1. Introduction
Cumulus convection has long been recognized as one of the fundamental processes in the atmosphere and considerable effort has gone into understanding and modeling convection. For climate and global numerical weather prediction systems this effort has been concentrated on the development of cumulus parameterizations, where the subgrid-scale forcing tendencies are defined in terms of the grid-scale parameters. For the convective heating and moistening tendencies the cumulus parameterization schemes have become extremely sophisticated, incorporating features like relaxed adjustments to some quasi-equilibrium states (Betts and Miller 1986; Moorthi and Suarez 1999; Kain and Fritsch 1993), microphysics effects (Donner et al. 2001), buoyancy sorting (Emanuel 1991, hereafter E91), prognostic closure schemes (Emanuel and Zivkovic-Rothman 1999; Pan and Randall 1998), and stochastic closure algorithms (Lin and Neelin 2002). This list is certainly not exhaustive and the reader is referred to Arakawa’s (2004) excellent review of cumulus parameterization for a complete overview of the state of the science in this research area.
In contrast to the increased sophistication of the heating and moistening tendencies in cumulus parameterizations, the treatment of the cumulus momentum transport (CMT) in global model parameterizations has varied greatly (Carr and Bretherton 2001) ranging from no treatment of CMT, as in the standard Arakawa–Schubert scheme (Arakawa and Cheng 1993) and the National Center for Atmospheric Research (NCAR) Community Climate Model (Kiehl et al. 1996), to treatments that include in-cloud pressure gradients and cloud momentum entrainment (Tiedtke 1993; Gregory et al. 1997).
Many observational and numerical studies have recognized the large influence of CMT both in the Tropics and in the midlatitudes. One of the earliest was Houze (1973), who found that the scale of the cumulus momentum transport is the same as the vertical turbulent momentum fluxes. Many later studies over different regions have confirmed the results of Houze (Sanders and Emanuel 1977; Stevens 1979; LeMone 1983; Flatau and Stevens 1987; Gallus and Johnson 1992). Complete reviews of the budget and observational studies are given in the excellent papers by Wu and Yanai (1994) and Carr and Bretherton (2001).
The purpose of this paper is to report on the data assimilation and medium-range forecast experiments using the Navy Operational Global Atmospheric Prediction System (NOGAPS) with various settings of the CMT parameter and certain regional configurations of CMT in the Emanuel cumulus parameterization scheme. The results show that tropical cyclone (TC) track forecasts in NOGAPS are very sensitive to the presence and amount of the CMT. Most of the improvement in the TC track forecast appears to be due to CMT in the immediate vicinity of the TC, but from a statistical point of view, CMT not in the immediate vicinity of the cyclone also plays a role in the overall improvement of the TC track forecasts. Section 2 provides a brief description of the NOGAPS data assimilation/medium-range forecast tests and the manner in which the formulation of CMT in the Emanuel cumulus parameterization allows the magnitude of the tendency to be controlled. The mathematical and numerical formulation of the Emanuel cumulus parameterization’s CMT formulation, which has not been previously described, is given in the appendix. Section 3 presents the results of six data assimilation/medium-range forecast experiments over the period August–September 2004. Four of the experiments explore the sensitivity of the Emanuel parameterization’s CMT parameter. Two additional experiments explore the impact of replacing the sophisticated CMT formulation with a simple vertical mixing algorithm. Section 4 describes two additional experiments, one where the CMT is limited to the immediate vicinity of a TC, and the other where CMT is set to zero near a TC but allowed in the region away from the immediate influence of a TC. The paper concludes with a brief summary and conclusions of the experiments.
