Summary of experiments

Special Project Interim Report Moist Singular Vectors and African Easterly Waves Summary of Results June 2008 R. J. Cornforth and B. J. Hoskins Department of Meteorology, University of Reading, UK 1 Summary of experiments In this last year we have used the ECMWF MSV package to see whether perturbations that were likely to grow into African easterly waves (AEWs), could be successfully identified given the assumption of linearity and the standard total dry energy metric. Trajectories were based on dates when meridional wind speeds in regional hovmoellers exceeded 1.5 ms−1 in the analyses. These dates ranged between the beginning of July and the middle of September 2006 to test the validity of the linearity assumption throughout the monsoon period. Early dry periods were sampled when the AEWs could be expected to behave more linearly and then compared to AEWs which grew later during the monsoon, when more non-linear behaviour would be expected given the dominance of moist processes. Figure 1: Evolution during JJAS2006 of the vertical profile of relative humidity (a) at Niamey. Evolution of the dry air characteristics (b) at 500 hPa in the East Sahel box [0-10E; 10-15N] as provided by the back trajectory analysis, for the areal fraction with RH below 5% and the areal fraction with latitude origin greater than 40N. Source: Lafore, Demi and Roca (2007, pers comms). The 2006 WAM dynamical onset occurred around the 25 June but with a delay in the active monsoon precipitation until mid-July. June through to the middle of July (05-06 to 15-07) was thus predominantly warmer and drier than usual with suppressed convection particularly around Niamey, possibly associated with the MJO, leaving the air dry and warm up to 3 Km as can be seen in Fig. 1. Two non-developing AEWs evolved, reaching the Greenwich Meridian (GM) on the 8th (W1) and 12th July (W2). The first developing AEW (W3) grew around 27◦ E on 13th July, reaching the GM on the 16th July before transforming into TC Chris over the Atlantic. The synoptic situation during W3’s evolution shows a dry mid-troposphere marked 1 by a thin moist layer around 5 Km with some further moistening below this. Singular vector trajectories based on 13th July 2006 are presented in this results summary as it is an example of a more linear regime. From mid-July to mid-September, the dry atmosphere became progressively moistened and moderate wave activity developed. In August the waves were initiated further west between 10 and 20E, but were still weak over Niamey (2.12◦ E and 13.52◦ N). From the end of August, the waves were stronger and became more coherent with several starting further east between 20 and 30E. Singular vector trajectories were run for 3 of the waves during this period with their starting dates based on each wave exhibiting a minimum curvature vorticity of 0.3x10−5 s−1 . The sensitivity of the MSVs to these starting dates has yet to be explored. Here we discuss the results for AEW 20 only as it is likely to be a good example of a highly non-linear AEW, and as shown in Fig. ??fig:wam, develops in the peak of the monsoon with deep moistening throughout the lower troposphere, in contrast to W3’s situation. W20 originated around 20◦ E on the 3rd September, reaching the GM by the 7th. On leaving the coast, W20 immediately showed signs of developing into a tropical cyclone, The wave became a tropical depression just south-south east of the Cape Verde Islands on the 12th September, eventually becoming TC Helene, the 4th and strongest hurricane of the 2006 season, peaking on the 18th September. Trajectories are presented here for the 6th September which provides continuity with other research within the AMMA community and with the later phases for the project when the impact of SV perturbations targeted on West Africa on TC track forecasts will be evaluated. Figure 2: Hovmoeller plots from 00 UTC 1st July to 12 UTC 26th September 2006 using 00 UTC and 12 UTC data for daily precipitation from CPC/NCEP/NOAA, computed by merging satellite estimate and raingauge data. The Hovmoeller plots are averaged over (a) 15 to 20◦ N; and (b) 6 to 16◦ N, the regions transected by the easterly waves used as case studies here. The dashed boxes represent their respective time-periods. The West African coast is at approximately 15◦ W. The experiments are summarised in Table 1 with the control experiments for W3 and W20 in boldface. Sensitivity studies were conducted to determine any key factors which might lead to improvements in the identification of the AEWs. These included: • the model physics (different cycles) • length of time for which the perturbation grew (OTI) • the trajectory date (and time; 12 UTC) • the region (projection operator) • the metric used to measure the perturbation (norm) (TBD) 2 Table 1: Summary of Experiments Experiment Name Cycle 32R1 b0im 20060703 b0io 20060710 b0ip 20060712 b0ku 20060713 b0ix 20060717 b0iz 20060721 Cycle 32R3 b0jl 20060713 b0jm 20060713 b0k3 20060713 b0k7 20060713 b0jr 20060728 b0js 20060728 b0jw 20060801 b0jx 20060804 b0jp 20060906 b0jq 20060906 b0ju 20060909 b0jv 20060909 b0k4 20060906 b0k6 20060906 Cycle 32R3 Forecasts b0k1 20060713 Trajectory Defn 12UTC 3rd July 12UTC 10th July 12UTC 12th July 12UTC 13th July 12UTC 17th July 12UTC 21st July 12UTC 13th July 12UTC 13th July 12UTC 13th July 12UTC 13th July 12UTC 28th July 12UTC 28th July 12UTC 1st Aug 12UTC 4th Aug 12UTC 6th Sept 12UTC 6th Sept 12UTC 9th Sept 12UTC 9th Sept 12UTC 6th Sept 12UTC 6th Sep t Wave Identifier W1 W2 W3 W3 W4 W6 W3 W3 W3 W3 W7 W7 W9 W9 W20 W20 W20 W20 W20 W20 Initial/Final Norms TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED TED/TED Projection Operator Lat ◦ N Lon ◦ E 5 5 5 5 5 5 to to to to to to 25 25 25 25 25 25 25 25 20 20 25 25 25 25 25 25 25 25 20 20 -35 -35 -35 -35 -35 -35 to to to to to to 35 35 35 35 35 35 OTI hrs 24 24 24 24 24 24 24 48 24 24 24 48 24 48 24 48 24 48 24 24 5 to 5 to 5 to 5 to 5 to 5 to 5 to 5 to 5 to 5 to 5 to 5 to 5 to 5 to -35 to 35 -35 to 35 -20 to 30 -20 to 15 -35 to 35 -35 to 35 -35 to 35 -35 to 35 -35 to 35 -35 to 35 -35 to 35 -35 to 35 -20 to 30 -20 to 15 Evolving from 13th July W3 TED/TED 5 to 25 -35 to 35 48 • the size of the initial perturbation in the forecast model (linear versus non-linear) All experiments use ECMWF’s new full physics linearized SV package. This includes vertical diffusion, surface drag, gravity wave drag, large-scale condensation, OLR and deep cumulus convection. The control cycle is 32R3 and is set up with 62 levels, a time step of 30 mins. and T95 truncation, which is sufficient to resolve the AEWs given their wavelength of approximately 2500 Km. Vertical capping is applied between 500 and 1000 mb and no diffusion. In the control, the projection operator is set between 5 - 25◦ N, and 35◦ W - 35◦ E. Results from W3 and W20 will be presented here, given the contrast in their synoptic environments and the different precipitation regimes during the courses of their evolution. These are indicated in the hovmoellers averaged over the propagation regions of W3 and W20 in Figs. 2(a,b) respectively. The results will include a comparison with analyses and normal-mode theory of the amplification factors, initial and final times energy profiles, energy spectra, and horizontal structures of W3 and W20. Discussion will focus 3 on the optimum experimental conditions in which to use ECMWF’s MSV package to generate AEW-like perturbations, what success is likely given these conditions and finally whether the linearity assumption and use of the total dry energy metric is applicable for AEWs through the duration of the WAM. The choice of case studies (W3 and W20) ensures continuity with the AMMA community’s preferred case studies and, since both these AEWs transformed into tropical cyclones over the Atlantic, continuity with the latter part of the project in which we determine whether the forecast skill of the full forecast model can be improved for TC tracks if the EPS is initialised with perturbations which include AEWs. 2 Quantifying improvements in forecast skill using MSV One of the first challenges that this project generated was in determining how well AEWs are currently forecast in the ECWMF operational model and to find a suitable metric for evaluating any changes in skill to this forecast using the moist singular vector approach. One idea was to use the objective analysis technique for identifying AEWs as described in Berry and Thorncroft (2006). This technique uses curvature vorticity, a diagnostic based on the 700-hPa streamfunction field which separates out and retains the vorticity associated with the AEW compared with that associated with the AEJ shear. This facilitates a completely objective comparison between AEWs with different structures on multiple scales (Berry and Thorncroft, 2006). Agusti-Panaredi and Beljaars (2008) have recently analysed the 2006 AEWs using this diagnostic with code provided by Gareth Berry. They calculated the RMS error of curvature vorticity for forecasts at different lead times as shown in Fig. 3. At 48 hours, the analysis is noisy and at 72 hours, the RMSE has a similar magnitude to the curvature vorticity associated with the AEWs themselves. The deterioration in the forecasts was linked to the lack of meso-scale convective systems represented in the forecasts. The smaller error associated with the boxes centred on 15 ◦ W is probably associated with the general increase in the AEWs ampltiudes as they propagate westwards and approach the coast. Figure 3: RMS error of 700 mb curvature vorticity from ECMWF forecasts at different lead times, averaged over boxes centred on 15◦ W, 0◦ W and 15◦ E. Source: Agusti-Panareda and Beljaars, ECMWF Newsletter, Spring 2008. This analysis provided a useful yard-stick for assessing the overall skill of the ECMWF forecast in the region but this project requires a method for evaluating the singular vector package on the forecasts of individual AEWs. A collaboration has thus been set up with Kevin Hodges at the ESSC to see whether it would be possible to adapt his novel method for tracking mid-latitude storms as described in (Hodges and Hoskins, 2006) to tracking individual easterly waves and comparing them with track forecasts based on singular vector perturbations. Different fields at 700, 800 and 850 mb levels were plotted in hovmoellers 4 averaged over different transects of West Africa to determine the cleanest signal for tracking AEWs given both their low-level more northerly amplitudes around 19◦ N (Cornforth et al., 2008) and their jet-level amplitudes around 14◦ N. Fig. 4(a) shows that the 700 mb meridional wind captures the essence of the midlevel AEWs more strongly than relative vorticity which can be clouded by meso-scale convective systems. This result is similar to recent work by Sanders and Jones (2008) applied to the Deutscher Wetterdienst (DWD). Figure 4: Hovmoeller plots from 00 UTC 1st July to 12 UTC 26th September 2006 using 00 UTC and 12 UTC data. (a) Meridional wind at 700 mb and (b) at 850 mb; (c) relative vorticity ay 700 mb. The West African coast is at approximately 15◦ W. Figure 5: African easterly wave tracks generated from the 2 to 6 day filtered meridional wind at 700 mb using 00, 06, 12 and 18UTC data from the periods between (a) 10th-19th July 2006; and (b) 3rd-16th September 2006. The 10 day forecasts are shown in panels (c) and (d) starting from 12 UTC on 13th July and 6th September respectively. Figures courtesy of Kevin Hodges, ESSC. The 700 mb meridional wind was input to the tracking algorithm and after trying different approaches 5 (Fourier versus Lanczos smoothing, 2-6 d versus 2-10 d filtering), individual easterly waves were successfully tracked. Figs. 5(a) and (b) track W3 and W20, and their 10 d forecasts are shown in (c) and (d) respectively. There are still a number of questions we need to resolve such as why the forecasts tend to displace the tracks polewards just before the coast and how to deal with the many meridional mergers of isolated potential vorticity structures with the borad cross-jet easterly wave structures that occur as an easterly wave tracks east-west across the region, but we have every confidence that an automated tracking system and means for quantitatively assessing the MSV approach is a real possibility. We aim to compare the tracks with the reanalysis data from AMMA 2006 as it becomes available, and to plot the tracks using curvature vorticity instead so that the objective analysis technique of Berry and Thorncroft (2006) may be evaluated for ECMWF. 