AIAA 2000-0624 A New Eddy Dissipation Rate Formulation for the Terminal Area PBL Prediction System (TAPPS) Joseph J. Charney, Michael L. Kaplan, Yuh-Lang Lin, and Karl D. Pfeiffer North Carolina State University Raleigh, NC 38th Aerospace Sciences Meeting & Exhibit January 10-13, 2000 / Reno, NV For permission to copy or republish, contact the American Institute of Aeronautics andAstronautics 1801 Alexander Bell Drive, Suite 500, Reston, Virginia 20191-4344 AIAA 2000-0624 A NEW EDDY DISSIPATION RATE FORMULATION FOR THE TERMINAL AREA PBL PREDICTION SYSTEM (TAPPS) Joseph J. Charney‡, Michael L. Kaplan†, Yuh-Lang Lin*, and Karl D. Pfeiffer§ Department of Marine, Earth, and Atmospheric Science North Carolina State University Raleigh, North Carolina 27695-8208 ABSTRACT INTRODUCTION The TAPPS employs the MASS model to produce mesoscale atmospheric simulations in support of the The Terminal Area PBL Prediction System Wake Vortex project at Dallas Fort-Worth (TAPPS) is being developed to produce meso-b scale International Airport (DFW). A post-processing scheme simulations of meteorological conditions in support of uses the simulated three-dimensional atmospheric the Wake Vortex project at Dallas Fort-Worth characteristics in the planetary boundary layer (PBL) International Airport (DFW).1 The centerpiece of to calculate the turbulence quantities most important to TAPPS is the Mesoscale Atmospheric Simulation the dissipation of vortices: turbulent kinetic energy and System (MASS)2, a mesoscale numerical weather eddy dissipation rate. TAPPS will ultimately be prediction model that provides real time, operational employed to enhance terminal area productivity by simulations of the planetary boundary layer (PBL) providing weather forecasts for the Aircraft Vortex conditions in the DFW area. TAPPS will ultimately be Spacing System (AVOSS). The post-processing scheme employed to enhance terminal area productivity by utilizes experimental data and similarity theory to providing weather forecasts for the Aircraft Vortex determine the turbulence quantities from the simulated Spacing System (AVOSS).3,4 The Wake Vortex project horizontal wind field and stability characteristics of the in general and AVOSS in particular is designed to, at a atmosphere. Characteristic PBL quantities important to given terminal, assess the wake vortex drift and these calculations are determined based on dissipation under varying weather conditions, and formulations from the Blackadar PBL compute the optimal safe spacing for landing parameterization, which is regularly employed in the commercial aircraft. MASS model to account for PBL processes in This study will focus upon the overall performance mesoscale simulations. The TAPPS forecasts are of the TAPPS system as well as presenting recent verified against high-resolution observations of the enhancements in the post-processing system. The post- horizontal winds at DFW. Statistical assessments of the processor has been developed by the Department of error in the wind forecasts suggest that TAPPS Marine, Earth, and Atmospheric Science at the North captures the essential features of the horizontal winds Carolina State University to compute the predictive with considerable skill. Additionally, the turbulence quantities from the TAPPS simulations required by quantities produced by the post-processor are shown to AVOSS. The scheme employs the simulated three- compare favorably with corresponding tower dimensional winds, thermal structure, and moisture observations. characteristics of the atmosphere to calculate the turbulence-related variables considered most important * Professor to the dissipation of vortices: the turbulent kinetic † Visiting Professor energy (TKE) and eddy dissipation rate (EDR).1 ‡ Visiting Assistant Professor § Graduate Research Assistant This paper is declared a work of the U. S. Government and is not subject to copyright protection in the United States. MASS/TAPPS MODEL CHARACTERISTICS u2 (cid:230) z (cid:246) Hydrostatic primitive equation model e = * (cid:231) 1.24+4.3 (cid:247) , (1) kz Ł Lł 3-D primitive equations for u, v, T, q, and p Cartesian grid on a polar stereographic map s p terrain-following vertical coordinate system where u*is the friction velocity, k ~ 0.4 is the von One-way interactive nested grid system Karman constant, and Lis the Monin-Obukhov length Time-dependent lateral boundary conditions scale. Above the surface