2. Description of the NOGAPS data assimilation/medium-range forecast tests
NOGAPS is the U.S. Department of Defense’s high-resolution global numerical weather prediction system. A description of the current status of the spectral forecast model component of NOGAPS is given in Peng et al. (2004). The data assimilation component of NOGAPS is the Navy Atmospheric Variational Data Assimilation System (NAVDAS; Daley and Barker 2001), which is a three-dimensional variational data assimilation system formulated in observation space. The data assimilation and medium-range forecast tests conducted in this study were run in a mode nearly identical to the operational data assimilation run, with a 6-h assimilation cycle performed at 0000, 0600, 1200, and 1800 UTC. NAVDAS comprises a three-dimensional variational wind, temperature, and moisture analysis of conventional and satellite data, with synthetic soundings in the vicinity of a warned TC (Goerss and Jeffries 1994). Sea surface temperature and sea ice concentrations are from U.S. Navy analyses. The data window is ±3 h about the analysis time. However, unlike operations, where 6-day forecasts are run every 6 h, 5-day (120 h) forecasts were run twice a day from the 0000 and 1200 UTC initial (analysis) conditions. The resolution of all the tests is T239L30 (a triangular truncation of 239 waves, corresponding to 0.5° resolution, and 30 levels in the vertical with a pressure top of 1.0 hPa), which is the same as the operational forecasts.
As with all NOGAPS NWP runs, standard statistical scores were computed for the medium-range forecasts. These included mean errors (individual and monthly mean), root-mean-square errors (RMSEs), anomaly correlations (ACs), and comparisons with radiosondes. For this study, two additional diagnostic programs were developed to diagnose the tropical performance of the test runs. The first was a sea level pressure tracking program that tracks all surface lows that are 1015 hPa or less. Throughout the study this diagnostic program was used to compute the TC tracks and compare the position of the forecasted track to the position of the warning location. The second diagnostic program located all 850-hPa cyclonic vorticity maxima in the forecast at every 12-h forecast interval and in the analysis in the tropical region 35°S–35°N with a magnitude greater than 5.0 × 10−5 s−1. Each forecast vorticity was binned as either forecasted early, forecasted on time, forecasted late, forecasted a false alarm, or did not forecast a vortex (a miss). The criterion for a hit is ±6 h of the analysis; the criterion for early and late is within 48 h of the analysis. The forecast vortex must also be within 4.0° of the analyzed vortex in order to be binned as a hit, early, or late forecast. Both diagnostic packages contain a simple statistical test analysis (Student’s t test) to gauge the significance of the results.
As explained in the appendix, the CMT formulation in the Emanuel parameterization code contains a tunable factor (1 − Cu) that is multiplied by the maximum potential zonal wind tendency [Eq. (A8)]. Since the code, which is available both from K. Emanuel and from the lead author, uses the factor (1 − Cu), this naming convention is retained throughout the paper. The value of Cu = 0.00 corresponds to full CMT as computed by the parameterization, while Cu = 1.00 corresponds to no CMT. In the initial implementation of the Emanuel parameterization into NOGAPS in May 2002 the value of Cu was set to 0.7. With the introduction of radiance assimilation into the NOGAPS analysis (Baker and Campbell 2005) in May 2004, the value of Cu was changed to 0.5. In the current operational NOGAPS (July 2006), Cu is 0.25 and the reason for this change is based on the results described in section 3. In that section the sensitivity of this parameter to the TC track forecasts is explored by showing results for four different values of Cu. An additional test is discussed in which Cu = 1.00 (i.e., no CMT) and in its place a simple diffusion algorithm is used to mix the winds in the presence of convection. Section 4 presents results of tests in which Cu is set to 0.0 and to 1.0 in the vicinity of tropical storms.
3. Sensitivity tests of the CMT parameter Cu and comparison with wind diffusion
The period for the data assimilation/medium-range forecast testing in this study is August–September 2004. This was a period of high TC activity with a total of 35 tropical cyclones that were warned in the various basins of the Atlantic, eastern Pacific, western Pacific, and Indian Ocean. The Cu tests were conducted for four values of the CMT parameter Cu equal to 1.0, 0.5, 0.25, and 0.0. These values correspond to no CMT, CMT reduced by 50% of (∂
CMTFULL: Full value of maximum CMT used (i.e., Cu = 0.00),
CMTTHRQ: Three-quarters of the maximum CMT used (i.e., Cu = 0.25),
CMTHALF: One-half of the maximum CMT used (i.e., Cu = 0.50), and
CMTZERO: No CMT (i.e., Cu = 1.00).
