENSEXT_DOWN_ALGORITHMS and GRID_ERA_DOWN_ALGORITHMS.

The below pictures visualize the advantage of the applied downscaling method. The downscaling (middle) added information to the raw data (left). Downscaled data and the OPE analysis (right) align.

Daily mean air temperature on 01 June 2010 as analyzed by the 0.75° ERA-Interim.
Same day, same source data but downscaled with grid-point- and time-specific method.
Daily mean air temperature on 01 June 2010 as analyzed by the 0.25° deterministic ECMWF OPE.


Finally, data available at the global OPE grid (both OPE data and downscaled ENS, ENSEXT, SEAS and ERA data), are interpolated to the 25 by 25 km agricultural grid of a specific regional window like Europe or China. The latter step is needed because:

  • different projected co-ordinated systems between the global OPE and local projected grid of a regional window
  • altitude differences between the global OPE grid and the local projected grid of a regional window

Data are downscaled applying an IDW interpolation and correcting for elevation differences (lapse rate). The correction factors used for the temperature and vapor pressure are respectively -0.006 (°C.m-1) and -2.5% per 100 meter increase (van der Voet et al., 1994). Therefore dewpoint temperature is first converted to actual vapour pressure while after applying the correction the actual vapour pressure is converted back into dewpoint temperature. The height models used are:

  • the 25 km based height model in case of downscaled and corrected ERA data
  • the 16 km based height model in case of downscaled and corrected SEAS, ENS, ENSEXT
  • the 16 km based height model in case of OPE data

Calculation additional parameters

After down-scaling, both at the global OPE grid and the local agricultural 25 by 25 km grid, the following additional parameters are calculated at daily timestep:

  • Actual vapour pressure
  • Evapotranspiration (crop reference, wet bare soil and open water)

Actual vapour pressure

Actual vapour pressure (ea) is derived from dew point temperature (Td) by applying a standard formula for calculating the saturated vapour pressure at a specific temperature (in this case the dew point temperature).


Evapotranspiration

In general, the evapotranspiration from a reference surface, the so-called reference crop evapotranspiration or reference evapotranspiration (ET0) can be described by the FAO Penman-Monteith (Allen et all., 1998). Evapotranspiration from a wet bare soil surface (ES0) and open water(E0) is calculated with the Penman formula (Penman, 1948). Follow the links here to get more details on the calculation of the Angot radiation and the calculation of evapotranspiration.

Processing line

ECMWF model data are delivered as described in section meteorological data from ECMWF models.


OPE data are directly loaded into the data base without any downscaling as the data are delivered at the global OPE grid (0.25 by 0.25 degree):

Processing-HIS-OPE-data.jpg


Down-scaling from coarser resolution global grid ECMWF data (ENS, ENSEXT, SEAS, ERA) to the global OPE grid according the IDW & grid specific correction (e.g. ENS):

Processing-ERA-ENS-ENSEXT-SEAS-data.jpg


Finally, the down-scaling from the global OPE grid to a 25 km local agricultural grid (e.g. for the European window):

Processing-OPE-ERA-ENS-ENSEXT-SEAS-data-2.JPG


In summary, the following down-scaling is applied per model and element (note B2 and C2 are only applied when down-scaling data from the global OPE grid towards a local agricultural 25 by 25 km grid):

Parameter ERA HIS OPE ENS ENSEXT SEAS
mean temperature B1+C1+B2+C2 B2+C2 B2+C2 B1+C1+B2+C2 B1+C1+B2+C2 B1+C1+B2+C2
maximum temperature B1+C1+B2+C2 B2+C2 B2+C2 B1+C1+B2+C2 B1+C1+B2+C2 B1+C1+B2+C2
minimum temperature B1+C1+B2+C2 B2+C2 B2+C2 B1+C1+B2+C2 B1+C1+B2+C2 B1+C1+B2+C2
dewpoint temperature B1+C1+B2+C2 B2+C2 B2+C2 B1+C1+B2+C2 B1+C1+B2+C2 B1+C1+B2+C2
precipitation B1+B2 B2 B2 B1+B2 B1+B2 B1+B2
snow water equivalent B1+B2 B2 B2 B1+B2 B1+B2 B1+B2
wind speed B1+C1+B2 B2 B2 B1+C1+B2 B1+C1+B2 B1+C1+B2
solar radiation B1+C1+B2 B2 B2 B1+C1+B2 B1+C1+B2 B1+C1+B2
  • B1 = IDW from coarse to global OPE grid
  • B2 = IDW from global OPE grid to 25 km local agricultural grid
  • C1 = grid specific correction applied after B1
  • C2 = lapse rate correction because of elevation differences

Storage of data

With the data available on the regular global OPE (0.25 by 0.25 degree) and the local agricultural grid of 25 by 25km, data can be stored in the MCYFS tables WEATHER_<MODEL>_GRID where <MODEL> is to be replaced by the abbreviation of one of the five ECMWF products (HIS, OPE, ENS, ENSEXT or SEAS).