3 3.1 Results for W3: Early monsoon period Basic state We begin our analysis with a consideration of the large-scale flow for the period 10th-19th July, during which W3 grew. The AEJ maximum in Fig. 6(a) is clearly defined at 700 mb, extending out over the eastern Atlantic. The jet axis tilts northwestwards towards the poles but is centred around 13◦ N with maximum values of -14 ms−1 at the west coast of Africa. A split in the jet occurs as the maximum extends north-east along the coast following the PV maximum on the 315 K isentrope indicated in Fig.6(b), associated with the intrusion of a mid-latitude trough during this period. A strip of high PV extends westwards from just east of the Greenwich Meridian, around Niamey. This strip results in a local reversal of the meridional PV gradient. As this is co-located with the positive meridional temperature gradient (fig. 6(c), this mean basic state can support baroclinic and barotropic growth of AEWs. The maximum in equivalent potential temperature lies southwards of the potential temperature maximum because of the combined influence of the cooler but moist southwesterly flow and the hotter dry Saharan air to the north. 3.2 Amplification factors The mixed barotropic-baroclinic growth potential of the mean state is reflected in the amplification of the moist singular vectors shown in Fig.7 for the first ten singular vectors for the control run and all the sensitivity cases for W3. The amplification factor is defined as the ratio between the perturbation norm (the square root of the total dry energy inner product) at the initial time and the perturbation norm at the final time. The perturbation growth in the presence of moist processes is positive but significantly reduced by a factor of 5 compared with MSV growth in mid-latitudes (Hoskins and Coutinho, 2004). This maybe partly associated with the greater stability of the new moist physics SV package used in cycle 32R3 and partly associated with the different mechanisms for growth of AEW-like perturbations on an AEJ. This is also suggested by the reduced amplification rates compared with Hoskins and Coutinho (2004) despite the increase to a T95 truncation which would be expected to allow an even better representation of the full physics processes at smaller scales, reflected in an increased growthrate. The maximum growth occurs consistently for the first 2 SVs in all the experiments, as discussed in Coutinho et al. (2003), and it is therefore these first few SVs that exhibit the greatest change that we will focus on in this report. Doubling the optimization time from 24 h to 48 h, generally increases the growth rates for all the SVs but not proportionally so. The increase is less for the higher SVs. Reducing the region of perturbation growth through the projection operator, nominally reduces the growth rates of all SVs as mid-latitude troughs are excluded along the more northerly boundary. 6 Figure 6: 10th-19th July 2006 mean zonal mean fields, averaged using 00 and 12 UTC analysis times. (a) Zonal wind at 700 mb, contoured every 2 m s−1 and shaded below -8 m s−1 ; (b) Ertel potential vorticity on the 315 K isentrope, contoured every 0.05 PVU (1 PVU = 1 x 10−6 K Kg−1 m−2 s−1 ) and shaded above 0.1 PVU; (c) Potential temperature at 925 mb, contoured every 2 K and shaded above 306 K; (d) Equivalent potential temperature at 925 mb, contoured every 4 K and shaded above 346 K. Figure 7: Amplification factors of the first 10 singular vectors for w3 (more linear case study, warm coloured lines) and w20 (more non-linear case study, cool coloured lines) with full moist physics, truncation T95 and cycle 32R3. The amplification factors for a range of different sensitivities are shown: The control runs for w3 and w20 are denoted by solid triangles, optimisation times of 24h and 48h for each case are denoted by squares; changes to the projection operator are denoted by diamonds and circles; and a different initialization date within the w20 case study, is denoted by a non-filled triangle. 7 When the region is further confined in a longitudinal direction to the main development region for AEWs, as suggested by the analysis of Hopsch et al. (2007), the growth rate of SV2 for W3 increases relative to the control and the experiment in which the projection operator is reduced initially. This indicates that targeting the projection operator to the waves’ main development region appears to enhance the growth of cleaner AEW-like perturbations. 3.3 Energy profiles and spectra Figure 8: Initial (black) and final (red) time energy profiles (a) and spectra (b) averaged for the first ten singular vectors of w3 for an OTI of 24 h. (a) Total (solid) and kinetic energy (dashed) profiles as a function of pressure; and (b) spectral distribution as a function of total wavenumber of the total energy. The mean vertical distribution of total energy for the first ten SVs for the control experiment for W3 is shown in Fig. 8(a). Both the initial (black solid line) and final (red solid line) profiles exhibit peaks at upper (Model Level 20 is equivalent to 205 mb) and mid-levels (ML 44≡765 mb, ML 42≡712 mb) though the final time mid-level peak splits further into peaks at 712 mb and 899 mb. These echo AEWs with amplitudes both at 700 and 850 mb. The upper level peak at 200 mb is likely to be associated with the mid-latitude trough that penetrated this region at this time. The profile contrasts with the mid-latitude case studies in which there is a tropopause peak as the initial perturbation increases in energy through its westward tilted component propagating upwards to the tropopause (Badger and Hoskins, 2001). This again suggests a different growth mechanism operating compared with the mid-latitudes. Figure 9: Initial (black) and final (red) time energy profiles and spectra for SV1, for w3 for an OTI of 24 h. (a) Total energy (solid) lines and kinetic energy (dashed) profiles as a function of pressure; and (b) spectral distribution as a function of total wavenumber of the total energy. 