All the tests started from the NOGAPS operational analysis of 20 July 2004, which allowed a spinup period of 11 days. All the tests were conducted at the current operational resolution of T239L30.
Figure 1 is a comparison the TC tracks errors, using the sea level pressure tracker described above, for the four experiments. The number of forecast tracks that were used as verification at each forecast time is listed below the forecast hour on the bar chart. The results demonstrate a clear reduction in TC track error with increasing CMT for the 96- and 120-h forecasts. Table 1 shows the differences in TC track errors between the experiment with no CMT (CMTZERO) and the other experiments. In Table 1 a positive difference indicates that the TC track error of CMTZERO was higher (worse) than the results of the given comparison experiment (e.g., CMTFULL). Also listed in Table 1 is the significance using a standard Student’s t test (Spiegel 1961), stating whether the results are not significant at the 90% confidence level or giving the percentage significance at 90% or greater. The significance test results listed in Table 1 are obtained using every common verifying forecast, but the same statistical significance results are obtained if every other forecast (i.e., just the forecasts from the 0000 UTC runs or the 1200 UTC) is used. These results were also verified, with the same statistical conclusions, if in place of sea level pressure the 850-hPa cyclonic vorticity maximum is used (with the same warning position as verification). The results listed in Table 1 show that the 72–120-h forecasts with full CMT had significantly better TC tracks than the forecasts with no CMT. If one uses as a measure the U.S. Navy goal of 50, 100, 150, 200, and 250 nautical mile (n mi) TC error at 24, 48, 72, 96, and 120 h, respectively, then the 90.4-n mi difference at 120 h represents almost a 2-day increase of skill in the CMTFULL test. Comparisons of the TC track errors were also performed with CMTTHRQ and CMTHALF as the standard. The results (not shown) are that 1) the TC track errors of CMTFULL and CMTTHQ were not significantly different at the 90% confidence level, and 2) the TC track errors of CMTFULL and CMTTHRQ were significantly better than CMTHALF at 120 h, but not at 96 h. The overall conclusion from these results is that the inclusion of CMT in the Emanuel parameterization is an important component in improving TC tracks in NOGAPS and is most evident at 120 h.
Of the 35 tropical cyclones that were identified during the 2-month period of August–September 2004, there were 17 that lasted 5 days or more. Of these 17 tropical cyclones, 11 had smaller forecast track errors in CMTFULL, CMTTHRQ, and CMTHALF than in CMTZERO. Furthermore, there were eight tropical cyclones that lasted for more than 8 days and of these 7 out of 8 had smaller forecast track errors with nonzero CMT. Figures 2a–d show an example of the NOGAPS TC tracks for western Pacific TC Chaba (19W) from the four different experiments. For Chaba the best-track performance is given by the CMTFULL forecasts (Fig. 2a) and the worst by CMTZERO (Fig. 2d), with CMTTHRQ (Fig. 2b) and CMTHALF (Fig. 2c) lying between these two experiments. With decreasing CMT there is a clear tendency of the TC to recurve too early, which is a common tendency of NOGAPS TC forecasts, and appears to be accentuated in the CMTZERO experiment.
Another feature of the results with decreasing CMT is that TC forecasts with smaller CMT had, on average, deeper forecasted central pressures. In the case of Chaba the 120-h forecasts from CMTFULL were underforecast (too shallow) relative to the NOGAPS analysis by 5 hPa while the 120-h forecasts for CMTZERO were overforecast (too deep) by 2 hPa. This over/underdeepening of the TC central pressures, relative to the NOGAPS analysis, appears to play a role in the forecast TC track. It is not suggested here that NOGAPS can accurately resolve the deep surface pressure wells (NOGAPS analysis values of central pressures for tropical cyclones typically run between 1000 and 990 hPa, but can be as deep as 970 hPa for larger storms) or can accurately forecast the maximum wind speeds of intense tropical cyclones. Table 2 gives the mean difference of the forecast and the analyzed sea level pressures versus forecast hour for the four CMT experiments. As can be observed from Table 2, on average, decreasing the CMT leads to deeper central pressures of the TC. The results shown in Table 2 are statistically significant at the 99.5% confidence level for all forecast times. Examining the individual TC forecasts of CMTZERO versus forecasts from CMTFULL and CMTTHRQ shows that the forecasts with no CMT were 6 times more likely to be deeper than the analysis at 96 h (159 forecasts out of 183 were deeper than the analysis in CMTZERO versus 24 out of 183 in CMTFULL) and 5 times more likely at 120 h (121 forecasts out of 144 were deeper versus 23 out of 144). The comparison of the track results with CMTZERO versus CMTHALF also showed this difference, but with slightly lower frequency of overdeepening versus underdeepening, specifically the CMTZERO was 5 times more likely at 96 h and 3 times more likely at 120 h to be deeper than CMTHALF. It should be noted that while there were minor differences in the analyzed (0 h) central TC pressures for the different experiments, overall the average 0-h central pressures were within 1 hPa of one another.
