Development and mechanisms of the nocturnal jet

Development and mechanisms of the nocturnal jet P A Davies, Met. Office, London Road, Bracknell, Berkshire RG12 2SZ, UK Meteorol. Appl. 7, 239 246 (2000) Forecasting the occurrence and strength of the nocturnal jet is important to aviation, especially to balloonists and small aircraft. Jets also have implications for pollution transportation and the clearance of low cloud and fog. A one-dimensional model showed that the main mechanism for the development of the nocturnal jet was a hybrid between an inertial oscillation in a layer within and above the jet core and a quasi-steady jet within the inversion. The model, supported by observations, suggests that a nocturnal inversion is required to produce a jet and that the strength of the jet maximum is approximately 1.3 times the geostrophic wind. A wind profile minimum is also predicted to occur when the inertial oscillation reaches a minimum in the stress-free layer and this was observed using a tethered balloon flown at Cardington. 1. Introduction A jet is defined as a narrow current of fast-moving air. Jets exist at different heights in the troposphere with variations in strength, width and length. Perhaps the most common jet observed in the troposphere is the Jet Stream. This jet is located at the top of the troposphere with typical vertical shears of 5 to 10 m s 1 per kilometre and is usually thousands of kilometres in length, hundreds of kilometres in width and can be as strong as 100 m s 1. However, other jets exist much lower in the atmosphere and are often only some tens or hundreds of kilometres in length. These jets are usually referred to as Low Level Jets. In the past the term Low Level Jet (LLJ) has sometimes been applied indiscriminately to low level wind maxima in a variety of settings. On the one hand, the LLJ is used to describe a wind maximum which exhibits strong diurnal oscillation in height, speed and direction, and on the other hand it is also applied to synoptically driven wind maxima that extend beyond the boundary layer, as detected by Browning & Pardoe (1973) and Sortais et al. (1993). It was because of this confusion that Chen et al. (1994) called for a differentiation between these two broad types of jets. Chen et al. (1994) defined a Boundary Layer Jet (BLJ) as one which develops in the boundary layer with strong wind shear and strong diurnal variation, whereas a jet usually associated with synoptic or subsynoptic scale weather systems was defined as a Low Level Jet (LLJ). Furthermore, a BLJ has been observed in close association with an overhead inversion (Lapworth, 1987) and there is evidence that a BLJ can form over the sea (Smedman et al., 1993). This paper will concentrate on the nocturnal jet which can form at night when skies are clear, sometimes lasting until the middle of the next day. The nocturnal jet will be classified as a BLJ since it is often associated with strong wind shears and a nocturnal inversion (which exhibits strong diurnal variation). The jet maximum can be significantly supergeostrophic, in some cases one and a half times the geostrophic wind speed and the jet can exist a few hundreds of metres off the ground. An example of a nocturnal jet can be seen in Figure 1. The nocturnal jet and its associated vertical wind shear is an important factor in the safety of many aviation activities. A rapidly increasing, then decreasing headwind component could result in a difficult climb-out and, in some cases, result in unnecessary stress to the engine. Also relevant is the recent increase in ballooning activities with a steady growth in the number of commercial operations that have been set up across the UK. A balloon encountering a nocturnal jet would find a dramatic increase in speed at low level which would be accompanied by severe shear. This was highlighted in the author s own forecasting experience in March 1995 when a balloon was forced to land among pylons as it encountered severe shear associated with a nocturnal jet. The nocturnal jet is also relevant to the transport of pollutants after emission from a tall chimney, from a chemical incident or from car fumes or other pollutants found within or near the top of an inversion. The pollutants might find their way into a zone of fastmoving air associated with the jet and be carried several hundred kilometres downwind, even though the surface and gradient wind may remain light. Maddox (1983) even argued that the jet could be a significant factor in the initiation of severe storms by advecting warm moist air into the genesis region of the storm in the US. 239

