Modification of Height Handling for GPSRO in WRFVAR: CWB Period: 2010022400 to 2010030918Z. Background. Review of definition of geopotental height used in meteorology (and WRFVAR) is reviewed.
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Review of definition of geopotental height used in meteorology (and WRFVAR) is reviewed.
Simulation of expected height differences when we use height data from GPS RO is introduced. The key is how to handle acceleration due to gravity.
Definition of geopotential
F: geopotential [m2 s-2]
g: acceleration due to gravity [m s-2]
Note: it depends on f and z
f: latitude [deg.]
z: geometric height [m] (CDDAC COSMIC RO)
Z: geopotential height [m] (NWP, WRF, Meteorology)
g0: standard gravity at mean sea level [m s-2]
Note: it doesn’t depend on f and z
Definition: the acceleration of a body in free fall at sea level at a geodetic latitude of about 45.5°
Textbook of meteorology approximate that g doesn’t change with height and latitude, and then Z is almost close to z, but we cannot use the approximation in RO world.
Plot in next slide:
Center of mass
Geoid height, 0m
O-B statistics for about 2 weeks (56 initializations) are computed to check improvement of handling of height in modified WRFVAR system (original vs modified)
Latitude dependency of O-B is also introduced because original WRFVAR has biases depending on height and latitude (see background)
Differences of vertical interpolation scheme is also introduced for further improvement of WRFVAR
Positive biases in original WRFVAR are disappeared in modified WRFVAR
As expected from slide 4, lower latitude has more biases due to larger height differences.
Logarithm interpolation prevents wavy pattern in O-B biases shown in linear interpolation
logarithm vertical interpolation works better than linear interpolation in refractivity
Statistics of O-B cost function is generated to check validity of observation errors assigned for GPSRO in current WRFVAR
Differences of vertical interpolation scheme is also introduced
Observation cost function intensify biases due to relatively small obs.error in higher atmosphere.
Logarithm interpolation shows better performance in obs. cost function (no wavy signal, and near zero)