8 The mean total energy spectra for the first ten SVs for the W3 control at initial (black solid line) and final times (red solid line) is shown alongside its energy profile in Fig. 8. The spectra peaks around wavenumber 20 (wavelength of 2000 Km). This is consistent with the recent dry linear instability study by Cornforth et al. (2008) and with observations of AEWs with shorter wavelengths during dry periods (Thorncroft et al., 2003), similar to the synoptic conditions of this case study. It is also consistent with Eady’s baroclinic theory using physically relevant scales for West Africa (see Cornforth et al., 2008). A very small upscale cascade of energy to smaller wavelengths (larger wavenumbers) occurs over the optimization time of 24 h as a result of the physical processes acting in the full moist physics SV package. The energy profile and spectra for SV1 for W3 is shown in Fig. 9 for comparison. The lower-mid-levels dominate its energy profile and there is a clearer shift in its spectrum to smaller scales at the final time from wavenumber 25 to 30. As it exhibits AEW-like characteristics and amplifies the most over 24h, the structure of this SV will be analyzed in more detail. Increasing the optimization time to 48 h results in a doubling in the total energy at the final time and the mid-level peak at 700 mb dominating the total energy profile for W3’s first SV as shown in Fig. 10(a). Figure 10: Initial (black) and final (red) time energy profiles (a) and spectra (b) averaged for SV1, for w3 at an OTI of 48 h. (a) Total (solid) and kinetic energy (dashed) profiles as a function of pressure; and (b) spectral distribution as a function of total wavenumber of the total energy. Figure 11: Initial (black) and final (red) time energy profiles (a) and spectra (b) for SV1 of w3 with an OTI of 24h and a projection operator targeted on the region, 5N-20N, 20W-30E. In (a) total (solid) and kinetic energy (dashed) profiles as a function of pressure; and (b) spectral distribution as a function of total wavenumber of the total energy. 9 In an effort to optimise the growth of AEW-like perturbations and exclude the influence of any midlatitude troughs that have penetrated the region, the optimization area was reduced in a meridional direction from 25 to 20◦ N (Fig. 11). This reduced the total energy exhibited at upper levels in the mean energy profiles. Its impact on the total energy profiles of SV1 was minimal however, consistent with the likelihood of SV1 representing an AEW-like perturbation in association with its two lower energy peaks and not being influenced by the MLT at upper levels. One further reduction in the projection operator, this time in its longitudinal extent from 30◦ E to 15◦ E, targeted the optimization region specifically on the main development region of the AEWs (Hopsch et al., 2007), just east of the Greenwich meridian. This made no further impact on the profiles or spectra for the first ten SVs or indeed, on SV1 and are therefore not shown here. 3.4 Geographical distributions and structure Figure 12: Geographical distribution of the vertically integrated energy of the first singular vector at the (a) initial and (b) final time for the control set-up for W3 for an OTI of 24 h. In Figs. 12(a) and (b), the geographical distribution of the first SV for W3 at the initial and final times is shown. This is the vertically integrated amplification factor weighted sum of its kinetic and potential energy. According to Eady’s baroclinic theory, a doubling in the total energy of the SV would be expected in a day. Here the SV’s magnitude increases 15-fold however, far more than predicted. Comparing the distribution of the initial and final time maxima with the 24 h average baroclinicity index for the same period in Fig. 13(a), shows that the perturbation grows in a region outside of the baroclinic maximum. At final time, both maxima, denoted 1 and 2, have moved downstream but to a region of similar or lower baroclinicity. This is comparable to Hoskins et al. (2000) in which structures moved downstream from regions of high baroclinicity to ones of lower baroclinicity as they grew, and indicates some role for baroclinic processes in the perturbations growth. If the initial and final time locations are compared with the basic state Ertel PV for the same period as shown in Figs. 13(c) and (d), the perturbations grow in the region of negative meridional PV gradients and move downstream into regions of zero PV. This suggests that part of the perturbation growth may be attributed to barotropic growth in which the SV tilts against the horizontal shear (Buizza and Palmer, 1999). We shall develop a barotropic index similar to that for baroclinicity in order to evaluate this more thoroughly. It is important to investigate this further as it is not clear-cut how the perturbations are growing, and how this will change from linear to more non-linear situations. The positions of W3’s first singular vector maxima have also been superimposed on the basic state total column water vapour at the initial and final times as shown in Figs. 14(a) and (b) respectively. Although the perturbations appear to be growing in the region of low total column water vapour they move downstream towards the local maxima in moisture and 10 Figure 13: (a) 24 h average baroclinicity (12th-13th July 2006) and (b) basic state Ertel PV at the initial time on the 13th July at 12UTC and (c) at the final time on the 14th July at 12 UTC. The black numerals denote the locations of the SV maxima at initial time, the light blue at final time. Figure 14: The basic state total column water vapour at (a) the initial time (13th July) and (b) final time (14th July) at 12 UTC along the steep surface gradient of equivalent potential temperature gradient (cf. Fig. 6). The