layer, First guess provided by large scale gridded analyses Reanalysis of rawinsonde, surface, and asynoptic data u2 (cid:230) z (cid:246) (cid:230) z(cid:246) 1.5 using a 3-D optimum interpolation scheme e = * (cid:231) 1.24+4.3 (cid:247) (cid:231) 1- 0.85 (cid:247) . (2) Blackadar PBL scheme kz Ł Lł Ł hł Surface energy budget Prognostic equations for cloud water, ice, rain water, For a statically unstable PBL, in which a convective and snow regime dominated by buoyancy prevails, the EDR is Convective parameterization scheme calculated as follows: Post-processing system to compute AVOSS input quantities 3 (cid:230) 2 (cid:246) 2 POST-PROCESSING SYSTEM e = u*3 (cid:231)(cid:231) 1+0.5 z 3 (cid:247)(cid:247) , (3) kz (cid:231) L (cid:247) Ł ł In order for AVOSS to effectively predict the drift and dissipation of vortices in the approach corridor of DFW, it is necessary for the post-processor to provide for the surface layer (z £ 0.1h). Above the surface highly-detailed forecasts of winds, particularly the layer in a convective regime, turbulent processes arising cross-runway (U) component, from the TAPPS due to the statically unstable conditions lead to well- simulations. Time-height cross-sections of the winds mixed atmospheric conditions up through the top of the are computed by the system with a temporal resolution PBL. In this so-called mixed layer, the EDR becomes: of 30 minutes, and a vertical spacing of 15m between the surface and 1000m. The variance and the shear of w3 (cid:230) z (cid:246) these winds are also very important for AVOSS, and e = * (cid:231)(cid:231) 0.8- 0.3 (cid:247)(cid:247) , (4) h Ł h ł must be computed with precision. Finally, in order to assess vortex dissipation, diagnostics are computed that evaluate the growth, dissipation, and magnitude of the where w is the convective velocity scale. * turbulence. The formulation for the TKE (e) follows a similar The current version of the TAPPS post-processor framework. For a statically stable or neutral PBL, the employs the model winds, temperature, and moisture scheme divides the results into two layers. For the fields in conjunction with a first-order closure scheme surface layer (z £ 0.1h), developed by Han et al. to calculate the EDR and TKE 1 for AVOSS. The scheme utilizes a series of equations e = 6u2, (5) developed from experimental data and similarity * scaling to determine the EDR and TKE from observations of the three-dimensional wind field and and above the surface layer, the moist thermodynamic stability characteristics of the atmosphere.5 The scheme assumes that the PBL has two (cid:230) z(cid:246) 1.75 regimes: 1) neutral and stable, and 2) unstable. e = 6u2(cid:231) 1- (cid:247) , (6) *Ł hł For a statically stable or neutral PBL, the scheme divides the results into two layers. For the surface layer, which is defined as (z £ 0.1h), where zis the height For a statically unstable PBL, the TKE is calculated as above the ground and his the PBL height, the EDR follows: e ( ) is given by: 2 American Institute of Aeronautics and Astronautics 2 regime, (3) the forced convection regime, and (4) the e = 0.36w2 +0.85u2(cid:231)(cid:230) 1- 3 z (cid:246)(cid:247) 3, (7) free convection regime. These regimes are determined * *Ł Lł by calculating the bulk Richardson number and assessing the buoyant characteristics of the PBL. Then for the surface layer (z £ 0.1h), and: u* becomes: (cid:230) kV (cid:230) 2 (cid:246) (cid:231) a , e =(cid:231)(cid:231)(cid:231)Ł 0.36+0.9(cid:231)Ł(cid:230) hz(cid:247)ł(cid:246) 3(cid:231)Ł(cid:230) 1- 0.8hz(cid:247)ł(cid:246) 2(cid:247)(cid:247)(cid:247)ł w*2, (8) u* = max(cid:231)(cid:231)(cid:231) ln(cid:231)(cid:231)Ł(cid:230) zzoa (cid:247)(cid:247)ł(cid:246) - Y m . (9) (cid:231) (cid:231) for the mixed layer. Ł u , *n There are three quantities in the above equations that must be defined before this scheme can be applied to the simulated fields: the PBL height (h), the friction where Vais the velocity at the top of the surface layer, velocity (u ), and the convective velocity scale (w ). z is the height of the surface layer, z is the roughness * * a o In previous versions of the post-processor, these length, and Y is the correction to the log profile of m quantities were derived by first evaluating the turbulent momentum due to deviations from neutral stratification character of the PBL from the resolved model winds within the various PBL regimes. u is a pre-defined