Validating the turbulence parameterization schemes of a numerical model using eddy dissipation rate and turbulent kinetic energy measurements in terrain-disrupted airflow
A number of turbulence parameterization schemes are available in the latest version (6.0) of the Regional Atmospheric Modelling System (RAMS). Chan in Meteorol Atmos Phys 103:145–157, (2009), studied the performance of these schemes by simulating the eddy dissipation rate (EDR) distribution in the vicinity of the Hong Kong International Airport (HKIA) and comparing with the EDR measurements of remote-sensing instruments at the airport. For the e-l (turbulent kinetic energy − mixing length) scheme considered in that study, the asymptotic mixing length was assumed to be a constant. This assumption is changed in the present paper, a variable asymptotic mixing length is chosen and simulations of EDR fields are repeated for terrain-disrupted airflow in the vicinity of HKIA. It is found that, with a variable asymptotic mixing length, the performance of the e-l scheme is greatly improved. With suitable choice of the empirical constants in the turbulence closure, the accuracy of the EDR profile (in comparison with LIDAR and wind profiler measurements) is found to be comparable with that predicted by the Deardorff scheme. A study on the sensitivity of the simulation results to these empirical constants has also been performed. Moreover, as a follow-up of the previous study of Chan in Meteorol Atmos Phys 103:145–157, (2009), case studies have been conducted on the following issues of the model simulation of turbulence for aviation application: (a) the effect of vertical gridding on the simulation results, (b) possibility of false alarm (such as over-forecasting of EDR value) in light turbulence cases, and (c) the performance in the simulation of other turbulence intensity metric for aviation purpose, e.g. TKE.
KeywordsTropical Cyclone Turbulent Kinetic Energy Turbulence Intensity Wind Profiler Vertical Gridding
The Hong Kong International Airport (HKIA) is situated in the vicinity of a complex terrain. To its south is the mountainous Lantau Island with peaks rising to about 1 km above mean sea level (AMSL) and valleys as low as 400 m in between. The airport is surrounded by sea in the west, north and east. To its northeast, at a distance of 10–12 km, there are a couple of mountains with a height of 500–600 m. Airflow disturbances arising from terrain disruption may bring about significant turbulence to aircraft landing at or departing from HKIA. Following the requirement of the International Civil Aviation Organization (ICAO), the turbulence intensity in aviation is quantified in terms of the cube root of eddy dissipation rate (EDR), ε. Forecasting of EDR1/3 by numerical weather prediction (NWP) models would be useful in the provision of turbulence alerting services to aircraft.
Chan (2009) demonstrated that the forecasting of EDR1/3 in typical cases of terrain-disrupted airflow around HKIA was possible by running the Regional Atmospheric Modelling System (RAMS) (Cotton et al. 2003) version 6.0 at high spatial resolution. The innermost model domain had a horizontal resolution of 50–200 m. The forecasting results had been shown to depend very much on the choice of the turbulence parameterization scheme. It turned out that the Deardorff scheme appeared to have the best performance in the selected cases. In RAMS 6.0, there were also a couple of new turbulence parameterization schemes available, such as the e-l [turbulent kinetic energy (TKE) − mixing length] scheme of Trini Castelli et al. (2005). However, this scheme was found to give too much turbulence near the ground and EDR1/3 dropped too rapidly with altitude in comparison with the other turbulence schemes and actual measurements.
The effect of vertical gridding;
Possibility of false alarm, namely, whether the model simulation would give larger EDR1/3 than actual measurements, especially in light turbulence situation; and
Performance of model simulation in forecasting other metrics of turbulence intensity for aviation application, e.g. TKE.
The above issues would also be examined in this paper based on case studies.