In addition to examining the TC tracks, all (land and sea) 850-hPa cyclonic vorticity maxima with magnitudes greater than 5.0 × 10−5 s−1 in the region 35°S–35°N were binned as either forecasted early, on time, late, or as a false alarm at every 12-h interval. The criteria for early and late are within 48 h of the analysis and within 4.0° of the analyzed vortex. Table 3 shows the total number of vortices counted in each experiment and the percentage of hits, the percentage of vortices that appeared too early in the forecast, the percentage of vortices that appeared later than that found in the analysis, and the percentage of vortices that were predicted but did not appear or appeared too weakly in the analysis (false alarms). Table 3 shows that the no CMT experiment (CMTZERO) had a 30% higher number of vortices counted with both a lower hit rate and a higher false alarm rate. The numbers in Table 3 indicate that the CMTZERO forecast had more vortices and was “more active” (with a higher false alarm rate) than the other experiments.
Similarly each vortex in the analysis is binned, as either corresponding to some forecast or entirely missed (i.e., there was no indication in the forecast that a vortex was going to develop). For the four experiments the percentage of vortices that were present in the analysis, but missed (i.e., they were not forecasted early, on time, or late) was 21.1% for CMTFULL, 20.3% for CMTTHRQ, 22.9% for CMTHALF, and 17.2% for CMTZERO. Using the criterion of lower missed vortices, the CMTZERO performed the best, but this is due to more vortices in the CMTZERO forecast translating to more vortices in the CMTZERO analysis. Restricting this diagnosis to just the 35 warned tropical cyclones, 28 out of 35 had either an early warning or were classified as a hit in all the experiments except CMTHALF, in which the number was 27 out of 35. These numbers indicate that over the forecast period of the summer of 2004, NOGAPS failed about 20% of the time to forecast tropical cyclone genesis, regardless of the amount of CMT.
Critical to evaluating all NWP tests of NOGAPS are the wind, height, and temperature statistics of the forecasts. Figure 3 presents the 1000-hPa Northern Hemisphere (NH; defined here as 20°–80°N) height AC versus forecast hour for the four Cu experiments. While the three experiments with CMT outperformed the experiment with no CMT (CMTZERO), the experiment with Cu = 0.50 (CMTHALF) performed slightly better than the other experiments in terms of 1000-hPa heights. This was also true for the 500-hPa height NH AC, the mean temperatures, and the mean wind speed errors, with CMTHALF performing best, CMTTHRQ next, followed by CMTFULL. The CMTZERO results were the outlier in most cases, having higher RMSE and a positive lower-level (1000–850 hPa) NH wind bias as opposed to a low wind bias for the other experiments. The results in the Southern Hemisphere (SH) were similar to the results of the NH for winds and temperatures, but the SH AC scores were nearly identical for the four Cu experiments.
Figure 4 shows the mean temperature error in the Tropics (20°S–20°N). All the experiments show a slight cold bias in the Tropics, with very small differences between the results in terms of temperature bias. Again the run with no CMT is the worst in terms of mean error and in terms of RMSE (not shown). Figure 5 is a comparison of the mean wind biases for 850 hPa. As noted above for the NH, the Tropics with no CMT have a clear positive wind speed bias, in contrast to the other runs. One of the few statistics for which the no-CMT test shows a positive result is the 250-hPa mean wind speed error (Fig. 6). The vector wind RMSE (not shown) was greatest in CMTZERO.
