School of Earth and Environmental Sciences, Seoul National University Dong-Kyou Lee Contribution: Dr. Yonhan Choi (UNIST/NCAR) IWTF/ACTS
CONTENTS Introduction Heavy Rainfall Cases Data Assimilation Summary and Conclusions
Introduction - Heavy rainfall is major severe weather over Korea producing devastating flash flood and consequently causing a number of fatalities and huge amount of property damages.
Introduction - Heavy rainfall occurs frequently over the Korean Peninsula during the warm season from late June through early September in association with synoptic-scale disturbances (Changma fronts), typhoons, or mesoscale convective systems (MCSs). - Transport of warm moist air by southerly/southwesterly low-level flows originating from southern China or the East China Sea, eastward/southeastward moving cold-core mid-latitude lows in northern China and westerly upper-level jet, and northwestward extending subtropical high are important synoptic-scale environments favorable for heavy rainfall over the Korean Peninsula.
Introduction Cold air L Cold air Upper level Jet Low level Jet Moist region H Warm air
Heavy Rainfall Cases Heavy Precipitation System (HPS) types are classified according to Lee and Kim (2007) using radar and satellite images. IS is for Isolated Thunderstorm, CB is for Convection Band, CC is for Cloud Cluster, and SL is for Squall Line. The below radar images show a typical example of each HPS type. CB-type IS-type CC-type SL-type
Heavy Rainfall Cases (2006) Cases Analysis Time (yyyymmddh h) Maximum of 24-h Rainfall 24-h Rainfall at Maximu m (mm) 1-h Rainfall at the peak (mm) Type* Characteristics 1 2006050512 Ganghwa 153.0 23.5 CC Low pressure 2 2006060918 Seosan 95.5 27.0 SL Trough 3 2006070918 Namhae 264.5 36.5 (Typhoon) Typhoon 4 2006072618 Seoul 187.5 32.0 CC & CB TL/AS & BBtype MCS 5 2006102218 Gangneung 292.5 64.5 IS (& CC) Orography
Heavy Rainfall Cases (2008) Cases Analysis Time (yyyymmddh h) Maximum of 24-h Rainfall 24-h Rainfall at Maximu m (mm) 1-h Rainfall at the peak (mm) Type* Characteristics 6 2008052712 Seogwipo 214.5 30.5 CC Low pressure 7 2008060200 Seoul 80.5 38.0 SL Trough 8 2008071200 Hongcheon 108.5 29.0 CB MCS 9 2008072312 Paju 282.5 55.0 CC & CB TL/AS & BBtype MCS 10 2008081112 Yanggu 121.5 18.0 IS Thunderstorm
Heavy Rainfall Cases Radar radial velocity data from 14 radar observation sites over the Korean Peninsula are assimilated. Radar data are preprocessed using the method of Park and Lee (2009), and preprocessed data have horizontal resolution of ~6 km, and vertical resolution of ~0.5 km. KMA (black), KAF (red), USAF (blue)
Heavy Rainfall Cases Time-lagged correlation coefficients of radar data for each HPS type Time required for dropping of autocorrelation to zero (i.e., life time of convective cell) for CC- and CB-types is longer than SLand IS-types. In ASDA, threat and bias scores for CCand CB-types are relatively better than those for SL- and IS-types.
Variational Data Assimilation In variational data assimilation methods, a cost function is defined as the sum of squared distances (weighted by the inverse of corresponding error covariance) to background and observations, and it is minimized to find the analysis. 3D-Var 4D-Var 1 1 J H H 2 2 J b T 1 1 ( ) ( ) b o T o x x x B ( x x ) [ y ( x)] R [ y ( x)] 1 2 b T 1 b ( x0 ) ( x0 x0 ) B0 ( x0 x0 ) 1 2 N o T 1 o [ yn Hn( M n( x0 ))] Rn [ yn Hn( M n( x0 ))] n 0
Variational Data Assimilation 4D-var has strength Observations can be assimilated at the time of their measurement which suits most asynoptic data, flow-dependent background error covariance is used implicitly, which is of vital importance in fast-developing weather systems, and a forecast model is used as a constraint, which enhances the dynamic balance of the analysis. 4D-var also has weakness It is difficult to develop and maintain tangent linear and adjoint models, it requires high computational cost due to its iterative minimization of the cost function, and it is based on a linearity assumption and hence the solution is optimal when the linearity assumption is valid. To reduce computational time in 4D-Var method, There are the Poorman s variational assimilation (PMV) method, the inverse 3D-Var (I3D-Var) data assimilation method, the Digital Filter Initialization (DFI). In this study, we develop the Adjoint Sensitivity-based Data Assimilation (ASDA) using the adjoint sensitivity, 3D-Var and observations.
