Tropical cyclone forecasting with model-constrained 3D-Var. II: Improved cyclone track forecasting using AMSU-A, QuikSCAT and cloud-drift wind data

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1 QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 133: (27) Published online in Wiley InterScience ( DOI: 1.12/qj.1 Tropical cyclone forecasting with model-constrained 3D-Var. II: Improved cyclone track forecasting using AMSU-A, QuikSCAT and cloud-drift wind data Xudong Liang, a,b * Bin Wang, a Johnny CL Chan b,c Yihong Duan, b Dongliang Wang, b Zhihua Zeng b and Leiming Ma b a LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, China b Laboratory of Typhoon Forecast Technique, Shanghai Typhoon Institute, China Meteorological Administration, China c Laboratory for Atmospheric Research, Department of Physics & Materials Science City University of Hong Kong, China ABSTRACT: Generally, the three-dimensional variational (3D-Var) data assimilation technique does not impose constraints on the numerical model such as the dynamics and physics, which are used in a 4D-Var technique. On the other hand, adopting the 4D-Var technique requires a large amount of computer resources, which limits its practical application. In Part I, a 3D-Var method was proposed by minimizing the distance between observations and model variables, and the time tendency of model variables which makes the optimized initial conditions satisfy the constraints of full dynamics and physics in the numerical model. The forward and adjoint models used in this method are the same as those in a 4D-Var method but are only integrated one time step to calculate the time tendency and gradient. Because a numerical model is adopted as weak constraint, this technique is labelled as MC-3DVar. Here the National Center for Atmospheric Research/Penn State Mesoscale Model 5 (MM5) is used. In this paper (Part II), AMSU-A retrieved air temperatures are assimilated into 32 tropical cyclone (TC) cases using this framework. The results show a significant decrease in track forecast errors. Meanwhile, one case-study of assimilating AMSU-A temperature, QuikSCAT sea-level winds, and cloud-drift winds gives dramatic track error decreases. The study shows that the assimilation of these data with MC-3DVar improves TC forecasts, and more satellite data give better performances. Copyright 27 Royal Meteorological Society KEY WORDS satellite data; data assimilation Received 2 June 26; Revised 12 October 26; Accepted 17 October Introduction As argued in Part I of this study (Liang et al., 27), an advantage of three-dimensional variational (3D-Var) is saving computer resources. On the other hand, generally, the result of 4D-Var is better than 3D-Var because of complicated dynamical and physical constraints, but its practical application is limited by its huge requirement of computer resources. Therefore, a 3D-Var technique with more complicated dynamical and physical constraints is required to get better analysis with limited computer resources. Recently, some researches have focused on using weak constraints to reduce the dynamic imbalance between model variables based on the idea that unbalanced initial conditions often generates high-frequency oscillations with amplitude larger than those observed in nature. There are two kinds of approaches, digital-filter initialization (DFI) proposed by Lynch and Huang (1992), and physical constraints used by Brausseur (1991), Brausseur * Correspondence to: Xudong Liang, Shanghai Typhoon Institute, 166 Puxi Road, Shanghai, 23, China. liangxd@mail.typhoon.gov.cn and Haus (1991), McIntosh and Veronis (1993), Sun and Crook (1, 1997, 1, 21), Gao et al. (1999) and Ishikawa et al. (21). In Part I, a new 3D-Var method was proposed by employing a numerical model as constraint following the idea of Ishikawa et al. (21). Applying the full physics and dynamics of a numerical model as constraints in 3D-Var (Model Constrained 3D-Var: MC-3DVar) not only makes sure of the balance between variables in the analysis fields, but also dramatically reduces the computer resources compared with 4D-Var. In MC-3DVar, the cost function is defined at the initial time only as J = [x(t ) x b (t )] T B 1 [x(t ) x b (t )] + [H{x(t )} y o (t )] T O 1 [H{x(t )} y o (t )] [ ] x(t ) T [ ] + R 1 x(t ), (1.1) t t where x is the analysis, x b the background, y o the observations, B the background error covariance, O the observations error covariance, H the observation Copyright 27 Royal Meteorological Society