P A Davies (a) Numerous theories have been proposed to explain the development and mechanisms for the nocturnal jet. These include an inertial oscillation due to frictional decoupling in the early evening (Blackadar, 1957) and Thorpe & Guymer (1977), stress divergence within the nocturnal inversion generating a quasi-steady jet (implied by the model of Nieuwstadt, 1984), baroclinicity produced in inclined boundary layers over the sloping terrain (Bonner & Paegle, 1970) and large-scale baroclinicity and interactions between upper-level jet streaks and diabatic processes associated with cyclogenesis (Johnson & Uccellini, 1979). However, if the terrain is flat then two main mechanisms, an inertial oscillation and a quasi-steady boundary layer, could potentially explain the jet. These two will be described in turn. 2.1. An inertial oscillation (b) Blackadar (1957) proposed the following scenario. If skies are clear then during the evening and night a nocturnal inversion will develop as the layer just above the surface cools. De-coupled from the surface, the layer immediately above the inversion is released of all frictional constraints. At or soon after sunset the ageostrophic component (which stems from the stress within the daytime boundary layer) undergoes an undamped inertial oscillation in the stress-free layer above the nocturnal inversion. The period of the rotation of the ageostrophic wind will remain constant in magnitude. The period is defined as 2π/f c where f c is the Coriolis parameter. Therefore, at 50 degrees latitude, the wind at the top of the inversion will become supergeostrophic (the nocturnal jet) about seven hours after sunset when the ageostrophic component is aligned with the geostrophic wind. Based on the above arguments, Thorpe & Guymer (1977) developed a simple slab model where the daytime boundary layer was split in two during the evening transition as described above. It was found that when the model was run for one night an inertial oscillation had taken place and this resulted in the development of a nocturnal jet. Figure 1. Sounding of (a) temperature and dew point and (b) wind speed at 0911 UTC on 21 November 1996. This shows a 28 knot nocturnal jet at 950 mb and its association with a nocturnal inversion. The purpose of this paper is to discuss some mechanisms for the development of the nocturnal jet using a simple one-dimensional model. Examples of nocturnal jets recorded using a tethered balloon at Cardington, near Bedford will also be shown. 2. Previous theories 240 2.2. A quasi-steady jet Mahrt (1981) showed that the strength of the jet may be related to the increasing stress divergence during the evening transition; the larger the stress divergence, the stronger the resulting nocturnal jet. An imbalance between the stress-divergence, pressure gradient force and Coriolis force is created as the stress divergence increases, causing an acceleration across the inversion. Nieuwstadt (1984) also showed that the stable layer associated with the nocturnal inversion reaches a steady state, and Derbyshire (1990) supported the Nieuwstadt quasi-steady assumption by showing that the gradient Richardson number reaches an asymptotic or critical value. It is because of this quasi-steady state within the stable layer that a nocturnal jet can exist within the nocturnal inversion (the large shear within the inversion would be responsible for forcing the Ekman-layer spiral into the jet profile at the top of the inversion). 2.3. Combined theory A combination of both of the above explanations might be used to describe the mechanisms of the nocturnal jet.