A possible explanation for the larger bias in the CMT cases is that for certain situations the Emanuel CMT formulation generates a too large downward transfer of momentum. It should be emphasized that the CMT formulation is not the same as simple diffusion and can increase wind shear as well as decrease it, depending on the convective wind and mass fluxes (see appendix A). Adding a simple diagnostic of binning the results of CMT to NOGAPS indicates that between 400 and 150 hPa the CMT increases shear in 40% of the cases where cumulus extends into the upper troposphere. Since all the data assimilation runs showed a negative wind bias at 250 hPa, this indicates that NOGAPS has other factors contributing to the mean wind bias.
4. CMT sensitivity tests in the vicinity and away from the tropical cyclones
As discussed in section 3, the contribution from CMT as parameterized in the Emanuel parameterization scheme greatly improved the TC track forecasts of NOGAPS and slightly improved most of the wind, height, and temperature forecasts in the NH, SH, and Tropics. While the results suggest that greatest impact comes from the CMT not over intensifying the TC relative to the NOGAPS analysis, it is informative to try to sort out the contribution that comes from limiting the strength of the TC versus the contribution that comes from an improved tropical environment. To test the relative importance of CMT computed in the vicinity of tropical cyclones versus that computed away from the TC, two additional data assimilation and medium-range forecast experiments were conducted over the period August–September 2004. In the first test, hereafter called CMTAWAY, the CMT tendency was set to zero in the vicinity of a verified TC (i.e., Cu = 1.00), but computed away from the vicinity of the storm. In the second test, hereafter called CMTNEAR, the opposite procedure of the first test was applied, so that Cu = 1.00 was set in the vicinity of a forecasted TC, but set to 1.0 away from the TC. The precise procedures of the two tests are
Each TC, which was warned and initialized in NOGAPS by synthetic wind soundings, was located in the forecast model at each time step by following the maximum of the vorticity at the model computational level corresponding to approximately 850 hPa.
At each time step, the maximum distance from the center of the TC to the location where the vorticity changes sign was computed, up to a maximum of 2200 km. This distance was compared to the radius of the 30-kt wind, which is taken from the initial warning, and the maximum of these two distances is defined as rTC.
For the experiment CMTAWAY, if a grid point is 4 × rTC or more away from the 850-hPa vorticity center then Cu = 0.00 (full CMT), if a grid point is within 2 × rTC then Cu = 1.00 (zero CMT), and if a point is between 2 × rTC and 4 × rTC then Cu is linearly interpolated between 1.0 and 0.0.
For the experiment CMTNEAR the above procedures 1) and 2) are the same and procedure 3) is reversed, that is, the Cu coefficient is set to 1 minus the value used in CMTAWAY. Thus, the coefficient is Cu = 1.00 for points greater than 4 × rTC and Cu = 0.00 for points within 2 × rTC of a vorticity maximum, and linear interpolation is performed for points that lie between 2 × rTC and 4 × rC.
The length limits defined above are not meant to signify an important TC parameter or an optimum length over which to apply or not apply CMT. Rather they were used to ensure that either no CMT or full CMT was applied for the full extent of a TC and should be viewed in the context of CMT sensitivity testing only.