and then inferring the other quantities based on as series *n of empirical relationships between the TKE and the minimum of the friction velocity that is generally used generally observed characteristics of the PBL. only in the stable regime (regime 1). This However, Eqns. 1-8 were designed to calculate the parameterization for u , which takes into account the * EDR using wind values taken from tower observations background thermodynamic and turbulence of PBL winds. The resolved winds from a mesoscale characteristics of the simulated atmosphere, provides atmospheric model (which has a horizontal resolution substantially better information about the turbulent on the order of 12km) will not, in general, display the characteristics of the PBL, which in turn leads to more same degree of small-scale variability that occurs in accurate and physically consistent EDR and TKE tower-based PBL observations. As a result, the model predictions. resolved winds will not provide information about the The Blackadar PBL parameterization also includes turbulent characteristics of the PBL, and thus will tend a formulation for the PBL height (h) in the convective to yield values for EDR and TKE that are significantly regime (regime 4) based on the buoyancy smaller than those calculated from observed winds. characteristics of the airmass.6,7 Outside of the In order to overcome this potentially serious convective regime, an empirical relationship that limitation, the post-processing scheme has been revised defines h for a stationary, neutral PBL is employed.5 such that the EDR and TKE calculations are more representative of the background turbulence than the The convective velocity scale is represented by: resolved mesoscale model fields. This was accomplished by using formulations from the Blackadar 1 (cid:230) g ( ) (cid:246) 2 PBL parameterization, which is employed within w = (cid:231)(cid:231) w'q ' h(cid:247)(cid:247) . (10) MASS to account for sub-grid scale PBL processes that * Ł T v s ł o cannot be explicitly calculated by the model due to its resolution.6,7 By using the Blackadar parameterization, where gis the gravitational acceleration, T is the representations for u , h, and w that are not wholly o * * ( ) dependent upon the resolved model winds can be reference temperature, and w'q ' is the mean surface v s obtained. heat flux. Since the surface heating parameterization Perhaps the most important of these modifications within the MASS model accounts for the shortwave to the overall performance of the post-processor is the radiative heating effects, a representation of the surface formulation for u . Within the Blackadar PBL * heat flux that is physically consistent with the u and parameterization, u is calculated by using a scheme * * that separates PBL conditions into 4 regimes: (1) the h calculations can be used. By incorporating this value stable regime, (2) the damped mechanical turbulence into Eqn. 10, the convective velocity scale will likewise 3 American Institute of Aeronautics and Astronautics be consistent with the rest of the input into the EDR and year presents a considerable challenge for AVOSS, and TKE scheme. that TAPPS regularly captures these features is also encouraging. Furthermore, that TAPPS is providing information about these features some 12 hours before PARAMETERS OF TAPPS DFW FORECASTS they actually occurred, shows in dramatic fashion the Horizontal grid resolution = 12km utility of these simulations to AVOSS as a whole. Vertical grid resolution = 56 levels between 5m and 16,000m STATISTICAL CALCULATIONS Length of forecast = 21 hours { } Forecast frequency = 2 per day, starting at 0300 UTC (cid:229)N X - X tapps obs and 1500 UTC Bias: i=1 Forecast time required = ~3 hours N Domain size = ~ 720 km X 720 km square centered on (cid:229)N X - X DFW tapps obs Mean Absolute Error = i=1 AVOSS products = U, V, U-variance, V-variance, N U-shear, q , EDR, and TKE v { } Vertical resolution of AVOSS products = 68 vertical (cid:229)N X - X 2 tapps obs levels from 0 to 1000m at 15m intervals RMS Error = i=1 N TAPPS RESULTS A statistical error analysis that assesses the overall In order to assess the performance of the post- performance of TAPPS in comparison to AWAS is processor, it is necessary to first verify that the model shown in Fig. 3. These statistics were computed from winds are in agreement with observations. Figs. 1-2 the differences between TAPPS and AWAS for 