2 156 X. LIANG ET AL. operator, and R the error covariance of time tendency term of the model variables. Because the time tendency ( x(t ))/( t) in the penalty term is calculated by a numerical model, the dynamics and physics of the numerical model also function as weak constraints to minimize the cost function. The numerical model and its adjoint are used here to calculate the time tendency ( x)/( t) and the gradient. A set of ideal experiments were carried out in Part I to validate the new method. Practically, the background x b is from the output of the numerical model, the variables in the background are balanced, and the time tendency of the background should be kept. Therefore, the cost function (1.1) should be changed in practice to J = [x(t ) x b (t )] T B 1 [x(t ) x b (t )] + [H{x(t )} y o (t )] T O 1 [H{x(t )} y o (t )] [ x(t ) + x ] b(t ) T [ R 1 x(t ) x ] b(t ). t t t t (1.2) The time tendency ( x b (t ))/( t) in (1.2) is calculated by a numerical model using the background. In this part, applications of MC-3DVar to improve tropical cyclone (TC) track forecasting are carried out. This paper is organized as follows. The applications of MC-3DVar to improve TC track forecasting are given in section 2. The discussions and conclusions are made in section Applications of MC-3DVar The MC-3DVar framework is developed by running the forecast and adjoint models of the 4D-Var system of MM5 (Zou et al.,1997) for one time step (6 s) to calculate the time tendency. One model domain with grid points of 85 91, 23 vertical levels, and grid space of 45 km is applied. In the 4D-Var system, physical processes include Blackadar high-resolution planetary boundary layer parametrization (Blackadar, 1979), Grell cumulus (Grell,1993), and large-scale precipitation. In the forecasting run, physical processes include Burk Thompson aerodynamic planetary boundary layer parametrization (Burk, 1989), Dudhia s simple ice explicit moisture scheme (Dudhia, 1989), dry convective adjustment, and the Grell cumulus parametrization scheme (Grell, 1993). The 12 h forecasts of the Aviation Model (AVN) are used to define the background and boundary conditions. For each run, the centre of the model domain coincides with that of the tropical cyclone under study AMSU data assimilation The Advanced Microwave Sounder Unit (AMSU-A) retrieved atmospheric temperatures were adopted by Zhu et al. (22) to improve hurricane prediction using the gradient balance equation, bogus sea-level pressure, and the hydrostatic equation. The track, intensity and precipitation structure forecasts of Hurricane Bonnie were significantly improved during the 24 h integration. In this paper, the MC-3DVar technique, which has more complicated dynamic and physical processes, is used to assimilate the AMSU-A retrieved atmospheric temperatures. The AMSU-A retrieved temperatures from NOAA-15 used in this paper were provided by the NOAA/National Environmental Satellite, Data, and Information Service (NESDIS) on a 1 latitude longitude grid at 4 pressure levels from 1 to.1 hpa. To show the performance of the MC-3DVar and assimilation of AMSU-A retrieved temperatures, detailed analyses are performed on TC Fung-wong (22). Between 22 and 24 July, it moved firstly southwestward and then turned south and finally northeastward (Figure 1) due to the effects of the stronger TC Fengshen, which had a mean-sea-level pressure (MSLP) lower than 95 hpa during this period. The control run using the 12 h forecast of the AVN model also produced a southward track but the turn occurred much further west (near 128 E, 23.5 N). As a result, the 48 h track error is 385 km. The AMSU-retrieved temperature field (Figure 2) shows a warm core between 3 and 2 hpa with maximum value of 3 C. It is also obvious from Figure 2 that the observations are contaminated by rainfall in the lower levels with cold temperature anomalies in the TC inner areas. To eliminate the rainfall contamination, Zhu et al. (22) improved the retrieval scheme. However, in this paper, the