Figure 7 compares the TC tracks for the experiments CMTNEAR and CMTAWAY, together with the experiments CMTFULL and CMTZERO from section 3. The mean TC track errors for the experiment CMTNEAR are very close to those of CMTFULL, while the track errors for CMTAWAY lie between CMTFULL and CMTZERO. Table 4 presents a comparison of the experiment CMTNEAR with the other experiments. As in Table 1 the TC track error difference is listed along with the t test confidence level. While the TC track error for CMTNEAR is statistically better than CMTAWAY at 96 h, it is not statistically better at 120 h using the standard Student’s t test. This indicates significant spread in the track results at 120 h. But it is interesting that both CMTFULL and CMTTHRQ had a small, but statistically significant, advantage in TC track forecasts at 24, 48, and 72 h, so that there appears to be a positive contribution when CMT is applied sufficiently everywhere. The track errors for CMTHALF and CMTNEAR are not significantly different throughout the forecasts, but at 96 and 120 h CMTZERO had the poorest TC track forecasts. As an example Figs. 8a,b show the tracks for western Pacific TC Chaba, which was better with all values of CMT tested in section 3 (Figs. 2a–d). The track forecasts of the test CMTNEAR are better than CMTAWAY, but the errors of both CMTNEAR and CMTAWAY lie between the two extremes of CMTFULL and CMTZERO. Similar to the results of comparing CMTFULL versus CMTZERO, the CMTNEAR forecasts tended to be weaker than the verifying analysis, while the CMTAWAY forecasts were deeper than the verifying analysis. Table 5 gives the mean difference (hPa) of the forecast and the analyzed sea level pressures versus forecast hour for the CMT experiments CMTNEAR and CMTAWAY, with the results of CMTFULL and CMTZERO also presented for comparison. The differences in the central pressures between CMTNEAR and CMTAWAY are statistically significant at the 99.5% confidence level. The small central sea level pressure differences of CMTNEAR and CMTFULL are not significant through 96 h, but are significant at 120 h at the 90% confidence level. The opposite is true for the comparison of the central sea level pressures of CMTZERO and CMTAWAY [i.e., they statistically differ (CMTZERO has deeper central pressures) up to 96 h, but are not significant at 120 h]. This leads to the conclusion that CMT applied away from the vicinity of a TC does act as a partial brake on the TC development, at least up to 96 h. Of the 17 storms that lasted more than 5 days, 12 were forecasted better in NOGAPS with both the CMTNEAR and CMTAWAY experiments than with CMTZERO. This last result is similar to what was found when comparing the TC tracks forecasts from CMTFULL, CMTTHRQ, and CMTHALF with those of CMTZERO.
Table 6 presents the number of 850-hPa cyclonic vorticity maxima counted in the forecast period August–September 2004 for CMTNEAR and CMTAWAY, as well as the percentage of vortex forecasts that were early, hits, and late. In Table 6 the results of the experiments CMTFULL and CMTZERO are also listed for comparison. The number of CMTFULL and CMTNEAR are nearly the same, while the number for the experiments CMTZERO and CMTAWAY also match up. Not surprisingly the results indicate that one needs to apply CMT throughout the Tropics, not just near a storm, in order to limit the genesis of (false alarm) vortices. Similar to the experiment CMTZERO, the number of missed vortices in CMTNEAR was 17.4%. One interesting note is that of all the tests performed, CMTNEAR had the highest number of reported tropical cyclones missed (10 out of 35). This indicates that if a global NWP model is to be a good predictor of TC genesis, then the CMT needs to be well modeled not just within the storms but also throughout the Tropics. Also shown in Table 6 are the vortex numbers for CMTAWAY, which are very close to CMTZERO. The percentage of missed vortices in CMTAWAY is 20.4%, almost the same as CMTFULL, and in CMTAWAY 28 of the 35 TCs warned were predicted early or on time.
As in the experiments described in section 3, standard NWP scores were computed for CMTAWAY and CMTNEAR. The anomaly correlation scores for the two experiments were nearly identical. In the NH, the AC scores of CMTAWAY and CMTNEAR were better than the CMTZERO scores, but worse than the three experiments in section 3 with CMT (CMTFULL, CMTTHRQ, and CMTHALF). In the SH the AC scores were essentially the same for the two runs and matched the other experiments described in section 3. For the temperature and wind statistics the CMTAWAY experiment was similar to the CMTFULL results and the CMTNEAR experiment was similar to the CMTZERO results. Both CMTAWAY and CMTNEAR were significantly better than the tests DIFW10 and DIFW40 in all NWP scores. Figure 9 shows an example of this for the 850-hPa mean wind speed error in the Tropics. The conclusion here is that while the CMTNEAR performed better for TC track forecasts, the CMTAWAY had overall better synoptic wind and temperature forecasts. Again, the two tests described in this section were meant only for a sensitivity study and the procedures used for CMTAWAY and CMTNEAR are not meant for consideration in any global model.