ASDA Method In this study, the adjoint sensitivity of a response function, where, g is gravitational acceleration, N is Brunt-Vaisala frequency, T r is a reference temperature, ρ is density of air, and c s is speed of sound. The response function is a forecast error at time t measured in dry total energy, and the forecast error is defined as the difference between the forecast ending at time t and the verifying 3D-Var analysis. The adjoint sensitivity of forecast error can be used as a perturbation to improve an original background (or first guess). where, α is a scaling factor, and A -1 is for unit conversion.
ASDA Method The sign and magnitude of the scaling factor is somewhat arbitrary, and hence it is important to determine the scaling factor objectively. In order to determine an optimal value of the scaling factor, an observational part of the 4D-Var cost function is minimized using the observations (except for observation at the initial time). The cost function is a quadratic function of the scaling factor. Therefore, the optimal value of the scaling factor, α opt, can be obtained by equating the first-order derivative of the cost function to zero.
ASDA Method The adjoint sensitivity of forecast error scaled by the optimal scaling factor is added to the original first guess to make the improved first guess. Finally, 3D-Var analysis is conducted using the improved first guess and observation at the initial time to make a final ASDA analysis.
ASDA Method Schematic diagram of the ASDA method t=0 t=t x t=0 NLM run with full physics x t=t 3D-Var analysis Scaling-factor determination R x 0 AM run with simplified physics x ref, R x t αa 1 R x 0 Final 3D-Var analysis x ASDA
Data Assimilation of radar radial velocity In this study, the Weather Research and Forecasting Data Assimilation (WRFDA) system version 3.4 (Barker et al., 2012) is used. Background error covariance is calculated using the National Meteorological Center (NMC) method (Parrish and Derber, 1992), where background error statistics are derived from the differences between 24-h and 12-h forecasts. The length of assimilation window is 30-minute and observations are provided every 10 minutes.
Data Assimilation of radar radial velocity Horizontal resolution # of horizontal grids # of vertical levels Initial/boundary conditions Domain 1 Domain 2 Domain 3 54 km 18 km 6 km 120 x 102 121 x 103 121 x 127 35 (50 hpa) NCEP FNL data Domain Initial time Forecast hours 1 00 UTC 26 36 2 12 UTC 26 24 3 18 UTC 26 18 Cumulus parameterization Microphysics Planetary boundary layer Longwave radiation Shortwave radiation Kain-Fritsch WSM6 YSU Dudhia RRTM None
A Heavy Rainfall Case (27 July 2006) Synoptic environments at 00 UTC 27 July 2006 Geopotential height (black solid), temperature (red dashed), water vapor mixing ratio (shading) at 850 hpa Geopotential height (black solid), wind speed (red solid), convergence (shading) at 850 hpa Geopotential height (black solid), wind speed (green solid), divergence (shading) at 200 hpa At 850 hpa, North pacific high was extended to the Korean Peninsula. Warm and moist air was transported to the Korean Peninsula by southerly or southwesterly flow. Low-level convergence appeared at the nose of low level jet, where wind speed decreased abruptly. At 200 hpa, the Korean Peninsula was located on the right of the entrance of upper level jet, and upper-level divergence related to the ULJ was maximized over the Yellow Sea.
A Heavy Rainfall Case Radar reflectivity at 4-km height from 18 UTC 26 to 12 UTC 27 July 2006 From 1800 UTC 26 to 0600 UTC 27 July 2006, MCS affecting the Korean Peninsula can be classified as Training Line/Adjoining Stratiform (TL/AS) type defined in Schumacher and Johnson (2005). Prolonged heavy convective rainfall was observed along the training line and stratiform rainfall occurred adjacent to convective rainfall. After 0600 UTC 27 July 2006, MCS affecting the Korean Peninsula can be classified as Back Building (BB) type also defined in Schumacher and Johnson (2005). Convective cells formed over the west coast of the Korean Peninsula, and moved eastward slowly, or they were often nearly stationary and merged into bigger cells.