AMSU-A retrieved temperatures below 6 hpa are discarded due to the large errors. The observation error of AMSU-A temperature is set to be 1.5 C (Zhu et al., 22). The background error covariance is diagonal and varying with vertical levels. For each variable on each vertical level, the error covariance is estimated as the square of the maximum differences of initial background and its 3 min forecasts. When the temperature observations are assimilated, the vertical gradient of pressure field is adjusted, because the vertical gradients of pressure fields are determined by temperature. To make the problem well-posed, top or bottom boundary conditions of pressure fields should be given. As in Zhu et al. (22), a pre-specified sea-level pressure (SLP) is specified in this paper according to Fujita s formula (Fujita, 1952): P bogus (r)=p C +dp 1 { ( r 2 R ) } 1 2 2, r Rout (2.1) where r is the distance from the TC centre, Rout the radius of the outermost closed isobar, P C the central SLP of the TC, R the radius of the maximum gradient of the SLP and dp the difference between P C and an estimation of the SLP at an infinite distance. The pre-specified SLP and AMSU-A retrieved temperature are assimilated using Copyright 27 Royal Meteorological Society Q. J. R. Meteorol. Soc. 133: (27) DOI: 1.12/qj

3 TROPICAL CYCLONE FORECASTING WITH MODEL-CONSTRAINED 3D-VAR. II N 25.5N 25N 24.5N 24N 23.5N 23N 22.5N 21.5N 21N 2.5N 2N 19.5N 19N 126E 127E 128E 129E 13E 131E 132E 133E 134E 135E 136E Figure 1. Track of Fung-wong in the control run (dotted line with solid TC symbol), AMSU-A assimilation run (solid line with empty TC symbol) from 12 UTC 22 July to 12 UTC 24 July 22, and the best track (long dashed line with symbols) from 12 UTC 22 July to 12 UTC 25 July. The interval between every two symbols is 12 h Pressure (hpa) E E 13E 131E 132E 133E 134E 135E 136E 137E 138E Figure 2. Vertical east west cross-section of AMSU-A retrieved temperature anomalies through the centre of TC Fung-wong at UTC 22 Jul 22. Unit: C. the MC-3DVar system. According to Xiao et al. (2), the error of the pre-specified SLP is set to be.8 hpa. The initial condition (IC) fields are greatly improved after the assimilation process with a MSLP of <993 hpa, which is nearly equal to the observational estimate of 99 hpa instead of >12 hpa in the background (Figure 3). Not only is the SLP field improved, the vertical structure of winds and height are also improved Copyright 27 Royal Meteorological Society Q. J. R. Meteorol. Soc. 133: (27) DOI: 1.12/qj

4 158 X. LIANG ET AL. (Figure 4), with a drop of height in the TC centre area and increase of wind speed around the eye. The assimilated IC also shows an enhanced warm core between 2 and 3 hpa and upward motion near the TC centre in the mid levels (Figure 5). It is obvious that the TC is stronger in the assimilated IC than that in the background with a reasonable structure. It is interesting that by only assimilating the SLP and AMSU-A temperature, the other variables such as horizontal winds, height and vertical motion are also changed. As a result, the 48 h integration using the assimilated IC gives a better result. In the 48 h integration of the background (control), the circulation of TC Fung-wong is very weak with MSLP greater than 12 hpa, while a MSLP less than hpa 34N 32N 3N N 26N 24N 2N E 123E 126E 129E 132E 135E 138E 141E 144E 147E Figure 3. SLP in the assimilated initial conditions (dot-dashed line) and background (solid line). Unit: hpa Pressure (hpa) E E 126E 129E 132E 135E 138E 141E 144E 147E Figure 4. Increments of geopotential height (shaded, unit: gpm) and wind speed (contour, unit: m s 1 ) between the assimilated IC and background on the vertical east west cross-section through the centre of TC Fung-wong. Copyright 27 Royal Meteorological Society Q. J. R. Meteorol. Soc. 133: (27) DOI: 1.12/qj

