Modification of Height Handling for GPSRO in WRFVAR: CWB Period: 2010022400 to 2010030918Z

1. Modification of Height Handlingfor GPSRO in WRFVAR:CWB Period: 2010022400 to 2010030918Z

2. Background 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.

3. Definition 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) • At sea level, difference between Z and z is zero because • Same geopotential height at sea level (geoid, g is same at reference height 0) • Biases between z and Z depending on latitude and height • Due to difference of g and g0 Geopotential height 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:

4. Ideal sphere Earth In meteorology Center of mass Real Earth (geodesy) Geoid height, 0m • In z (geometric height) –Z (geopotential height) plot above, positive value in equator shows g in equator is smaller than g0. • Negative value near pole in lower atmosphere is because g in pole is larger than g0, but positive value in higher atmosphere (15km~) is, again, because g in higher altitude is smaller than g0

5. Observation minus Background (O-B) Statistics 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

6. O-B Statistics in Original and Modified WRFVAR Positive biases in original WRFVAR are disappeared in modified WRFVAR Original Modified

7. Latitude Dependency of O-B Biases As expected from slide 4, lower latitude has more biases due to larger height differences.

8. O-B Statistics for Linear and Logarithm Vertical Interpolation in Modified WRFVAR Logarithm interpolation prevents wavy pattern in O-B biases shown in linear interpolation Modified Modified +Logarithm

9. O-B Statistics for Linear and Logarithm Vertical Interpolation logarithm vertical interpolation works better than linear interpolation in refractivity Original Modified Modified +Logarithm

10. Observation Cost Function 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

11. Statistics of Obs. Cost Function in Original and Modified WRFVAR Observation cost function intensify biases due to relatively small obs.error in higher atmosphere. Original Modified

12. Statistics of Obs. Cost Function in Linear and Logarithm Vertical Interpolation in Modified WRFVAR Logarithm interpolation shows better performance in obs. cost function (no wavy signal, and near zero) Modified Modified +Logarithm