perturbations may thus be using the moisture funnelled inland in the south westerlies at low levels to grow despite this air being cooler. In mid-latitudes, large-scale condensation is important to the growth of the SVs (Coutinho et al., 2003) but it is not obvious that this will be the case here given that the cooler air in this region is actually the more moist air. It may also be that the MSVs are sensitive to something other than the total dry energy and we need to use another metric such as Lq, a dynamic soil moisture or reflect the dust-radiative changes to the surface fluxes. Horizontal cross-sections of the 700 mb meridional wind for SV1 are presented in Figs. 15(a) and (b) at the initial and final times respectively. The observed horizontal wind field is shown below in Fig. 16 for comparison, with W3 developing around 22◦ E on 13th July and moving downstream to 18◦ E by the 14th. It is encouraging that the location and structure of W3’s first singular vector is consistent with observations of W3. This supports the hypothesis drawn from the analysis of SV1’s energy profile with the two lower peaks being consistent with an AEW-like perturbation. The additional twist in both the SV and observed wave structure to the north is the result of the superpositioning of an eastward propagating wave across the 11 Figure 15: Horizontal cross-sections of the meridional wind at 700 mb for the first singular vector in the control run at (a) the initial time and (b) the final time for an OTI of 24 h. north Africa coast associated with a mid-latitude trough. Figure 16: The basic state meridional wind at 700 mb at (a) the initial time (13th July) and (b) the final time (14th July) at 12 UTC Analysis of SV between 6 and 10 show components further east towards the Red Sea. Reducing the longitudinal-latitudinal extent of the projection operator, removes these. The caveat to this optimization is the potential reduction in forecast lead times for AEWs as such perturbations may act as AEWs precursors. 4 4.1 Results for case study 2: Peak monsoon period Basic state The large-scale flow for W20, our second and contrasting case study, is averaged over the easterly wave’s evolution between 3rd and 16th September. The AEJ maximum in Fig. 17(a) is slightly weaker at -12 ms−1 but distributed over a larger area with a more zonal structure compared with the July period. It is again clearly defined at 700 mb and extends out over the eastern Atlantic. Its axis is tilted again but centered further north around 16◦ N, consistent with the progression of the monsoon and the movement of the ITCZ. Its maximum tracks the similarly more zonal Ertel PV maximum on the jet’s equatorwards flank as shown in Fig. 17(b)) on the 315 K isentrope. The strip of high PV extends further east than before resulting in a local reversal of the meridional PV gradient. This is co-located with the positive meridional temperature gradient which is also displaced polewards and extends zonally over a greater longitudinal region (fig. 17(c). As before this mean basic state can support baroclinic and barotropic growth of AEWs and its greater longitudinal extent eastwards suggests that the AEWs will grow further east of the Greenwich Meridian, with the jet entrance region situated around 15◦ E. This is demonstrated in the Hovmoeller of the meridional wind in 12 Fig.??(a). The maximum in equivalent potential temperature (theta-e) has increased and lies further east though still southwards of the potential temperature maximum. Figure 17: 3rd-16th September 2006 mean zonal mean fields, averaged using 00 and 12 UTC analysis times. (a) Zonal wind at 700 mb, contoured every 2 m s−1 and shaded below -8 m s−1 ; (b) Ertel potential vorticity on the 315 K isentrope, contoured every 0.05 PVU (1 PVU = 1 x 10−6 K Kg−1 m−2 s−1 ) and shaded above 0.1 PVU; (c) Potential temperature at 925 mb, contoured every 2 K and shaded above 306 K; (d) Equivalent potential temperature at 925 mb, contoured every 4 K and shaded above 302 K (cf. the July basic state). 4.2 Amplification factors The amplification factors for the set of experiments basing their trajectories on W20, are reduced compared with those for W3 (Fig. 7). For an optimization time of 24 h, the maximum amplification occurs for a trajectory initialised not on the 6th September, but 3 days later when the AEW reaches its maximum amplitude in the hovmoeller plot (Fig.??(a)). Doubling the optimization time to 48 h, similarly increases the amplification factor to W3 but again, not proportionately so. W20 evolves during the peak monsoon period and transforms into a strong TC and as such should be utilizing the moist physics package to grow strongly. The reduced amplification factors for W20, compared with W3 however, suggests that the MSVs are sensitive to something other than the total dry energy, one which accounts for the initial moisture distribution. This will be explored in subsequent work. The maximum changes in the SVs are seen in the first 3 SVs and these will thus be presented in more detail below. 4.3 Energy profiles and spectra The mean vertical distribution of total energy for the first ten SVs for the control experiment for W20 is shown in Fig. 18(a). Similar to W3, the mean energy profile exhibits upper and mid-level peaks but at slightly lower levels at the initial and final times (264 cf. 205 mb, 765 mb cf. 712 mb). The upper level peak is stronger and in contrast to W3, dominates the initial and final time profiles of the first SV (Fig. 19(a)). 