The following is a summary of the results of the experiments CMTNEAR and CMTAWAY:
On average, TC track errors for CMTNEAR were smaller than for CMTAWAY and were closer to the track errors of the experiment CMTFULL. However, the results were not statistically significant for 120 h and the results were not consistent on a storm-by-storm basis.
CMTNEAR significantly underdeepened tropical cyclones; CMTAWAY significantly overdeepened TCs compared to the NWP analysis.
The CMTNEAR experiment generated over 30% more tropical vortex tracks than the CMTAWAY, but had a larger number of missed TCs.
The height statistics for both CMTAWAY and CMTNEAR are not as good as the results with uniform CMT. The wind and temperature statistics are better for CMTAWAY than CMTNEAR.
5. Summary and conclusions
This study presented the formulation of CMT in the Emanuel cumulus convective scheme and described sensitivity tests with various configurations of the CMT and two tests with constant wind diffusion replacing the CMT algorithm. The formulation of the CMT uses the updrafts and downdrafts computed according to the buoyancy-sorting assumptions, and is similar to the transport of a passive tracer in the parameterization. The scheme includes a tunable parameter Cu that controls the magnitude of the CMT. Four data assimilation tests, using the operational NOGAPS/NAVDAS configuration, were conducted for the period August–September 2004 to examine the sensitivity of the CMT. The NOGAPS results, discussed in section 3, showed that having values of smaller Cu (larger CMT) gave statistically better TC tracks. With no CMT the forecasted TC central pressures tended to be deeper than the analysis. All nonzero values of Cu improved most NWP performance scores, with Cu = −0.50 giving the best height AC scores, but the upper-tropospheric winds were degraded for all nonzero CMT. With no CMT, NOGAPS is clearly more active in the Tropics with significantly more tropical cyclones tracked with vorticity greater than 5.0 × 10−5 s−1. Two tests were conducted with a simple wind diffusion algorithm replacing the sophisticated treatment of CMT described in appendix A. Both tests, one slightly overdeepening the TC central pressure and one underdeepening the TC central pressure, gave poor results in both TC tracks and standard NWP statistics. This indicates that while CMT in NOGAPS limits TC central pressure growth, it is not the same as a simple diffusion mechanism and replacing it with such leads to very poor weather prediction forecasts. Two additional data assimilation experiments were conducted over this 2-month period, one in which the CMT is computed only in the vicinity of a TC (CMTNEAR) and one in which CMT is set to zero near the TC (CMTAWAY). For NOGAPS TC track forecasts, the results of section 4 show the primary importance of modeling the CMT the vicinity of the TC, but also that there is a clear secondary importance in applying CMT throughout the Tropics.
In the current operational NOGAPS, Cu = 0.25, corresponding to experiment CMTTHRQ and representing an optimum blend of TC track performance, anomaly correlation, and wind statistics. This change was implemented operationally in September 2004 and was based on tests that were forerunners to those reported here.
Acknowledgments
The authors thank Kerry Emanuel of MIT for his beneficial comments on this paper. The lead author, Timothy Hogan, gratefully acknowledges the support of Captain Michael Huff, METOC, IO, and ISR Program Manager (PMW-180), Project Number 0603704N.
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APPENDIX
The CMT Formulation in the Emanuel Cumulus Parameterization
The key features of the Emanuel cumulus parameterization (E91) as implemented in NOGAPS are 1) the scheme computes undiluted updrafts, unsaturated downdrafts, and upward and downward buoyancy-sorted mass fluxes, which are based on the buoyancy sorting hypothesis of Raymond and Blyth (1986); 2) the conversion of cloud water to rain is based on a stochastic coalescence model (Emanuel and Zivkovic-Rothman 1999); 3) the rate of mixing of the undiluted air is a function of the buoyancy and a mixing parameter given by Eq. (4) of Peng et al. (2004), which replaces the gradient buoyancy formulation in Emanuel and Zivkovic-Rothman (1999); 4) the cloud-base mass flux is determined by a prognostic equation, which has been modified, as explained in Peng et al. (2004), to include an updraft source level; and 5) the inclusion of a CMT algorithm, which is consistent with the mixing of moisture in the parameterization.