5 TROPICAL CYCLONE FORECASTING WITH MODEL-CONSTRAINED 3D-VAR. II 159 Pressure (hpa) E E 126E 129E 132E 135E 138E 141E 144E 147E Figure 5. As Figure 4 except for increments of warm core (shaded, unit: C) and vertical motion w (contour, unit: cm s 1 ). 34N 32N 3N N N 24N N 12E E 126E 129E 132E 135E 138E 141E 144E 147E Figure 6. As Figure 3 except for 48 h forecasts of control run (solid line) and assimilation run (dash-dotted line). TC Fung-wong (22) is at the lower-left and Fengshen (22) at the upper-right side. with a clear circulation exists in the forecast using the assimilated IC (Figure 6). The track forecast is also much improved (see Figure 1). Because the difference between the integrations of the background and the assimilated IC for TC Fengshen is not obvious (Figure 6), the improvement is likely to be mostly contributed by the improvement of the IC of Fung-wong. Xiao et al. (2) and Zou and Xiao (2) used a BDA (Bogus Data Assimilation) scheme in which the pre-specified SLP is used to develop other variables in the 4D-Var system. Because hydrostatically the vertical pressure gradient is mostly determined by the temperature, assimilating temperature observations with SLP will give a better analysis of the three-dimensional pressure field Copyright 27 Royal Meteorological Society Q. J. R. Meteorol. Soc. 133: (27) DOI: 1.12/qj

6 16 X. LIANG ET AL. and wind field. In the study of Zhu et al. (22), both the AMSU-A retrieved temperature and a pre-specified SLP are included, but the gradient and hydrostatic equations used to retrieve the three-dimensional pressure and wind fields are very simple compared with the full physics and dynamics in the numerical model used in MC-3DVar. To examine further the performance of the MC- 3DVar scheme in TC track forecasts, AMSU-A retrieved temperatures and the bogus SLP are assimilated in 11 TCs in 22 (32 cases) listed in Table I. Each of these cases is run with the same configuration as the Fungwong case with a control run (using the first-guess IC) and an assimilated run (using assimilated IC). The track forecasts of these cases are significantly improved after assimilating the AMSU-A retrieved temperatures compared with the control experiments (Figure 7). After assimilation, the mean 12, 24, 36 and 48 h forecast errors are reduced to 8, 128, 172 and 214 km respectively from 13, 164, 288 and 357 km in the control runs QuikSCAT sea-level winds and cloud-drift winds assimilation Recently, sea-level winds observed by NSCAT (NASA Advanced Scatterometer), QuikSCAT and SeaWind provide plentiful low-level wind structure information of TCs. Assimilating NSCAT data at the European Centre for Medium-Range Weather Forecasts (ECMWF) has been shown to have a positive impact on TC track forecasts (Leidner et al., 23). Besides AMSU-derived temperature data, cloud-drift winds can also be used to improve the definition of the upper-level structure of TCs. Early studies (Velden et al., 1992; Goerss et al., 1995; Soden et al., 21) using simple schemes found that cloud-drift winds can be beneficial in reducing the TC track forecast errors. Recently, Xiao et al. (22) examined the impact of cloud-drift data using 4D-Var technique in five experiments. Although they only obtained a slight positive impact on TC track forecasts, a significant improvement is achieved by assimilating cloud-drift winds using 4D- Var in the study of Wang et al. (26) when the cloud wind distributions are dense. Their analyses of 22 cases Track error (km) AMSU assimilated h Control h 36h integrating time (h) h 357 Figure 7. Averaged control and AMSU data assimilation track forecast errors (unit: km) of 32 TC cases in 22. show that in addition to the data assimilation technique, the density and quality of data can also have a significant impact on the improvement of TC track forecasts. All these studies support the possible advantage of using cloud-drift winds in TC track forecasts. The impact of assimilating individual data such as AMSU-A, cloud-drift winds and QuikSCAT sea-level winds to the TC track forecast have been examined in a few previous studies. However, the performance of a numerical TC track forecast model using a combination of all these satellite data has not been examined. Here, one case is chosen to assimilate AMSU-A, QuikSCAT sea-levelwinds, andcloud-drift winds data using the MC- 3DVar scheme. In the 32 AMSU-A assimilation cases listed in Table I, the Vongfong case has very large track errors (Figure 8) even after AMSU-A temperatures have been assimilated. In this case, the information of AMSU-A retrieved temperatures are limited to give accurate initial conditions. More data should be employed. On 17 August 22, tropical storm Vongfong (22) moved northwestward but turned northward on the 18th, finally making landfall on the 19th. QuikSCAT data are useful to improve the low-level wind structure. The QuikSCAT data used in this paper Table I. The name, number of experiments, and dates of the TC cases in 22. Name Number of experiments Dates (MMDDHH) Rammasun , 72, 7312, 74 Chataan , 79 Halong , 714 Nakri Fengshen , 724, Fung-wong 2 722, Phanfone , 816, 817, Vongfong Rusa 5 827, 82712, 828, 829, Sinlaku , 94, 9512, 96 Higos , 928, 92912, 93 Copyright 27 Royal Meteorological Society Q. J. R. Meteorol. Soc. 133: (27) DOI: 1.12/qj