2 Meteorological equipment
Radar wind profilers only measure the vertical wind and turbulence profiles above their antennae. To give an overview of the wind patterns around HKIA arising from airflow disruption by complex terrain, two other types of remote-sensing equipment have also been used by HKO. For non-rainy weather condition, the Doppler light detection and ranging (LIDAR) systems are used to give the line-of-sight velocities up to a distance of 10 km away. Two LIDARs have been installed at HKIA (locations in Fig. 1), with each LIDAR monitoring a particular runway of the airport. They are identical and use infrared laser beam with a wavelength of about 2 μm to track the motion of aerosols in the air blown along with the winds. The range resolution is about 100 m and the accuracy of Doppler velocity measurement is within 1 m/s. Further technical details about the LIDAR systems could be found in Shun and Chan (2007).
The measurement range of LIDAR would be very much limited in rain or very humid weather due to attenuation of laser beams in suspending/falling water droplets. In such situations, the wind patterns around HKIA would be monitored by a terminal Doppler weather radar (TDWR) to the northeast of the airport (location in Fig. 1). This is a C-band microwave radar to measure the line-of-sight velocity by tracking the motion of water droplets in the air blown along with the wind. The range is about 90 km and the radial resolution is about 250 m. The lowest elevation scan, namely, elevation angle of 0.6° from horizon, is mostly used for detecting microburst and giving an overview of the wind situation inside and around HKIA. Further technical details of the TDWR could be found in Shun and Johnson (1995).
In order to assess the performance of numerical model in the simulation of other turbulence intensity metric for aviation application (such as TKE), the minisodar at shoreline anemometer site (location in Fig. 1) has also been considered in the present paper. The sodar emits acoustic waves with a frequency of 4.5 kHz. The measurement range is configured to be 200 m with a vertical resolution of 5 m starting from about 20 m above ground. Vertical profiles of the three components of the wind and TKE are available every 1 min. In the present paper, only the TKE profile would be considered.
3 Turbulence parameterization schemes and numerical model setup
To find out the performance of e-l scheme, simulations have also been made using the more conventional schemes available in RAMS, namely, Mellor–Yamada 2.5 scheme (Mellor and Yamada 1982) and Deardorff scheme (1980). Same turbulence parameterization schemes have been considered in the previous study (Chan 2009).
The model setup is similar to that in Chan (2009). The initial and boundary conditions for RAMS are obtained from a meso-scale operational regional spectral model (ORSM) of HKO. ORSM is a hydrostatic model with a horizontal resolution of 20 km. Sigma-p hybrid vertical co-ordinates are used with a model top of 10 hPa. There are 40 model levels in the vertical. Planetary boundary layer is handled in such a way that non-local specification of turbulent diffusion and counter-gradient transport in unstable boundary layer are considered. In case of rain, three-dimensional multivariate optimal interpolation is performed. The heating rate of the precipitation process is adjusted to correspond to the rainfall amount observed.
4 Summer monsoon case
A moderate southwest monsoon case on 1 July 2008 is studied. This is a typical situation of south to southwesterly flow over southern China in the summer time. The LIDAR measurements around HKIA at the time of interest (01:20 UTC on that day) are shown in Fig. 3a. It could be seen that the wind pattern around HKIA is not uniform. In the broadly southerly flow, there are streaks of higher and lower wind speeds coming out from Lantau Island. These streaks probably arise from the disruption of the southerly flow by the complex terrain (Chan 2007).
The numerical simulation starts at 00 UTC, 1 July 2008. The results at 01:20 UTC on that day are considered here. The model-simulated wind field using the e-l scheme with c μ = 0.4 is shown in Fig. 3b. The horizontal wind vector has been resolved and coloured with respect to the line-of-sight directions of one of the LIDAR systems for direct comparison with the actual observations (Fig. 3a). It could be seen that, apart from a slightly easterly component of the wind field (which comes from the outer meso-scale model), the general pattern of Doppler velocity is consistent with the LIDAR measurements. Velocity streaks show up in the simulation results as well. The successful capturing of such features is believed to result partly from the input of complex terrain around HKIA in high spatial resolution and the reasonable treatment of the sub-grid scale turbulence.