A Heavy Rainfall Case Simulated 18-h accumulated rainfall distribution 187.5 mm 189.0 mm 104.2 mm 171.5 mm 178.5 mm 205.7 mm 216.5 mm 3DVAR 4DVAR ASDA In CONTROL, simulated rainfall band is shifted northeastward compared to the observations and rainfall amount at Seoul is much underestimated. 3DVAR is similar to CONTROL. The rainfall bands in 4DVAR and ASDA are similar to observation. Locations of two localized rainfall maxima are close to observations although 18-h accumulated rainfall amount is slightly underestimated (overestimated) in the 4DVAR (ASDA).
A Heavy Rainfall Case RMSEs of radial velocity against radar observations At 18 UTC 26 July 2006 (analysis time), RMSEs of radial velocity for CONTROL, 3DVAR, 4DVAR, and ASDA experiments are 3.10, 2.12, 2.09, and 2.08, respectively. Compared to CONTROL (O-B), RMSEs of data assimilation (O-A) are reduced. Overall, RMSEs of radial velocity for 4DVAR and ASDA are smaller than those for 3DVAR and CONTROL during the 24-h forecast.
A Heavy Rainfall Case Pseudo Single Observation Test (Analysis increment of U and V) Single radial velocity observations: 37.00 N, 127.58 E, 4000 m, 1930 UTC 26 July
A Heavy Rainfall Case Cost-function minimization and computational time 3DVAR 4DVAR ASDA Computing time on Linux cluster with 8 cores Assimilation method Number of iterations Computing time per an iteration Total computing time 3DVAR 16 < 1 minute ~3 minutes 4DVAR 54 ~30 minutes ~27 hours ASDA 18 (final 3D-Var) Two 3D-Var analyses, one NLM run, one AM run, and scalingfactor ~1 hour
Ten Heavy Rainfall Cases Threat and bias scores (24-h rainfall, 25-mm threshold)
Ten Heavy Rainfall Cases RMSE of radial velocity (temporal average)
Ten Heavy Rainfall Cases Sea Level Pressure (SLP) tendency (Average over the cases) As a measure of the removal of spurious high-frequency noises from the initial condition, the time variation of the domain-mean of absolute SLP tendency is calculated. The magnitudes of high-frequency noises in 4DVAR and ASDA are much controlled, especially near the initial time, because a forecast model is used as a constraint.
Ten Heavy Rainfall Cases Domain-averaged cloud water mixing ratio (Average over the cases) As a measure of spin-up, time variation of cloud water mixing ratio averaged over the whole domain is calculated. Although only radar radial velocity is assimilated, cloud water mixing ratio in 4DVAR and ASDA increases rapidly after initialization due to the integration of an adjoint model. In 3DVAR, cloud water mixing ratio increases gradually during the first 30-minute cycling.
Summary and Conclusions ASDA method uses an adjoint sensitivity of forecast error as the perturbation to improve an original first guess. The sign and magnitude of the perturbation are determined by minimizing the observational part of the 4D-Var cost function. In this study, characteristics of the TL/AS- and BB-type MCSs and the corresponding rainfall are appropriately simulated through the assimilation of radar radial velocity data in ASDA and 4D-Var. Overall, threat and bias scores of rainfall and RMSEs of radial velocity in ASDA are comparable to those of 4D-Var. However, the relative performance of ASDA to 4D-Var is likely better for CC- and CB-type than SL- and IS-type. The computational cost of ASDA is much less than that of 4D-Var, because it is not involved with the iterative minimization of a cost function. A big advantage! ASDA method can be applied to the forecast of fast developing rainfall systems, but it needs to test a longer assimilation window than 30 minutes and the assimilation of other asynoptic observations (e.g., AWS observations). It will be also applied for typhoon-causing heavy rainfall forecasts.
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