Development and mechanisms of the nocturnal jet Assuming no advection and ignoring the friction and gravity term, the momentum equation will be of the form: U ( uw ) = fc( V Vg) (1) V ( vw ) = fc( U Ug) (2) I II III where U and V are the wind components in the x and y directions, U g and V g are the corresponding components of the geostrophic, u w and v w are the vertical momentum fluxes in the x and y directions, and z is the height above the surface. Term I is the inertia term, II is the geostrophic departure term and III is the stress divergence term. These equations show that if the inertia, Term I, and geostrophic departure, Term II, are in balance then the main process responsible for the jet development is an inertial oscillation of the ageostrophic component (Blackadar, 1957; Thorpe & Guymer, 1977). However, if the geostrophic departure Term II is in balance with the stress divergence Term III, then the main mechanism driving the jet is the strong shear across the inversion resulting in a quasi-steady jet, as in the theoretical model of Nieuwstadt (1984). 3. Model calculations and observations A simple one-dimensional model was used with the aim of discovering the mechanisms of the nocturnal jet and to see if the results compare favourably with observed jets recorded at Cardington. This first-order closure model incorporated a strong Richardson number (Ri) dependence in its formulation and cut off all turbulent transport for Ri greater than the critical Richardson number (Ri c ) of 0.25. A description of the model can be found in the Appendix. 3.1. Characteristics of the nocturnal jet using model results and observations from Cardington The one-dimensional model was run for 5 10 4 seconds (about 14 hours, a typical winter s night) with results collected every 10 4 seconds (about 3 hours). The surface temperature was allowed to fall from 20 C to 0 C with the geostrophic wind set at 10 m s 1. A time sequence of the u-component of a developing nocturnal jet is shown Figure 2. The jet reaches its maximum strength of 13 m s 1 (26 knots) equivalent to 1.3 U g after about seven or eight hours. Figure 2. Time sequence of the speed of the u-component of wind. The jet reaches a maximum strength at about 7 hours (1.3U g ) with a minimum developing above the nocturnal inversion 15 hours after sunset. Observational evidence for the existence of a jet comparable with model results can be found on the morning of 16 September 1996 (see Figure 3). The geostrophic wind was measured at 8 knots and skies were largely clear during the night. The jet maximum was found to be 1.3U g as predicted by the model and the maximum is aligned where the potential temperature gradient ( θ /) is largest (the jet would breakdown very quickly if there was not enough stability to support the shear associated with the jet maximum). No nocturnal jets were observed at Cardington when skies remained cloudy and no inversions were present. Therefore, skies must be clear in order for both an inversion and the resulting jet to develop. A jet is also unlikely to develop near the coast when the winds are onshore since air originating from the sea will exhibit little diurnal variation in temperature. (A sample of 1400 ascents from Hemsby, 2 km from the North Sea in East Anglia, showed that when winds were southwesterly (offshore), 64% of ascents at midnight recorded a nocturnal inversion. However, when winds were north-easterly (onshore) only 8% of midnight ascents recorded an inversion.) It can be seen from Figure 2 that a minimum had developed at 150 m, around 14 to 15 hours after sunset. Interestingly, this is equivalent to a full inertial oscillation. A concave profile in the wind profile above daytime elevated stable layers (overhead inversions) has been observed at Cardington (Lapworth, 1987) when the inertial oscillation reached a minimum. An example of a nocturnal jet with a large minimum above the jet core occurred on 11 April 1996 (see Figure 4). The jet maximum was observed to be 16 knots which was 1.3U g and again the jet was associated where θ / was large. The results in this paper do support Thorpe & Guymer s ideas of a two-layered structure within the 241