28 real- show comparisons between the TAPPS simulated U time simulations in November 1999. These simulations (cross-runway) and V (along-runway) components of were initiated at 0000 UTC on each date. Results were the horizontal winds and the wind consensus profiles analyzed for every 30-minute time period for which produced by MIT Lincoln Labs from tower, profiler, there were both observations and model output, lidar, and other in situ observations at DFW (referred to resulting in a sample size on the order of 1300 for each as the AVOSS Winds Analysis System, or AWAS).8 level. For the purpose of understanding these results, it Fig. 1 shows time-height cross sections of the two wind is worth noting that the estimated error in the components for 2 November, 1999, while Fig 2 instruments that provided data for the AWAS profiles is corresponds to 19 November, 1999. These two cases on the order of 1 m/s.8 The bias statistics suggest that were chosen because both situations involve the there is little overall bias in the TAPPS predictions, passage of a synoptic-scale front, which is traditionally particularly in the lowest levels. Even at the highest a difficult feature for mesoscale models to predict. As levels, the overall bias is less than the estimated errors evidenced by the sharp reversal in direction of the V- in the observations. wind components (Figs. 1c,d and 2c,d), TAPPS and the The mean absolute error (MAB) is on the order of observations both clearly indicate the passage of the 1.5 m/s in the lowest 500m of the profile, and increases fronts in these cases. to near 2 m/s at the higher levels. The increase in MAB It is noteworthy that TAPPS reproduces with some at the higher levels can be attributed to the typically degree of accuracy both the level and magnitude of the higher wind speeds in the upper levels, which causes wind maximums associated with the approaching larger magnitude differences should the model develop fronts. In particular, the agreement between TAPPS and phase errors in the simulated weather systems. AWAS for the U-wind component maximum on 2 Nevertheless, overall MAB values on the order of 1.5 November (Fig. 1a,b) and for the V-component m/s in the lowest 500m, which is the layer most vital to maximum on 19 November (Fig. 2c,d) shows the performance of AVOSS, is very encouraging. The considerable skill. The high degree of agreement RMS errors are, as expected, somewhat larger than the between the overall structures in both wind components mean absolute errors. However, since RMS error during the passage of these fronts suggests that TAPPS calculations are designed to punish particularly large can reproduce mesoscale features in the horizontal wind differences between TAPPS and AWAS, RMS errors fields that are often difficult to replicate. Although not less than 1 m/s greater than the MAB in all cases shown here, it is also notable that TAPPS also verifies suggests that there are few extremely large "misses" well in situations where a nocturnal low-level jet (LLJ) during the month. is observed by the AWAS. The almost ubiquitous Finally, Figs. 4 and 5 show an example of TAPPS nature of LLJs in the DFW area during much of the TKE and EDR predictions respectively at three 4 American Institute of Aeronautics and Astronautics different times on 15 November, 1999. The TAPPS NASA Cooperative Agreement #NAS 1-99097. The profiles are compared against EDR and TKE profiles authors would like to thank Dr. Fred H. Proctor for his inferred from 5m and 45m tower observations by using technical support. Additionally, we would like to the technique described in Han et al.5 These profiles acknowledge the support of David A. Hinton, the show that, in this particular case, TAPPS generated AVOSS Principal Investigator, and R. Brad Perry, the TKE and EDR values that are of the same order of Reduced Separation and Operations Manager of the magnitude as those inferred from the tower NASA-Langley Airborne Systems Competency, for their observations, which is very encouraging. The vertical support and helpful comments on numerous occasions. structure of the quantities is also well represented in the We would also like to thank J. Al Zak and W. G. Buddy early times in particular (Figs 4a,b and 5a,b), when the Rodgers for providing us with the DFW tower PBL was in a stable regime. In the afternoon (4c and observations and Han et al. model results used for 5c), the vertical structure of the EDR and TKE are less comparison purposes in this study, as well as for their comparable, due to disagreements between the TAPPS many valuable comments regarding the performance of simulations and the tower observations of EDR and the new post-processor. TKE in the convective regime. Nevertheless, the fact that the two techniques agree within an order of magnitude shows a considerable improvement over the 1 Kaplan, M. L., R. P. Weglarz, Y.