13 Figure 18: Initial (black) and final (red) time energy profiles in (a) and spectra in (b) averaged for the first ten singular vectors. (a) Total (solid) and kinetic energy (dashed) profiles as a function of pressure; and (b) spectral distribution as a function of total wavenumber of the total energy for w20 for an OTI of 24 h. The lower peak in the mean which is consistent with an AEW-like perturbation, gains energy in the third SV, as shown in Fig. 19(b). There is no apparent upwards propagation in energy at final time in the mean distribution indicative of a different growth mechanism operating compared with the mid-latitudes. The mean energy spectra for the first 10 SVs shown in Fig. 18(b) shows a small upscale transfer of energy at the final time but an overall reduction in total energy suggesting the optimization time needs to be longer for W20 especially if the total dry energy metric is not optimal here. Figure 19: Initial (black) and final (red) time energy profiles as a function of pressure for SV1 and SV3 for w20 for an OTI of 24 h. Total energy is shown as solid lines and kinetic energy as dashed. The upper level energy peak in SV1 is associated with a wavenumber of 20 as shown in Fig. 20(a). This is similar to the peak for SV3 in Fig. 20(b) but the SV3 spectra has an inflection around wavenumber 13 (equivalent to a wavelength of 3000 Km) which is similar to observed AEW wavelengths during the full monsoon. If the OTI is increased to 48 h, the lower peak in SV3 around 765 mb grows at the expense of the upper peak (Fig. 21(b)), and its spectral distribution shifts downscale to peak around the previous inflexion point at wavenumber 13 (Fig. 22(b)). This continues to contrasts with SV1’s spectral distribution which remains centred around the higher wavenumber of 25, and whose upper level peak in the energy profile (Fig. 21(a)) only strengthens. These results support the findings for W3, a relatively dry wave in comparison with W20. The lower 14 Figure 20: Initial (black) and final (red) time energy spectral distribution of SV1 and SV3 for w20 for an OTI of 24 h as a function of total wavenumber of the total energy. Figure 21: Initial (black) and final (red) time energy profiles as a function of pressure of SV1 and SV3 for w20 for an OTI of 48 h. Total energy is shown as solid lines and kinetic energy as dashed. Figure 22: Initial (black) and final (red) time energy spectral distribution of SV1 and SV3 for w20 for an OTI of 48 h as a function of total wavenumber of the total energy. 700 mb peak in its first SV was associated with a spectral peak around wavenumber 25. Over 48 h, moist processes act more strongly in W20, given its more moist synoptic situation. This triggers SV3’s 700 mb peak to strengthen and as it does, its spectral distribution peaks around wavenumber 13 at the expense of wavenumber 20. These findings are consistent with observations of wavelengths in dry periods versus full 15 monsoon periods (Grist et al., 2002) and with idealised modeling experiments in Cornforth et al. (2008) in which moist processes caused an inherent natural variability in the wavelength associated with AEWs, and in which shorter wavelengths were associated with the dry modelled AEWs. Changing the optimization area for the SVs, whilst maintaining an OTI of 24 h, had a significant impact on the first three SVs’ distributions of total energy and their spectra, in contrast to the lack of sensitivity shown by W3. Figure 23: Initial (black) and final (red) time energy profiles as a function of pressure of SV1 and SV3 for w20 for an OTI of 24 h and a projection operator targeted on a latitudinally-reduced optimization region of 5N-20N and 20W-30E. Total energy is shown as solid lines and kinetic energy as dashed. Reducing the area by 5◦ in the meridional direction and 5◦ longitudinally, decreased the total energy at upper levels for SV1 and generated a new lower peak around 765 mb. In contrast, the lower peak in SV3 diminished in preference to a new upper level peak (Fig.23. The spectra shifted accordingly as shown in Fig. 24 with SV1 gaining an inflexion around wavenumber 13 and SV3 losing its inflexion and peaking solely around wavenumber 25. This is consistent with the hypothesis above relating the upper level peaks to wavenumber 25 and the 700 mb peaks to wavenumber 13 during moist periods. Figure 24: Initial (black) and final (red) time spectra for SV1 and SV3 for W20 for an OTI of 24 h and a projection operator targeted on a latitudinally-reduced optimization region of region, 5N-20N, 20W-30E. The spectral distribution are shown as a function of total wavenumber of the total energy. A further reduction of the optimization region, had little impact on SV1 other than reducing its total energy, but resulted in the upper level peak being excluded from SV3 (Fig. 25, note the change of scale on the total energy axis). Interestingly, SV3’s energy spectra still peaks around wavenumber 25. This suggests 16 Figure 25: Initial (black) and final (red) time energy profiles as a function of pressure of SV1 and SV3 for w20 for an OTI of 24 h and a projection operator targeted on a further reduced optimization region of 5-20N and 20W-15E. Total energy is shown as solid lines and kinetic energy as dashed. that maybe a moisture source that contributes to its growth has now been excluded geographically so that the lower peak exhibits only characteristics of the drier AEW-like perturbations (Fig. 26. Figure 26: Initial (black) and final (red) time spectra for SV1 and SV3 for W20 for an OTI of 24 h and a projection operator targeted on a further reduced optimization region of 5-20N and 20W-15E. The spectral distribution are shown as a function of total wavenumber of the total energy. A further sensitivity experiment tested the choice of trajectory date with the experiment being moved forward in time to when W20 had grown to a significant amplitude and therefore exhibited more non-linear behaviour. The trajectory was initialized on 9th September when observations showed W20 was approaching the coast. Both SV1 and SV3 exhibit strong low-level peaks around 765 mb at the initial time (Fig. 28, characteristic of an AEW-like perturbation. At final time however, SV1 has less total energy whilst SV3’s growth has increased significantly and, for the first time, has moved to the tropopause, similar to midlatitudes. This suggests a different growth mechanism is now operating (cf. Badger and Hoskins, 2001) which may result from the increased non-linearity. The total energy spectra for SV3 is multi-modal once more (Fig. 28) but it is hard to understand without further experiments to elucidate the growth mechanisms. 