P A Davies (a) (a) (b) (b) Figure 3. Sounding of (a) temperature and dew point, and (b) wind speed at 0715 UTC on 16 September 1996. The jet is aligned where the potential gradient, which can be inferred from the temperature profile, is largest with a clear minimum above the jet core. Figure 4. Sounding of (a) temperature and dew point, and (b) wind speed at 0708 UTC on 11 April 1996. This is a good example of a large minimum occurring above the jet maximum. nocturnal boundary layer (an inversion with a stressfree layer above) and also the existence of a jet of similar magnitude (1.3U g ) seven hours after sunset, although their model did indicate that a jet may not exist after 10 clear hours as the inertial oscillation would be expected to move towards a minimum and the flow in the upper layer would become subgeostrophic (a minimum of around 0.6U g between 15 and 16 hours after sunset). The structure of the nocturnal jet also depends on the depth of the inversion. If the geostrophic wind (U g ) remains constant then a reduced cooling rate would lead to a deeper nocturnal inversion and a broader jet (the momentum and heat flux would be felt over a larger part of the boundary layer as there would not be enough stability in the developing nocturnal inversion 242 to prevent turbulent mixing through shear). In other words, the height of the jet maximum and also the height of the nocturnal inversion would be expected to increase as the cooling rate decreases. However, model results suggest that the jet maximum remains roughly constant at 1.3U g despite a marked increase in stability associated with a shallower inversion due to an increased cooling rate. The size of the jet minimum also depends on the rate of surface cooling as this will determine the magnitude of the eddy viscosity above the jet maximum. 3.2. Possible mechanism of the nocturnal jet The momentum balance across the boundary layer after 5 10 4 seconds is shown in Figure 5. The domi-

Development and mechanisms of the nocturnal jet Figure 5. Model momentum balance across a nocturnal jet after 50000 seconds. This shows that the mechanism of super-geostrophy (layer B) could be a hybrid between an inertial oscillation and a quasi-steady jet. The dominant mechanism above the jet (layer A) is an inertial oscillation, whereas below the jet (layer C) there is no inertial oscillation since the inertial term is zero. nant mechanism above the jet (layer A) is an inertial oscillation (the inertial term V/ is in balance with the geostrophic departure term f(u U g )), whereas below the jet (layer C) there is no inertial oscillation since the inertial term is zero. However, within the jet itself (layer B) there is a contribution from both processes indicating that the modelled jet is in fact a hybrid between an oscillating jet and a quasi-steady jet. Smedman et al. (1993) also showed that energy production was through shear in a thin layer above the jet and in areas from the jet maximum to the surface. The stress divergence in the v-direction for the same time (see Figure 6) is positive from 70 m and below, but associated with the super-geostrophy in the u-direction is a negative component of the stress divergence. Equations (1) and (2) show that the stress divergence in one direction affects the wind speed in the perpendicular direction and it is this negative component of stress divergence which is responsible for the formation of the jet. The evolution above the jet maximum is solely inertial and this allows an oscillation to take place. 4. Conclusions The prevalence of a nocturnal jet is now widely accepted. However, reliable and detailed boundary layer observations, such as turbulence measurements (which are required to explain fully the mechanism of the jet), are still few in number. One of the major advantages of using a simple model that incorporates a parameterisation of the boundary layer turbulence based on sound and detailed observational evidence is that it allows the user to focus on the physics of the nocturnal jet. It is for this reason that a simple onedimensional model was used with the results from the model verified against wind and temperature data collected by a tethered balloon flown at Cardington. The mechanism of the jet is found to be a hybrid between an oscillating jet, as proposed by Thorpe & Guymer (1977), and a quasi-steady jet as discussed by Nieuwstadt (1984). A jet minimum was also found to occur in the layer above the jet maximum and this antijet was found to change shape in response to an inertial oscillation. Lapworth (1987) showed that a minimum can occur in jets found through a boundary-layer capped inversion. The physics for its development is thought to be similar to that found in the nocturnal case. The following points may be of value to forecasters in predicting the occurrence and strength of the nocturnal jet. (a) There should be sufficient radiative cooling (clear skies) to allow a nocturnal inversion to develop. A fully developed jet is likely to breakdown through turbulent mixing if the stability across the jet is unable to absorb the turbulence generated by the jet (through vertical wind shear). This is why a nocturnal jet needs to co-exist with an inversion. (b) When the length of the night is equal to half of the inertial period 2π/f c, the strength of the jet maximum is predicted to be 1.3 times the geostrophic wind (U g ). However, the jet is still expected to exist with a maximum of 1.1U g when the length of night is equal to a full inertial period (i.e. when the inertial oscillation moves towards a minimum). (c) A jet could be stronger than 1.3U g if there is an increase in local pressure gradients, for example, funnelling of the wind flow into a valley. 243