-L. Lin, D. B. techniques that were previously employed as part of the Ensley, J. K. Kehoe, and D. S. Decroix, 1999: A TAPPS system. However, there is clearly a need for terminal area PBL prediction system for DFW. 37th more comprehensive statistical comparisons between Aerospace Sciences Meeting and Exhibit, Reno, TAPPS and observations of EDR and TKE. There are Nevada, AIAA Paper No. 99-0983, 27 pp. plans to start calculating the EDR and TKE by using 2 MESO, Inc., 1995: MASS Reference Manuel AWAS and profiler data in the near future, which will Version 5.10, 129 pp. [Available from MESO, Inc., 185 provide more comprehensive verification information Jordan Road, Troy, NY 12180] with which the overall performance of the post- 3 Hinton, D. A., 1995: "Aircraft Vortex Spacing processor can be assessed. System (AVOSS) Conceptual Design." NASA Tech. Memo. No. 110184. [Available from NASA-Langley CONCLUSIONS Research Center, Hampton, Virginia 23681]. 4 Hinton, D. A., J. K. Charnock, D. R. Bagwell, and D. Grigsby, 1999: NASA Aircraft Vortex Spacing A new formulation for predicting the evolution of System development status. 37th Aerospace Sciences turbulence variables in the PBL from TAPPS Meeting & Exhibit, Reno, Nevada, AIAA Paper No. simulations has been presented. The physics of the new 99-0753, 17 pp. formulation, which utilizes elements of the Blackadar 5 Han, J., S. Shen, S. P. Arya, and Y.-L. Lin, 1999: PBL parameterization to account for the sub-grid scale An estimation of turbulent kinetic energy and energy characteristics necessary to reproduce the details of dissipation rate based on atmospheric boundary layer turbulent flow, was described. similarity theory. [Submitted as a NASA contract The overall performance of TAPPS was assessed report] by comparing TAPPS and AWAS horizontal winds in 6 Blackadar, A. K., 1979: High resolution models the lowest 1000m of the atmosphere. Examinations of of the planetary boundary layer. Advances in two specific cases as well as an overall statistical Environmental Science and Engineering, Vol. 1, No. 1, assessment of the differences suggested that TAPPS J. Pfafflin and E. Ziegler, eds., Gordon and Breach, pp. reproduces the salient PBL characteristics in the 50-85. horizontal wind fields with considerable skill. 7 Zhang, D.-L. and R. A. Anthes, 1982: A high Comparisons between TAPPS simulation results from resolution model of the planetary boundary layer - the redesigned post-processor and tower-based sensitivity tests and comparisons with SESAME-79 observations of EDR and TKE showed that the new data. J. Appl. Meteor. , 21, 1594-1609. formulation agreed well with observations for one 8 Daisey, T. J, R. E. Cole, R. M. Heinrichs, M. P. particular case. Both the temporal evolution and the Matthews, and G. H. Perras, 1998: Aircraft Vortex magnitudes of the simulated quantities were shown to Spacing System (AVOSS) initial 1997 system be representative of the conditions at DFW. deployment at Dallas/Ft. Worth (DFW) airport. NASA Project report NASA/L-3. [Available from the National Technical Information Service, Springfield, Virginia ACKNOWLEDGEMENTS 22161]. This research is being supported by NASA’s Terminal Area Productivity (TAP) program under 5 American Institute of Aeronautics and Astronautics a) TAPPS b) AWAS Figure 1: Time-height cross section of the horizontal wind components for 2 November, 1999 at DFW in m/s. a) TAPPS U-component. b) AWAS U-component. c) TAPPS V-component. d) AWAS V-component. 6 American Institute of Aeronautics and Astronautics c) TAPPS d) AWAS Figure 1: Continued 7 American Institute of Aeronautics and Astronautics a) TAPPS b) AWAS Figure 2: Time-height cross section of the horizontal wind components for 19 November, 1999 at DFW in m/s. a) TAPPS U-component. b) AWAS U-component. c) TAPPS V-component. d) AWAS V-component. 8 American Institute of Aeronautics and Astronautics c) TAPPS d) AWAS Figure 2: Continued 9 American Institute of Aeronautics and Astronautics