Adjoint-based forecast sensitivities of Typhoon Rusa

GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L21813, doi:10.1029/2006gl027289, 2006 Adjoint-based forecast sensitivities of Typhoon Rusa Hyun Mee Kim 1 and Byoung-Joo Jung 1 Received 20 June 2006; revised 13 September 2006; accepted 6 October 2006; published 9 November 2006. [1] Sensitivities of the forecast to changes in the initial state are evaluated for Typhoon Rusa, which passed through the Korean Peninsula in 2002, to understand the impact of initial condition uncertainties on the forecast and thence to diagnose the sensitive regions for adaptive observations. To assess the forecast sensitivities, adjoint-based sensitivities were used. Sensitive regions are located horizontally in the right half circle of the typhoon, and vertically in the lower and upper troposphere which coincide with the inflow and outflow regions near the typhoon. Forecast error is reduced around 18% by extracting properly weighted adjoint-based forecast sensitivity perturbations from the initial state, and the correction occurs primarily in the lower to midtroposphere where the forecast error is the largest. In contrast to the improvement in the overall forecast, the track and intensity forecast are not improved much through the modification of the initial condition by adjoint-based forecast sensitivities. Citation: Kim, H. M., and B.-J. Jung (2006), Adjoint-based forecast sensitivities of Typhoon Rusa, Geophys. Res. Lett., 33, L21813, doi:10.1029/2006gl027289. 1. Introduction [2] Typhoon Rusa landed on the Korean peninsula on 31 August 2002, causing a record-breaking daily rainfall amount of 870.5 mm over the eastern coast of the Korean peninsula. Because of the abnormal precipitation along the typhoon track as it passed through the Korean peninsula (Figure 1), Typhoon Rusa caused many casualties and extensive property damage. [3] To assess the impact of initial condition uncertainties on the forecast of this event and to detect sensitive regions for adaptive (or targeted) observations, adjoint based forecast sensitivities were applied. Adjoint sensitivity represents the gradient of some forecast aspect with respect to the control variables of the model (i.e., initial conditions, boundary conditions, and parameters) [Errico, 1997] as well as to the observations [Baker and Daley, 2000]. Since adjoint sensitivity indicates the sensitivity of specific forecast aspects with respect to the model variables or observations at the initial time, it has been used in adaptive observations [e.g., Bergot, 1999]. The goal of adaptive observations is to decrease the forecast error by placing observations in sensitive regions where they might have the most impact. These regions may be considered sensitive in the sense that changes to the initial condition in these regions are expected to have a 1 Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea. Copyright 2006 by the American Geophysical Union. 0094-8276/06/2006GL027289 larger effect on a particular measure of forecast skill than changes in other regions. [4] Rabier et al. [1996] suggested that adjoint sensitivity can be used to indicate the sensitivity of forecast errors with respect to initial conditions under the proper response function. Klinker et al. [1998] further suggested that key analysis error can be estimated by iteratively applying the adjoint sensitivity to the initial conditions. Based on this concept, adjoint sensitivity has been used to reduce uncertainties in the analysis and to understand the dynamical evolution of initial condition uncertainties of extratropical cyclones [e.g., Kleist and Morgan, 2005]. But few studies have used adjoint sensitivity to assess the initial condition uncertainties of a tropical cyclone forecast. Wu et al. [2006] suggested adjoint-derived sensitivity steering vector (ADSSV) to detect sensitive regions for adaptive observations of tropical cyclones. [5] In this study, adjoint-based forecast sensitivities are used to understand the sensitivity of forecast error with respect to the initial conditions for Typhoon Rusa, and thence to determine the sensitive regions in terms of adaptive observations. 