P A Davies Figure 6. Model stress divergence fields across the boundary layer after 50000 seconds showing a negative component of stress divergence associated with the jet. (d) If the geostrophic wind is too strong, it will destroy the nocturnal inversion; if it is too light, it will produce a weak jet. (e) The frequency of jet occurrences is expected to be lower when winds are onshore. The air originating from the sea will have little diurnal variation and therefore will be unable to produce a nocturnal inversion. (f) The structure of the surface may also determine the strength of the jet. If the geostrophic wind remains constant but the surface roughness increases, then the jet would also increase. Acknowledgements The research reported in this paper was accomplished as part of a MSc degree supported by the Meteorological Office and supervised by Professor Trevor Davies (Climate Research Unit, University of East Anglia) and Dr Steve Derbyshire (APR, Met. Office, Bracknell). I would particularly like to thank both my supervisors for all their support (Dr Derbyshire supplied the one-dimensional model which was used extensively in this paper). In addition, I would like to thank a number of my colleagues and associates for their comments and suggestions, particularly all the staff at Hemsby for collecting unprocessed radiosonde data during 1996. such as shear across inversions or from buoyancy forces such as surface heating due to insolation. Richardson derived a dimensionless ratio of the rate of consumption of turbulent kinetic energy by working against gravity to the production associated with vertical wind shear. Rf = Consumption Production where Rf is referred to as the Flux Richardson Number : Rf = ( ) ( ) + ( ) g w θv θv uw U vw V where: g is the acceleration due to gravity. θ v is the virtual potential temperature. U and V are the wind speeds in the x and y direction. z is the height above the surface. w θ v is the kinematic potential temperature (heat) flux in the vertical. u w and v w are the kinematic flux of the U and V momentum in the vertical respectively. Appendix. Boundary layer model of the nocturnal jet A one-dimensional boundary layer model is used here to describe the behaviour of a turbulent fluid. The sources of turbulence originate from mechanical forces 244 However, if we define: g Ri = θ v θv 2 2 U V z +

Development and mechanisms of the nocturnal jet then Rf Ri F = h Fm where Rf and Ri are the Flux and Local Richardson Number and F h and F m are the stability coefficents for the heat and momentum flux. Experimental results suggest low turbulence intensities for Critical Richardson Number, Ri c > 0.25. Nieuwstadt (1984) showed evidence that Ri reaches an asymptotic value around 0.2 throughout the nocturnal boundary layer. This is consistent with a turbulence closure in which turbulence cuts off at Ri ~ 0.25. Neglecting any large-scale advection term the momentum equation is of the form: U τ xz = fv ( Vg ) (A1) V τ yz = fu ( Ug ) (A2) where U g and V g is the geostrophic wind in the x and y direction, τ is the Reynolds stress and z is the height above the surface. By definition, the Reynold s stress τ is given by: τ xz τ yz = ρu w = ρv w (A3) (A4) where u w and v w are the vertical momentum fluxes in the x and y directions. Therefore replacing the stress term in equations (A1) and (A2) with equations (A3) and (A4) gives: U ( uw ) = fv ( Vg ) V ( vw ) = fu ( Ug ) I II III (A5) (A6) Term I is the inertia term, II is the geostrophic departure term and III is the stress divergence term. The unknowns in equations (A5) and (A6) are the momentum fluxes u w and v w, so to close the above set of equations, we must parameterise the turbulent fluxes. This assumes that the geostrophic wind is known as a prescribed boundary condition. The above expressions can be closed by assuming a relationship between the turbulent flux and the gradient of the associated mean variables. This is known as K-theory. ζ ujζ = K x where ζ can be wind, potential temperature or humidity. Therefore, for a positive K the flux flows down the local gradient of ζ. This assumption can be used to parameterize and to