17 Figure 27: Initial (black) and final (red) time energy profiles as a function of pressure of SV1 and SV3 for w20 for an OTI of 24 h, with the trajectory initialised 3 days later on 9th September 2006 at a time of peak wave activity. Total energy is shown as solid lines and kinetic energy as dashed. Figure 28: Initial (black) and final (red) time spectra for SV1 and SV3 for W20 for an OTI of 24 h, with the trajectory initialised 3 days later on 9th September 2006 at a time of peak wave activity. The spectral distribution are shown as a function of total wavenumber of the total energy. 4.4 Geographical distributions and structure In Fig. 29, the geographical distribution of the first SV and third SVs for W20 at the initial and final times are shown for comparison given that SV1 only exhibited an upper level peak in its energy profile whilst SV3 had both upper- and lower level components. SV1 distribution is centered further north and maybe growing in association with an eastward propagating disturbance passing through the region at the same time that W20 was growing. SV3 is situated around 15◦ N in the storm track of the easterly waves. SV3 at the final time is 2.5 times larger than at the initial time which is more consistent with Eady’s baroclinic theory, which predicts a doubling in total energy over a day, than compared with W3. To validate whether baroclinic processes are contributing to the SVs growth, the distribution of the initial maxima (denoted by 1 and 5) and final time maxima (denoted by 2 and 6) for SV1 and SV3 respectively, are compared with the 24 h average baroclinicity index for the same period in Fig. 30(a), shows that the perturbation grows in a region outside of the baroclinic maximum. At final time, both maxima, denoted 1 and 5, have moved downstream to a region of similar or lower baroclinicity which suggests that baroclinic processes have some, but by no means exclusive, role in the growth of perturbations, similar to W3. If the initial and final time locations are compared with the basic state Ertel PV for the same period as 18 Figure 29: Geographical distribution of the vertically integrated energy of the first and third singular vectors at the (a, c) initial and (b, d) final times for the control set-up for AEW 20 for an OTI of 24 h. shown in Figs. 30(b) and (c), the perturbations grow in the region of negative meridional PV gradients and move downstream into regions of zero PV. This suggests that part of the perturbation growth may again be attributed to barotropic growth in which the SV tilts against the horizontal shear (Buizza and Palmer, 1999). Inspection of the Ertel PV shows that SV3 is situated in an AEW trough, with its characteristic inverted-V signature centered around 12◦ N and predominantly on the equatorwards flank of the AEJ (Fig.17). The SV1 Figure 30: (a) 24 h average baroclinicity (6th-7th July 2006); and basic state Ertel PV for (b) 6th September, and (c) 7th September at 12 UTC and SV3 maxima at initial and final times have also been superimposed on the basic state total column water vapour as shown in Figs. 31(a) and (b) respectively. Similar to W3, the perturbations appear to be growing in the region of lower total column water vapour but moving downstream towards the local moisture maxima 19 in moisture. In mid-latitudes, large-scale condensation is important to the growth of the SVs (Coutinho et Figure 31: The basic state total column water vapour at (a) the initial time (6th July) and (b) final time (7th July) at 12 UTC al., 2003) but it is not obvious that this will is the case here given that the cooler air in this region is actually the more moist air. It may also be that the MSVs are sensitive to something other than the total dry energy and we need to use another metric such as Lq, a dynamic soil moisture or reflect the dust-radiative changes that impact the surface fluxes. This is consistent with the lower amplification factors calculated for W20 compared with W3 (see Fig. 7). Figure 32: Horizontal cross-sections of the meridional wind at 700 mb for the first and third singular vectors in the control run for W20 at the initial (a, c) and final (b, d) times for an OTI of 24 h. Horizontal cross-sections of the 700 mb meridional wind for SV1 and SV3 are presented in Figs. 32(a) and (b) at the initial and final times respectively. The observed horizontal wind field is shown below in Fig. 33 for comparison, with W20 developing around 5◦ E on 6th September and moving downstream towards the Greenwich Meridian by the 7th. It is again encouraging that having seen a lower peak at the appropriate energy level, SV3 yields similar horizontal structures and locations to W20 at the initial time and final times. Unfortunately this has dissipated after an OTI of 24 h, as forewarned by its total energy spectra in Fig. 22 for example. Increasing the OTI to 48 h, strengthened SV3’s lower peak and its final total energy was greater, but as can be seen in Fig.34, the AEW-like perturbation has dissipated in preference for some structure located 20 Figure 33: The basic state meridional wind at 700 mb at (a) the initial time (6th September) and (b) the final time (7th September) at 12 UTC on the west banks of the Nile. This may in fact be the precursor to W21 which is retained in preference to W20. This may be due to different growth mechanisms operating. The total dry energy metric may still be relevant to W21 in its early stages but the maturing W20 may need a metric which accounts for the initial moisture distribution Figure 34: Horizontal cross-sections of the meridional wind at 700 mb for the first and third singular vectors for W20 at the initial and final times for an OTI of 48 h. Reducing the optimization region, filters out the perturbation growing to the east and SV1 in Fig.35 closely resembles W20 at initial and final times, though suffers a dissipation of energy at the final time. This is consistent with the new peak appearing for SV1 at lower levels in its energy profile. SV3 conversely, loses this marked lower peak and fails to generate an AEW-like perturbation. The filtering of the eastern component