7 TROPICAL CYCLONE FORECASTING WITH MODEL-CONSTRAINED 3D-VAR. II 161 Track error (km) (a) 3 Control AMSU 25 AMSU+QuickScat AMSU+QuickScat+Cloud Wind h integrating time (h) N 2N control AMSU AMSU+QuickScat AMSU+QuickScat+Cloud wind best track (b) 18E 11E 112E 114E 116E Figure 8. (a) Track forecast errors and (b) tracks of control and different satellite datasets assimilation experiments of Vongfong (22) from 12 UTC 17 Aug to 12 UTC 19 Aug 22. are obtained from the website of Remote Sensing Systems ( together with SSM/I (Special Sensor Microwave/Imager) rain rates. Before being assimilated into the initial conditions, the QuikSCAT data are pre-processed according to the error distribution and characteristic of the TC circulation. Due to rainfall contamination near the TC eye, QuikSCAT sealevel winds have large errors near the eyewall areas. For example, the QuikSCAT sea-level winds of Vongfong (22) at 1 UTC 17 Aug 22 in the rainfall areas have obviously irregular distributions (Figure 9(a)). Using Fourier analysis, azimuthal waves shorter than wave number 3 are eliminated within 3 latitude radius around the TC centre (Figure 9(c)). Then, the QuikSCAT winds near the TC centre (within a radius of 3 latitude) are replaced by the sum of wave number, 1 and 2 (Figure 9(b)), which gives a smoother structure. The difference between the original and filtered fields indicate that the removed components are largely concentrated in the rain-contaminated areas (Figure 9(c)). Following Leidner et al. (23), the observation error of QuikSCAT is set to be 2 m s 1. After assimilating AMSU-A temperatures and Quik- SCAT sea-level winds, the track forecast errors are greatly reduced to 71, 78, 142 and 136 km in the 12, 24, 36 and 48 h forecasts respectively (see Figure 8). The SLP and wind fields are fairly symmetric in the control run (Figure 1(a)) with generally weak precipitation. After AMSU temperatures are assimilated, the SLP distribution is more asymmetric with enhanced westerly winds on the south side and reduced wind in the north (Figure 1(b)). The maximum 1 h rainfall southwest of the TC centre is very similar to the SSM/I observed rainfall shown in Figure 9. The improvement of the TC structure improved the first 12 h track forecast (see Figure 8). At 2 hpa in the control run (Figure 11(a)), there is cyclonic flow near 15 N, 116 E and anticyclonic flow near 15 N, 116 E. Assimilating AMSU temperatures enhances the anticyclonic flow in the north (Figure 11(b)), which apparently makes the TC Copyright 27 Royal Meteorological Society Q. J. R. Meteorol. Soc. 133: (27) DOI: 1.12/qj

8 162 X. LIANG ET AL. 25N 25N 2N 2N 15N 15N 1N 1N b 5N 1E (a) a 15E 11E 115E 12E 2 125E 5N 1E (b) 15E 11E 115E 12E 3 125E c (c) 11E 112E 114E 116E Figure 9. Original (a), filtered (b) and the eliminated parts (c) of QuikSCAT sea-level winds of Vongfong (22) at 1 UTC 17 Aug 22. Shaded is the rainfall area according to SSM/I rain rates extracted from the website listed in the text. move northward faster than the control run and hence gives a larger track error after the 12 h forecast (see Figure 8). On the other hand, although rainfall in the southwest area of this TC is increased, the amplitude of the asymmetric rainfall around the eye is still small, which differs from the SSM/I observations (Figure 9). Assimilating QuikSCAT sea-level wind further increases the asymmetric rainfall structure (Figure 1(c)). The study of Chan et al. (22) shows that TCs often have a tendency to move towards the area of strong convection. The increased rainfall apparently caused the TC to move more westward. The enhanced easterly winds at 2 hpa (Figure 11(c)) near 18 N not captured in the control and AMSU assimilation runs also favour a westward displacement of the TC (see Figure 8(b)). A better track forecast is therefore observed after assimilating the QuikSCAT sea-level wind data. Although assimilation of the QuikSCAT data gives a better result, these winds only provide additional information at the low levels. Cloud-drift winds can be used to provide flow structure at the higher levels with a larger spatial scale. The outflow and environmental winds, which can be improved by assimilating cloud-drift winds, also play important roles in the development and motion of TCs. The cloud-drift winds used in this paper are derived from GMS-5 infrared and water vapour images provided by the China National Satellite Meteorological Center (Xu et al., 1997). A simple quality control similar to the first-guess check in the ECMWF system (Bormann et al., 23) is applied to reduce the larger errors. Following Wang et al. (26), the cloud-drift wind error in the upper troposphere is set to be 6 m s 1. Any cloud-drift winds with a difference from the background greater than 3 times this error, i.e. 18 m s 1, are rejected. Assimilating AMSU-A temperatures, QuikSCAT and cloud-drift winds gives a further improvement in the track forecasts (see Figure 8). The forecast errors at all the four forecast times are less than 1 km. Assimilating cloud-drift winds gives the strongest rainfall in the southwest (Figure 1(d)). It makes the TC move westward in the first 24 h as observed (see Figure 8(b)). The anticyclonic flow in the north shown in Figure 11(d) at 2 hpa is reduced greatly, so that northward flow is reduced and so is the northward motion of the storm, and hence the smallest track errors. Copyright 27 Royal Meteorological Society Q. J. R. Meteorol. Soc. 133: (27) DOI: 1.12/qj

9 TROPICAL CYCLONE FORECASTING WITH MODEL-CONSTRAINED 3D-VAR. II 163 2N 1N 18E (a) E 112E 114E 116E E 2N N 18E 11E 112E 114E 116E (b) E 2N N 18E 11E 112E 114E 116E (c) E 2N N 18E (d) E 112E 114E 116E E Figure 1. SLP (contour, unit: hpa), sea-level winds (barbs), and 1 h rainfall (shaded, unit: cm) in the initial conditions of (a) control, (b) AMSU-A temperature, (c) AMSU-A temperature plus QuikSCAT winds, and (d) AMSU-A temperature plus QuikSCAT winds and cloud-drift winds assimilation experiments. 3. Conclusions and discussion Including the numerical model as a penalty term in the cost function, a new 3D-Var data assimilation technique is proposed (the MC-3DVar). This method can be implemented in the same way as a 4D-Var scheme except that the numerical model is used to calculate the time tendency instead of using time integration (Liang et al., 27). Without the requirement of long time integration of the forward and adjoint model (only one time step is necessary), the MC-3DVar technique can save computational time dramatically. A MC-3DVar framework is developed in this paper based on the MM5 4D-Var system. Using the MC-3DVar system, AMSU-A retrieved air temperatures are assimilated into 32 TC cases (11 TCs) in the western North Pacific in the year 22. The average track errors are reduced from 164 to 128 km for the 24 h forecast and from 357 to 214 km at 48 h. A casestudy of tropical storm Vongfong gives dramatic track error decreases from 143 to 11 km at 24 h and from 219 to 8 km at 48 h after the AMSU-A temperatures, QuikSCAT sea-level winds and cloud-drift winds are assimilated into the initial conditions. All the experiments show that the MC-3DVar data assimilation method can be used to improve the initial conditions of tropical cyclone numerical forecasting. In addition, more satellite data such as AMSU-A temperatures, QuikSCAT sea-level winds and cloud-driftou winds are also shown to be favourable for improving the numerical TC forecasts. Acknowledgements Comments from the editor and reviewers lead to improvements in the content of the paper, and are gratefully acknowledged. This research was sponsored by the National Natural Science Foundation of China Grant 44512, and the Ministry of Science and Technology of China Grant 22DIB26 and 25BA98B15. Copyright 27 Royal Meteorological Society Q. J. R. Meteorol. Soc. 133: (27) DOI: 1.12/qj

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