2. Experimental Framework [6] This study uses the Fifth-Generation Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) Mesoscale Model (MM5), together with the MM5 adjoint modeling system [Zou et al., 1997], to calculate adjoint sensitivities. The model domain for this study is 100 x 100 horizontal grids (centered at 36 N in latitude and 123 E in longitude), with a 45 km horizontal resolution and 20 evenly spaced sigma levels in the vertical from the surface to 50 hpa. The model s initial and laternal boundary condition is the National Centers for Environmental Prediction (NCEP) Reanalysis 2 (2.5 2.5 global grid). The Optimum Interpolation Sea Surface Temperature (OISST) version 2 [Reynolds et al., 2002], produced by the National Oceanic and Atmospheric Administration (NOAA), is used for the lower boundary condition over the ocean. For a more realistic simulation, the Geophysical Fluid Dynamics Laboratory (GFDL) bogussing algorithm [Kwon et al., 2002] is used. Physical parameterizations used in the simulation include the Grell convective scheme, a bulk aerodynamic formulation of the planetary boundary layer, horizontal and vertical diffusion, and dry convective adjustment. [7] Simulations of 36 hours in length, from 1200 UTC 30 August to 0000 UTC 1 September 2002, were performed. Figure 1a shows the observed and predicted tracks of Typhoon Rusa near the Korean peninsula. Typhoon Rusa moved northwestward after its formation on 23 August, then moved northeastward after landfall on the Korean peninsula. Even though the predicted track is shifted slightly L21813 1of5

uncertainties in the initial conditions of the simulation or from model errors due to suboptimal model resolution. 3. Calculation of Adjoint-Based Forecast Sensitivities [8] We selected an energy-weighted forecast error inside a box surrounding the typhoon center at the verification time as a forecast aspect of interest (i.e., response function) (Figure 2b). Vertically, the response function is defined to include the typhoon top, from the surface to level 17 of the model domain. The response function of the energy-weighted forecast error is + R ¼ *Pe 1 f ; CPe f ; ð1þ 2 Figure 1. (a) Typhoon tracks and (b) mean sea level pressure at typhoon center from 1200 UTC 30 August to 0000 UTC 1 September: observed (solid circles), simulated (open circles), modified by adjoint sensitivity-based iterative procedures (open triangles), and KMA GDAPS analysis (solid triangles). The observed track is from 0000 UTC 28 August to 0000 UTC 1 September. to the west compared to the observed track, it generally simulates the observed track well. At the beginning of the simulation, the mean sea level pressure (MSLP) of the simulated typhoon is around 970 hpa which is 20 hpa higher than that of the observed typhoon. Compared to the rapid increase of observed MSLP (990 hpa at the final time), the predicted MSLP increases slowly up to 980 hpa. These inconsistencies in typhoon intensities may come from where e f is the MM5 forecast error at 0000 UTC 1 September 2002 (i.e., the deviation of the 36h MM5 forecast state (x f ) from the analysis (x a ) of Korea Meteorological Administration (KMA) Global Data Assimilation and Prediction System (GDAPS) (0.56 0.56 grid) [Korea Meteorological Administration, 2002]), P is a local projection operator which constrains the response function to a box surrounding the model predicted typhoon center, and C is a matrix that converts the response function to dry energy [Zou et al., 1997]. Because the true state is not known, the KMA GDAPS analysis is assumed to be the true state because it has a higher similarity to the observed typhoon track and intensity near the Korean peninsula than other analyses (i.e., NCEP GDAS, NCEP/NCAR reanalysis, and NCEP reanalysis 2). The track of the KMA analysis is similar to the observed track (Figure 1a), but the MSLP of the KMA analysis is overall higher than the observed MSLP, even though the KMA analysis captures the rapid increase of the MSLP after landfall compared to rather smooth increase of the predicted MSLP (Figure 1b). Figure 2. (a) Vertically integrated energy-weighted adjoint sensitivity distributions (JKg 1, shaded) and mean sea level pressure (solid) at 0h (1200 UTC 30 August). (b) Mean sea level pressure of the simulated typhoon at the final time (solid) at 36h (0000 UTC 1 September 2002). The box denotes a geographic region for defining a response function at 36h. 2of5

Figure 3. (a) Vertically integrated energy-weighted adjoint sensitivities in the lower level (970 730 hpa) (JKg 1, shaded), radial winds (ms 1 ) at 850 hpa, and mean sea level pressure (solid) at 0h. Vertically integrated energy-weighted adjoint sensitivities in the upper level (450 210 hpa) (JKg 1, shaded) and mean sea level pressure (solid) at 0h, with (b) radial winds (ms 1 ) at 300 hpa and (c) total winds (ms 1 ) at 300 hpa. Ranges of color shading are the same for the lower and upper level sensitivities. [9] An approximation to the change in R can be obtained as * + * + dr ¼ ; dx f ¼ ; Mdx 0 @x f @x f * + * + ¼ M T ð2þ ; dx 0 ¼ ; dx 0 @x f where M T is an adjoint operator of the tangent linear model M and x 0 is the initial state. From