The turbulence intensity (EDR1/3) field from the model simulation is given in Fig. 3c. More turbulent flow (coloured light blue in Fig. 3c) extends up to 5–6 km downstream of Lantau Island. The turbulence is particularly strong just close to the downstream side of Lantau terrain. The overall turbulence pattern appears to be reasonable considering the mechanical generation of turbulence as the airflow impinges on the complex terrain.
5 Winter monsoon case
The model simulation starts at 00 UTC, 3 December 2008 and the results at 05:30 UTC on that day are analysed here. The model-simulated wind field using the e-l scheme with c μ = 0.4 is shown in Fig. 5b. It could be seen that, apart from the generally easterly flow, there is an area of southerly flow to the west of the HKA. The occurrence of the latter is generally consistent with the Doppler velocity field measured by the LIDAR (Fig. 5a), though the spatial extent of the southerly flow (arising from terrain disruption) may be exaggerated. This feature with RAMS simulation has also been reported in similar case study before (e.g. Chan and Cheung 2009).
The model-simulated EDR1/3 field at that time is given in Fig. 5c. More turbulent air is forecast downstream of Lantau Island. Once again, the result appears to be reasonable considering the mechanical generation of turbulence as the airflow impinges on Lantau terrain.
6 Spring-time easterly case
Easterly flow in a stable boundary layer also occurs in the spring time. Due to the mountainous terrain of Lantau Island, mountain wake and other terrain-induced airflow disturbances would appear in the vicinity of HKIA. The present case is similar to that discussed in Sect. 5, but with slightly higher wind speed for the easterly wind and thus more turbulent airflow just downstream of Lantau Island. This case is used to illustrate the performance of e-l scheme in slightly more turbulent airflow and the optimum value of c μ .
7 Tropical cyclone case
The model simulation starts at 06:00 UTC, 19 April 2008. The use of Mellor–Yamada scheme or Deardorff scheme manages to give simulation results at least for 12 h. However, e-l scheme is rather unstable no matter what the value of c μ was. Simulation could only be done up to about half an hour and afterwards the Courant–Friedrich–Levy (CFL) limit is exceeded. This situation appears for different choices of the time steps (e.g. even when the time step is reduced to a few seconds for the innermost domain of the simulation). However, from the model simulation results, it appears that the terrain disruption of the airflow has been developed to a considerable extent despite the rather short period of the model simulation. For instance, the model-simulated wind field using the e-l scheme with c μ = 0.4 is shown in Fig. 9b. In this case, the simulated radial velocity of the TDWR is depicted. It could be seen that there are streaks of higher and lower wind speeds in the easterly flow downstream of Lantau Island, and the results are generally consistent with the actual TDWR observations. Please note that Fig. 9a refers to the line-of-sight velocity with respect to the TDWR only, but not the full 2D velocity vector, which is not measured directly with the radar.
The model-simulated EDR1/3 field at that time is given in Fig. 9c. Compared with the winter-time case in Sect. 5, the turbulence intensity is much higher downstream of the mountains in the present case. This is possibly related to the mechanical generation of stronger turbulence in higher wind speed.
The study of the performance of e-l scheme in tropical cyclone situation may be limited because of the short simulation time (about half an hour) that could be achieved. The wind field may not have been fully adapted to the terrain for the innermost domain (in which the Lantau Island is present). The results in the present section should be interpreted with that perspective. Model simulation has been performed for this tropical cyclone case at an earlier time, e.g. 12 h ago (starting from 18 UTC, 18 April 2008). The resulting wind and turbulence fields are similar to those presented in this paper. Simulations starting at even earlier time have not been attempted because the forecast locations of the tropical cyclone with respect to Hong Kong in ORSM become rather different from that predicted in the run starting at 06 UTC, 19 April 2008.
8 Optimal value of c μ
The “optimal” c μ value giving the smallest r.m.s differences is about 0.4–0.45. This is consistent with the results in the literature (between 0.40 and 0.55).
The r.m.s. differences are much greater for the tropical cyclone case than the moderate wind cases.
