Difference between revisions of "Interpolation of forecasted weather"
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!Resulting linear equation:
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Revision as of 16:50, 18 October 2021
Forecasted weather data, at daily timesteps, come initially on regular latitude longitude grids in the tables WEATHER_HIS_GRID, WEATHER_OPE_GRID, WEATHER_ENS_GRID_RAW and WEATHER_ERA5_GRID. The OPE model is stored on a 0.25x0.25 degrees resolution; the ENS model on a 0.5x0.5 degrees resolution, the ERA5 model on a 0.25x0.25 degrees resolution. The final target grids for the MCYSF 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 ENS and ERA5 daily data on the target grids downscaling methods are applied.
As summarized in section Meteorological data from ECMWF models ENS forecasts are delivered into the MCYFS on coarser grid 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 the ENS forecastss 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.
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 model data set.
For every cell in the target OPE grid, an inverse distance interpolation (also called ) for all weather variables is done to the 4 nearest cells of the source grid. As the ENS 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) and the target model (OPE). Essentially the model data are tuned to the OPE model, 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.
|Data sets used to derived the grid specific corrections|
* hindcast model data of ENS, first forecast day
The MOS routine is used to carry out a linear regression between OPE data and the IDW-interpolated ENS 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 table GRID_ENS_DOWN_ALGORITHMS.
Finally, data available at the global OPE grid (both OPE data and downscaled ENS data), are interpolated to the 25 by 25 km agricultural grid of a specific regional window like Europe or Russia-Ukraine-Kazakstan (RUK). 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 16 km based height model in case of downscaled and corrected ENS
- 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).
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). This processing is done in a similar way as for the observed weather. Therefore please follow the links here to get more details on the calculation of the Angot radiation and the calculation of evapotranspiration.
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):
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):
Finally, the down-scaling from the global OPE grid to a 25 km local agricultural grid (e.g. for the European window):
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):
|snow water equivalent||B1+B2||B2||B2||B1+B2||B1+B2||B1+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