the right hand side of (2), the adjoint sensitivity of the forecast error to the initial conditions may be obtained by backward integration of the forecast error using the adjoint model: ¼ M T : ð3þ @xf [10] To assess the key analysis error in the initial state, perturbations are generated from the adjoint sensitivities [i.e., Klinker et al., 1998]: dx ð1þ 1 0 ¼ ac : [11] These properly-weighted perturbations are added to the initial condition to get a new initial condition x 0 (1) in (6). The weighting a is determined by the ratio between the energy norm forecast error at the final time and the energyweighted adjoint sensitivity at the initial time [Langland et al., 2002] as ef ; Ce f a ¼ 1 * 2 ; C 1 ð4þ + : ð5þ [12] Deviation between the KMA GDAPS analysis and a new 36h forecast state integrated from x (1) 0 becomes a new response function and from this response function new (2) adjoint sensitivity and associated perturbations dx 0 can be calculated. By this iterative procedure, an optimal initial 3of5

condition x 0 (n) in (6) can be obtained. x ð1þ ðþ 0 : 0 ¼ x 0 þ dx 1 x ðþ n 0 ¼ x 0 þ dx 0 þ dx 2 0 þþdx n 0 : ð6þ 4. Results [13] The adjoint sensitivity with respect to the initial state that would have the biggest impact on the 36h forecast error inside a box surrounding the typhoon center (Figure 2b) is shown in Figure 2a. The shading denotes the vertically integrated energy-weighted [i.e., Langland et al., 2002] adjoint sensitivity field. Sensitive regions are geographically more aggregated in the right half circle of the typhoon. One of the maxima is located in the rear right quadrant relative to the typhoon motion, which is related with the inflow regions of the environmental flow into the typhoon (Figures 3a and 3b), similar to the singular vector (SV) maximum [Peng and Reynolds, 2005]. The other maximum resides in the front right quadrant of the storm motion, which is related with inflow (outflow) regions of the environmental (storm) flow into (out of) the typhoon in the lower (upper) troposphere (Figures 3a and 3b). As denoted in Figure 3c, the maximum in the front right quadrant is associated with a mid-latitude trough in the upper troposphere. Interaction with the mid-latitude trough implies that Typhoon Rusa may undergo extratropical transition and influence development of states downstream. [14] Figures 4a and 4b show vertical distributions of energy-weighted adjoint sensitivity at 0h and energy norm forecast error at 36h. While the forecast error has the largest magnitude at the lower troposphere, with several secondary peaks throughout the troposphere from the surface to the top of the typhoon (Figure 4b), the maxima of the adjoint sensitivity are mostly located in the lower and upper troposphere (Figure 4a), with larger magnitude in the lower troposphere. As denoted by the lower and upper level adjoint sensitivities and radial flows (Figures 3a and 3b), the large adjoint sensitivity in the lower troposphere (Figure 4a) is related primarily with the inflow of the environmental flow into the typhoon (Figure 3a). In contrast, the large adjoint sensitivity in the upper troposphere (Figure 4a) is associated with inflow (rear right quadrant) and outflow Figure 4. Vertical distributions of the energy-weighted (a) adjoint sensitivity at 0h, (b) forecast error at 36h, and (c) differences between forecast errors of the control run and each modified run by the adjoint sensitivity-based iterative procedures (open squares for 5 iterations and solid squares for 10 iterations). R represents the response function. Figure 5. Energy-weighted forecast error for each iteration process. R represents the response function. (front right quadrant) near the typhoon, depending on the horizontal locations of the adjoint sensitivities (Figure 3b). [15] To assess the forecast error correction by the adjoint sensitivities, the iterative procedure described in section 3 is performed. Ten iterations are conducted with constant scaling factor a (= 1.148685e 4 ). The energy weighted forecast error decreases as iterations proceed. Compared to the control experiment with the unperturbed initial state, the modified initial state using the above perturbations can remove 18% of the forecast error after 10 iterations (Figure 5). The forecast error correction occurs mostly in the lower to mid-troposphere, with moderate correction in the upper troposphere (Figure 4c). Compared to the overall reduction of forecast error by the iterative procedures, typhoon track and intensity errors at the surface are decreased very little (Figure 1). This implies that it may be more difficult to reduce forecast error of the typhoon s track and intensity than to reduce the error for the overall threedimensional state of the typhoon, at least when using iterative procedures with adjoint-based forecast sensitivities for a total energy response function. Using a different response function that reflects track and intensity of the typhoon may result in a bigger impact on reducing the typhoon s track and intensity errors. 