The r.m.s. differences between the model-simulated EDR1/3 profiles and the actual measurements from the wind profiler at Sha Lo Wan and Siu Ho Wan for the various turbulence parameterization schemes
e-l scheme (best performing)
Sha Lo Wan
19 April 2008
1 July 2008
3 December 2008
8 February 2010
Siu Ho Wan
19 April 2008
1 July 2008
3 December 2008
8 February 2010
For e-l scheme and Deardorff scheme, the r.m.s differences with actual observations are generally in the order of 0.03–0.07 m2/3 s−1 in moderate wind situation. This is still lesser than 0.1 m2/3 s−1. As such, the forecast EDR1/3 fields by these turbulence parameterization schemes could be useful in the monitoring of low-level turbulence in an area of complex terrain, which is a safety hazard to the aircraft. On the other hand, the performance in tropical cyclone cases is more questionable. The simulation results for Deardorff scheme could still be useful for the monitoring of low-level turbulence in the first few hundred metres or so, as discussed in Chan (2009). However, the results of e-l scheme should be treated with caution in view of the unreasonably large values of EDR1/3 near ground.
9 Effect of vertical gridding
In Chan (2009), a fixed vertical gridding is used for all model simulations, namely, with a stretching ratio of 1.15 according to the vertical gridding method of RAMS. As an illustration of the potential effect of vertical gridding on the simulation results of turbulence intensity profile, a case study is considered in this paper, namely, southerly winds in the morning of 1 July 2008. Moreover, for simplicity, only the Deardorff scheme is used in this case study. Three vertical griddings have been used, namely, with a stretching ratio of 1.15, 1.35 and 1.55.
The above features of turbulence distribution could largely be reproduced from RAMS simulations. The simulated EDR1/3 patterns with different vertical griddings are very similar, as shown in Fig. 12b–d. The height of about 300 m is considered in the model simulations, which is about the height of the location of light turbulence gap flow to the east of the airport.
10 Light turbulence case
The cases considered so far (in the present paper and in Chan 2009) are moderate to severe turbulence situations. In order to apply the model forecasting results to actual turbulence alerting, the possibility of producing false alarms from the model simulations has to be considered, for instance, for light turbulence situation, the model should not over-forecast the values of EDR1/3. In order to study this aspect, a light turbulence case is considered, namely, light to moderate northeasterly winds on 6 November 2009, when the southern China was under the influence of moderate northeast monsoon.
11 Simulation of TKE
The studies so far concentrate on EDR1/3, which is the intentionally adopted metric for turbulence intensity in aviation application. Other metrics have been considered for aviation purpose, such as TKE. The performance of RAMS in the simulation of TKE has also been examined in a couple of examples. Deardorff scheme is employed in all the simulations.
In order to assess the quality of the model-simulated TKE, the actual measurements by the minisodar at shoreline anemometer site has been considered. Data are available up to about 200 m above sea level, and they are plotted in Fig. 16a. Simulation is carried out starting from 00 UTC, 8 February 2010 and the simulation results after 3 h are used. The simulated TKE profile with a vertical gridding of the stretching ratio of 1.15 seems to be generally consistent with the actual measurements. This comparison result supports the use of the stretching ratio of 1.15 for the vertical gridding in the simulation study for easterly flow.
Another case is considered here is the stronger turbulence in the southerly wind case of 5 March 2010. Simulation is carried out starting from 00 UTC, 5 March 2010 and the simulation results after 7 h are considered. The sodar-measured profile and the model-simulated profile of TKE are compared in Fig. 16b. Again, the actual profile appears to be captured well by the model simulation (Deardorff scheme, stretching ratio of 1.15 for the vertical gridding), though the simulated results have higher values of TKE. The simulation results based on the stretching ratio of 1.15 for vertical gridding have the best comparison with the actual observations, which supports the selection of this stretching ratio value.
The minisodar with a measurement range of 200 m has been working at the airport since January 2010. More data would be collected for assessing the performance of RAMS simulations of TKE, e.g. in summer monsoon and tropical cyclone situations.
