1985 Hurricane Elenna taken from the Space Shuttle Hurricane/Typhoon Data Assimilation using Space-Time Multi-scale Analysis System (STMAS) Koch S., Y. Xie, J. McGinley and S. Albers Global Systems Division Earth System Research Lab Boulder, Colorado

Outline Observation systems; Space and Time Multi-scale Analysis System (STMAS); Hurricane and typhoon data assimilation; Benefit through temporal consistency; Model constraint for STMAS: a sequential 4DVAR; Future plan.

Observation Systems Aircraft: G-IV, P-3, C-130 and unmanned aircraft; Satellite radiance, Doppler Wind Lidar (DWL), quikscat and so on; Radar radial wind and reflectivity; Dropsonde, buoy, ship; Microwaves, such as SSM/I and Step-Frequency Microwave Radiometer (SFMR).

Observation Systems (cont.) Synoptic scale observations: satellites, aircraft, balloon, etc. designed for hurricane track analysis and prediction. Mesoscale observations: radar, SFMR, DWL, manned and unmanned aircraft. designed for hurricane intensity.

Space and Time Multi-scale Analysis System (STMAS) Developed for FAA storm boundary detection; A two-step DA processes: retrieval and statistical analysis (Standard 3/4-DVAR is a statistical analysis only); Variational analysis naturally transiting from information retrieval to statistical analysis; Extended from mesoscale analysis to full spectrum analysis from global scales down to hurricanes, even tornado scales; A sequential 4DVAR with a model constraint in a near future.

Current Applications FAA/MIT storm boundary detection and nowcasting; CWB data assimilation and reanalysis; NOAA/MDL boundary detection and nowcasting; NOAA Storm Prediction Center nowcasting; NOAA/ESRL/GSD Finite volume-Flow following Icosahedron Model data assimilation; NOAA/AOML hurricane data assimilation; NMDIS SST and height analysis and DA; Vaisla/Radiometrics. Inc possible tornado DA; … …

STMAS for hurricane/typhoon Due to dramatic difference of hurricanes, statistical information is difficult to obtain. Thus, hurricane DA, particularly intensity, more rely on the observations. STMAS’ retrieval capability seems even more attractive for hurricane DA.

Difference on longer waveDifference on shorter wave Retrieve resolvable information of observations

Resolvable wave missed from BKG Katrina 08/28 at 1100 RUC40 1h background H-eye is 70km off Observation: Aircraft, Quikscat and sondings

Approximation Theory Any smooth function can be decomposed by a series of base functions that is complete. where  k can be Fourier based functions, wavelets, or any smooth function with decreasing scales with k. STMAS uses a sequence of truncated series to approximate the the information contained in obs and background

Multigrid Technique Using the number of grid points to control the base functions: more gridpoints allow shorter waves

STMAS Multigrid Solve each variational DA problem on these grids with appropriate constraints and balances: Model constraints hydrostatic bal geostrophic bal

STMAS Dennis analysis (850mb) Wind observations (pre-analyzed radar and aircraft data

Standard Statistical Analysis JbJb JoJo 1. The hurricane eye of J b may be different from the one of J o 2. G-IV obs should be accurate as pilots can see the eye 3. Inaccurate B results two hurricane eyes in the analysis 4. STMAS retrieves the correct one from the obs in the following experiments.

STMAS Dennis analysis (850mb) STMAS (V)Background (V)

STMAS Dennis analysis (850mb) STMAS (V)Background (V)

STMAS Dennis analysis (850mb) STMAS (U)STMAS wind

A scheme for radar only analysis For a typhoon case of 2002, only radar data available; First order approximation of wind by a symmetry assumption, derived wind; STMAS adds radar radial wind on top of the first order approximation.

STMAS: A typhoon test (Cont.) Analysis: radial+derived wind uv Analysis: Derived wind only Derived wind

STMAS: A typhoon test (Cont.) Increments over the radar data region Analysis of radial+derived wind - Derived wind (where it is available) uv Analysis of Derived wind - Derived wind (where it is available)

Temporal Consistency Adv. STMAS allows users to specify the temporal window and temporal scales of their analysis; For limited observation resource, a longer temporal analysis window could benefit STMAS analysis to close to the reality; STMAS analysis of Hurricane Katrina over 1 hour and 3 hour time steps demonstrates that a longer temporal scale analysis is more realistic.

Hurricane Katrina Obs 2005/08/28/0900

Hurricane Katrina Obs 2005/08/28/0930

Hurricane Katrina Obs 2005/08/28/1000

Hurricane Katrina Obs 2005/08/28/1030

Hurricane Katrina Obs 2005/08/28/1100 Note: quikscat data available at this time window

Hurricane Katrina Obs 2005/08/28/1130 Note: quikscat data available at this time window

Hurricane Katrina Obs 2005/08/28/1200

Hurricane Katrina Obs 2005/08/28/1230

Hurricane Katrina Obs 2005/08/28/1300

Hurricane Katrina Obs 2005/08/28/1330

Hurricane Katrina Obs 2005/08/28/1400

Hurricane Katrina Obs 2005/08/28/1430

Hurricane Katrina Obs 2005/08/28/1500

Hurricane Katrina Analysis at h3h

Hurricane Katrina Analysis at h3h

Hurricane Katrina Analysis at 1400 with obs 1h3h

STMAS Model Constraints a sequential 4DVAR STMAS Katrina analysis is straightforward obs information retrieval; STMAS Dennis and the typhoon analyses retrieve the information from obs with simple constraints, geostrophic over large scale, hydrostatic and continuity over small scale. With a full dynamic model constraint, STMAS could be a sequential 4DVAR and provide a temporally dynamically consistent analysis for hurricanes.

Future Plan Radar reflectivity analysis operator associated with LAPS cloud analysis/Hot start; Satellite radiance analysis using CRTM with help from NESDIS; Model constraints; adjoint development: manual and/or auto-adjoint generator; More hurricane and typhoon case studies; Initialization of a hurricane HR model with STMAS analysis; Comparison with other DA, such as EnKF; Model forecast impact; …