5. Summary [16] In this study, the adjoint sensitivity of the forecast error to the initial state is evaluated for Typhoon Rusa. Horizontally sensitive regions denoted by the adjoint sensitivities are located mostly in the right half circle of the typhoon. Unlike large adjoint sensitivities in the lower troposphere in the case of extratropical cyclones [e.g., Kleist and Morgan, 2005], the sensitive regions of Typhoon Rusa vertically reside in the lower and upper troposphere. While the sensitive regions in the lower troposphere coincide with the inflow regions, those in the upper troposphere are associated with the inflow and outflow regions depending on the horizontal locations of the adjoint sensitivities near the Typhoon. Overall forecast error is reduced around 18% by extracting properly weighted adjoint-based forecast sensitivity perturbations from the initial state. This correction occurs primarily in the lower to mid-troposphere, where the forecast error is the largest. In contrast, the track and intensity forecast are not improved much by the above adjoint sensitivity-based iterative procedures. The remaining 82% error might be improved by using better model configurations (i.e., fine resolution, more physics, etc.) and 4of5

by assimilating adaptive observation data with a more comprehensive data assimilation system. Based on the forecast error reduction by the adjoint sensitivities, we may infer that the adjoint-based forecast sensitivities can serve as an adaptive observing guidance for typhoon forecasts. [17] Acknowledgments. This study was supported by the Korea Meteorological Administration Research and Development Program under grant CATER 2006-2102. The authors thank Numerical Weather Prediction Division in Korea Meteorological Administration and Remote Sensing Laboratory in Meteorological Research Institute for providing analysis data for this study. References Baker, N. L., and R. Daley (2000), Observation and background sensitivity in the adaptive observation-targeting problem, Q. J. R. Meteorol. Soc., 126, 1431 1454. Bergot, T. (1999), Adaptive observations during FASTEX: A systematic survey of upstream flights, Q. J. R. Meteorol. Soc., 125, 3271 3298. Errico, R. M. (1997), What is an adjoint model?, Bull. Am. Meteorol. Soc., 78, 2577 2591. Kleist, D. T., and M. C. Morgan (2005), Application of adjoint-derived forecast sensitivities to the 24 25 January 2000 U.S. east coast snowstorm, Mon. Weather Rev., 133, 3148 3175. Klinker, E., F. Rabier, and R. Gelaro (1998), Estimation of key analysis errors using the adjoint technique, Q. J. R. Meteorol. Soc., 124, 1909 1933. Korea Meteorological Administration (2002), Improvement of Korea Meteorological Administration global data assimilation and prediction system in 2001, Tech. Note KMA/NWP/TN 2001 1, 81pp.,Numer. Weather Predict. Div., Seoul. Kwon, H. J., S.-H. Won, M.-H. Ahn, A.-S. Suh, and H.-S. Chung (2002), GFDL-type typhoon initialization in MM5, Mon. Weather Rev., 130, 2966 2974. Langland, R. H., M. A. Shapiro, and R. Gelaro (2002), Initial condition sensitivity and error growth in forecasts of the 25 January 2000 east coast snowstorm, Mon. Weather Rev., 130, 957 974. Peng, M. S., and C. A. Reynolds (2005), Double trouble for typhoon forecasters, Geophys. Res. Lett., 32, L02810, doi:10.1029/2004gl021680. Rabier, F., E. Klinker, P. Courtier, and A. Hollingsworth (1996), Sensitivity of forecast errors to initial conditions, Q. J. R. Meteorol. Soc., 122, 121 150. Reynolds, R. W., N. A. Rayner, T. M. Smith, D. C. Stokes, and W. Wang (2002), An improved in situ and satellite SST analysis for climate, J. Clim., 15, 1609 1625. Wu, C.-C., J.-H. Chen, P.-H. Lin, and K.-H. Chou (2006), Targeted observations of tropical cyclone movement based on the adjoint-derived sensitivity steering vector, paper presented at 27th conference on hurricanes and tropical meteorology, American Meteorological Society, 24 28 April 2006, Monterey, California. Zou, X., F. Vandenberghe, M. Pondeca, and Y. -H. Kuo (1997), Introduction to adjoint techniques and the MM5 adjoint modeling system, NCAR Tech. Note NCAR/TN-435STR, 110 pp., Natl. Cent. for Atmos. Res., Boulder, Colo. H. M. Kim and B.-J. Jung, Department of Atmospheric Sciences, Yonsei University, Shinchon-dong 134, Seodaemun-ku, Seoul 120-749, South Korea. (khm@yonsei.ac.kr) 5of5