close the set of equations above, such that for momentum flux: K m, known as the eddy viscosity, is a function of flow and will vary as the flow and stability vary. Thus, one must parameterize K m as a function of other variables such as the Richardson number. This, when compared with equations (A7) and (A8) leads to the final expression for calculating momentum flux: where l is the neutral mixing length, being representative of the scale of the individual eddy motions; F m (Ri) a stability function which is dependent on the Richardson number, U/ and V/ are the components of the shear. Equation (A9) indicates that the magnitude of K m should increase as the shear increases (a measure of the turbulence) and as the mixing length increases (a measure of the ability of turbulence to cause mixing). However the function of stability F m for Ri 0 is empirically specified. Observations from an extended version of the dataset (Derbyshire, 1995) show a linear dependence of a non-dimensional mixing length l m /z on Ri (see Figure A1). The stability function takes the form: In the model used in this paper the stability function describing the momentum flux F m (Ri) will be the same for the heat flux F h (Ri) as found by Webb (1970) at moderate stability, except that in this thesis Ric is taken as 0.25 as compared to 0.2. The modelled jet was found to be sensitive to the choice j U ( uw ) = K m (A7) V ( vw ) = K m (A8) 2 2 K = 2 U V l F ( m m Ri ) z + (A9) Ri Fm ( Ri)= 1 Ri c 2 245

P A Davies Figure A1. A linear dependence of a non-dimensional mixing length (l m /z) against Richardson number (Ri). Observations from an extended dataset (Derbyshire, 1995). of both physical and model parameters. The choice of stability function does have a significant effect on the strength and shape of a resulting nocturnal jet. The stability function used in the current Met. Office operational Unified Model scheme is: This displays a very smooth and weak jet of 10.62 m s 1 as compared to 11.9 m s 1 with the geostrophic wind set to 10 m s 1, although owing to the simplifications made, this comparison should be viewed purely as a sensitivity test. References F ( m Ri )= 1 (1 + 10 Ri) Blackadar, A. K. (1957). Boundary layer maxima and their signifcance for the growth of nocturnal inversions. Bull. Am. Meteorol. Soc., 38: 283 290. Bonner, W. D. (1966). Case study of thunderstorm activity in relatiothe low level jet. Mon. Wea. Rev., 99: 167 178. Bonner, W. D. & Paegle, J. (1970). Diurnal variations in boundary layer winds over the south central United States in summer. Mon. Wea. Rev., 98: 735 744. Browning, K. A. & Pardoe, C. W. (1973). Structure of lowlevel jet streams ahead of mid-latitude cold fronts. Q. J. R. Meteorol. Soc., 99: 619 638. Chen, Y. L., Chen, X. A. & Zhang, Y. X. (1994). Diagnostic study of the low level jet during TAMEX IOP 5. Mon. Wea. Rev., 122: 2257 2284. Corsmeier, U., Kalthoff, N., Kolle, O., Kotzian, M, & Fiedler, F. (1997). Ozone concentration jump in the stable nocturnal boundary layer during a LLJ-event. Atmos. Environ., 31: 1977 1989. Derbyshire, S. H. (1990). Nieuwstadt s stable boundary-layer revisited. Q. J. R. Meteorol. Soc., 116: 127 158. Derbyshire, S. H. (1994). A balanced approach to stable boundary layer dynamics. J. Atmos. Sci., 51: 3486 3504. Johnson, D. R & Uccellini, L. W. (1979). The coupling of upper and lower tropospheric jet streaks and implications for the developmen of severe convective storms. Mon. Wea. Rev., 107: 682 703. Lapworth, A. J. (1987). Wind profiles through boundarylayer capping inversions. Boundary Layer Meteorol., 39: 333 378. Maddox, R. A. (1983). Large-scale meteorological conditions associated with mid-latitude mesoscale convective complexes. Mon. Wea. Rev., 111: 1475 1493. Mahrt, L. (1981). The early evening boundary-layer transition. Q. J. R. Meteorol. Soc., 107: 329 344. Nieuwstadt, F. T. M. (1984). The turbulent structure of the stable boundary-layer. J. Atmos. Sci., 41: 2202 2216. Smedman, A., Tjerstrom, M. & Hogstrom, U. (1993). Analysis of the turbulence structure of a barine low level jet. Boundary Layer Meteorol., 66: 105 126. Sortais, J. L, Cammas, J. P, Yu, X. D. & Rosset, R. (1993). A case study of coupling between low and upper level jet front systems: Investigation of dynamical and diabatic processes. Mon. Wea. Rev., 121: 2239 2253. Thorpe, A. J. & Guymer, T. H. (1977). The nocturnal jet. Q. J. R. Meteorol. Soc., 103: 633 653. Webb, E. K. (1970). Profile relationships: the log-linear range, and extension to strong stability. Q. J. R. Meteorol. Soc., 96: 67 90. Wyngaard, J. K. (1973). On surface-layer turbulence. In Workshop on Micrometeorology, Am. Meteorol. Soc. Crown Copyright 2000 246