By choosing an optimal value of c μ and the use of variable asymptotic mixing length, the performance of e-l scheme could be comparable with the best-performing turbulence parameterization scheme as found in the previous study, namely, Deardorff (1980) scheme, for moderate winds.
Considering r.m.s. difference between the model-simulated results and the radar wind profiler measurements, the optimal value of c μ in the e-l scheme is found to be 0.4–0.45, which is consistent with the results in the literature.
The e-l scheme requires further improvements in strong wind situations, e.g. in association with tropical cyclones. Numerically, the scheme is very unstable in strong winds. Meteorologically, it gives unreasonably high EDR1/3 values near ground, which is not supported in the available observations. Please note that, for the simulations presented in this paper, the model-simulated wind and turbulence fields have been output every minute and such fields have been found to develop fully in general in response to the complex terrain at the Hong Kong International Airport (e.g. the horizontal extent of the wake downstream of the mountains on Lantau Island remains basically the same) though the simulation times are relatively short, particularly for the e-l scheme (apart from the tropical cyclone situation on 19 April 2008).
The Deardorff (1980) scheme is still found to be the most robust among the turbulence parameterization schemes available in RAMS. The only shortcoming is that, for strong winds in tropical cyclone situations, the EDR1/3 values fall with height too rapidly in comparison with actual observations. Nonetheless, the forecast EDR1/3 field is still found to be useful in the monitoring of low-level turbulence, which is a safety hazard to the aircraft. For this purpose, the e-l scheme (with an optimal value of c μ ) could also be used in moderate wind situations.
The Mellor–Yamada (1982) scheme is an ensemble 1D scheme that uses only vertical mixing. There is an issue of double counting of turbulence when the horizontal grid spacing is less than ~1 km. As such, it may have limitations in the application for model simulation with a horizontal resolution of 200 m in the innermost domain for the present study. Therefore, it is not surprising to see that the simulation results for EDR based on Mellor–Yamada (1982) scheme is not as good as the other turbulence schemes that consider 3D mixing, e.g. in the comparison with EDR profiles from radar wind profilers. Nonetheless, Mellor–Yamada (1982) scheme is found to be rather stable and, as found in the present study and in Chan (2009), appears to give a reasonable spatial distribution of EDR for terrain-disrupted airflow, though the magnitude of EDR is generally smaller in comparison with actual observations. On the other hand, for 3D mixing schemes such as Deardorff (1980) scheme and e-l scheme, the magnitude of the simulated EDR with a horizontal resolution of 200 m seems to be more reasonable compared with the wind profiler data. The vertical gridding has a size of several tens of metres to a couple of hundred metres, at least in the lower part of the boundary layer, and such a size of the vertical grids is comparable with the horizontal resolution. As such, the 3D mixing schemes work better in simulating the magnitude of turbulence intensity, as expected. However, these schemes are less stable and, particularly for the new e-l scheme, simulation may blow up for a forecasting period of half an hour to an hour in strong wind situation, e.g. in association with tropical cyclones. The stability of the scheme would need to be taken into account if day-to-day forecasting of terrain-induced turbulence is to be attempted, such as in aviation applications.
The choice of the vertical grid (in the case of RAMS, the choice of the stretching ratio) has an impact on the simulation of EDR1/3. Though the horizontal distribution of turbulence intensity does not change significantly, the different vertical gridding could affect the forecast magnitude of EDR1/3, and the selection made so far (stretching ratio of 1.15) appears to be a reasonable value in comparison with the actual EDR1/3 data.
Apart from moderate and severe turbulence cases, RAMS seems to have the capability to handle light turbulence situation as well. There does not appear to be over-forecast problem as demonstrated in a light turbulence case.
Based on results of limited case studies, the vertical TKE profile in the first 200 m or so above ground appears to be simulated well by the model, particularly for heights above 100 m, using a vertical gridding with a stretching ratio of 1.15. This provides further support that this choice of the stretching ratio is reasonable.
The author would like to thank Dr. Silvia Trini Castelli for useful discussions about the e-l turbulence parameterization scheme. The author is also grateful to the comments provided by the anonymous reviewers.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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