may be detrimental in a forecast however, as this may be a precursor to the next AEW. A further longitudinal reduction in the optimization region to target the main development region of AEWs, is advantageous as it strengthens the AEW-like component in both SV1 and SV3 as shown in Fig. 36. In one final sensitivity experiment, the trajectory was initialized in the maturing stages of W20 as it approached the west coast. The first SV fails to pick up W20 perturbations but instead generates perturbations near the Nile at the initial time. These have total energy peaks at 765 mb which is likely to be associated 21 Figure 35: Horizontal cross-sections of the meridional wind at 700 mb for the first and third singular vectors for W20 for an OTI of 24h and a projection operator targeted on a reduced longitudinal-latitudinal region, 5N-20N, 20W-30E at initial (a, c) and final (b, d) times. Figure 36: Horizontal cross-sections of the meridional wind at 700 mb for the first and third singular vectors for W20 at the initial (a, c) and final (b, d) times for an OTI of 24h and a projection operator targeted on a further reduced longitudinal-latitudinal region, 5N-20N, 20W-15E. with an AEW-like perturbation, given the previous experiments. In the analysis these disturbances in the meridional wind field do eventually evolve into W22 (Fig. 38(a)). There is some dissipation of the SV1 perturbation at the final time (Fig. 37(b)) however. SV3 generated an AEW-like perturbation in the correct location at the initial time as shown in Fig. 37(c) and comparing with the 700 mb meridional wind from the analysis in Fig. 38(a). This is consistent with the strong low-level peak in its total energy profile in Fig. 27(b). SV3 weakens considerably in this location at 700 mb after 24 h (Fig. 38(b)). Since the final time 22 total energy profile showed an upward propagation of the SV3’s total energy profile (Fig. 27(b), red solid line), the SV3 amplitude may have dissipated to an upper levels (cf. Badger and Hoskins, 2001). Figure 37: Horizontal cross-sections of the meridional wind at 700 mb for the first and third singular vectors for W20 at the initial (a, c) and final (b, d) times for an OTI of 24h and a trajectory initialized 3 days later on 9th September. Figure 38: The basic state meridional wind at 700 mb at (a) the initial time (9th September) and (b) the final time (10th September) at 12 UTC 5 Summary and future work The MSV approach has generated AEW-like perturbations both in the earlier dry period of the WAM and during its peak, consistent with the case studies selected. It is also encouraging that using trajectories based on the early stages of developing AEWs, the SV perturbations exhibited similar propagation characteristics to the case studies over a 24 h and 48 h optimization time. With an optimum choice of initial parameters (projection operator, OTI, trajectory date), the SV structures were co-located with the AEWs in the analysis and exhibited peaks in their total energy profiles in the lower and mid-troposphere, around 765 mb. SVs with peaks at upper levels tended to grow in association with mid-latitude troughs to the north of the main development region of the AEWs. Reducing the projection operator in a latitudinal direction helped to 23 strengthen the lower energy peaks. Some SVs had amplitude in the region of NE Africa, towards the Nile. These could be removed by reducing the longitudinal extent of the projection operator, but in the analyses these more easterly perturbations often subsequently developed into an AEW. This may have important ramifications for the forecast skill so needs to be applied with discretion. A 48 h OTI is likely to be used in future experiments as this longer optimization time allowed the SV to gain more energy in the relevant lower levels considering the reduced amplification factors attained here in the tropics with this new more stable moist physics package compared with the mid-latitudes and earlier model cycles. One further interesting aspect to this work has been the multi-modal energy spectra peak, with maxima or inflexion points variously at wavenumbers 13 or in a range between 20-24. The earlier drier wave’s spectra tended to peak at the higher wavenumbers around 20. This is equivalent to a wavelength of 2000 Km, consistent with Eady’s baroclinic theory with relevant African parameters input and a recent dry normal mode instability analysis (for both, see Cornforth et al., 2008) and observations from drier periods during the monsoon (Thorncroft et al., 2003; and Grist et al., 2002) . more variability was shown however for the more moist wave, W20. Its lower 700 mb peak in its energy profile for the first SV was associated with a spectral peak around wavenumber 20. When an OTI of 48 h was used instead, the 700 mb peak strengthened and as it did, the spectral distribution shifted to peak around wavenumber 13. Although this needs further investigation, recent idealised modeling experiments by Cornforth et al. (2008) showed that moist processes caused an inherent natural variability in the wavelength associated with AEWs, and shorter wavelengths were associated with the dry, more adiabatic modelled AEWs. This is consistent with our findings thus far. More work will now be undertaken to understand the MSV growth mechanisms in this region. Although baroclinic and barotropic processes played some part in their growth, it seems that the MSVs are sensitive to something other than the total dry energy metric. The reduced amplification factors for W20 compared with the drier W3 for example, is consistent with this. This will be explored by introducing a moist metric and comparing the characteristics of the SVs using optimum initial conditions to see if the use of a moist metric leads to different growth mechanisms. Linear and non-linear integrations will be conducted with both metrics to evaluate the validity of the linear approximation. In conjunction with this MSV work, the means for individual tracking of AEWs and assessing forecast skill using MSVs will coninue to be developed with Kevin Hodges. 24