The total tendency is the sum of (A6) and (A8). A similar procedure is performed for the meridional wind. Following these sums, the wind tendencies are summed over the entire column and these sums are then subtracted from the tendencies. This ensures conservation of both the total mass integrals of
The TC track errors in n mi as a function of forecast hour for the four CMT value experiments. The results are based on the SLP tracker described in section 3. The number of forecast tracks used as verification at each forecast time is listed below the forecast hour.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
(a) The TC track forecasts for the western Pacific tropical storm Chaba (19W) for the experiment CMTFULL. The hurricane symbol marks the warning position and each colored symbol marks out the 120-h forecast track at each 12-h interval. The headings above the figure indicate the number of forecasts at each 12-h interval (N CASES) and the mean track error in n mi (DEL DIS). (b) Same as in (a), but for experiment CMTTHRQ. (c) Same as in (a), but for experiment CMTHALF. (d) Same as in (a), but for experiment CMTZERO.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
The 1000-hPa NH (20°–80°N) height anomaly correlation vs forecast hour for the four test runs in section 3. CMTFULL and CMTTHRQ have the same scores.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
The 5000-hPa tropical (20°S–20°N) average temperature error vs forecast hour for four of the test runs described in section 3.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
The 850-hPa tropical (20°S–20°N) wind speed error vs forecast hour for four of the test runs described in section 3.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
The 250-hPa tropical (20°S–20°N) wind speed error vs forecast hour for four of the test runs described in section 3.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
The TC track errors in n mi as a function of forecast hour for the two experiments described in section 4 and the two experiments CMTFULL and CMTZERO described in section 3. The results are based on the SLP tracker described in section 3. The number of forecast tracks used as verification at each forecast time is listed below the forecast hour.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
(a) Same as in Fig. 2a, but for test CMTNEAR. (b) Same as in Fig. 2a, but for test CMTAWAY.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
The 850-hPa tropical (20°S–20°N) wind speed error vs forecast hour for the two experiments described in section 4 and experiments CMTFULL and CMTZERO described in section 3.
Citation: Monthly Weather Review 135, 4; 10.1175/MWR3365.1
Differences in TC track error (n mi) between the experiment with no CMT (CMTZERO) and the experiments having Cu = 0.0 (CMTFULL), Cu = 0.25 (CMTTHRQ), and Cu = 0.5 (CMTHALF). In addition, the two tests with constant wind diffusion (DIFW10 and DIFW40) are compared with the test with Cu = 0.0 (CMTFULL). The abscissa is the forecast hour and the ordinate denotes the experiments being compared. The entries are the difference in n mi and the statistical significance in percent using a Student’s t test. Here NS means that there was no significance found at the 90% confidence level.
The mean difference (hPa) of the forecasted TC central SLP and the analyzed TC central SLP vs the forecast hour for the four CMT experiments and the two wind diffusion experiments presented in section 3.
The total number of 850-hPa cyclonic vorticity maxima counted with magnitudes greater than 5.0 × 10−5 s−1 in the region 35°S–35°N for each 12-h forecast interval for four of the forecast experiments discussed in section 3. Each vortex is binned as either forecasted early, on time, late, or a false alarm. The criteria for early and late are within 48 h of the analysis and within 4.0° of the analysis position.
Differences in TC track error (n mi) between experiment CMTNEAR described in section 4 and experiments CMTAWAY, CMTFULL (section 3), CMTTHRQ, CMTHALF, and CMTZERO. The abscissa is the forecast hour and the ordinate denotes the experiments being compared. The entries are the difference in n mi and the statistical significance in % using a Student’s t test. Here NS means that there was no significance found at the 90% confidence level.
The mean difference (hPa) of the forecast and the analyzed TC central SLP vs forecast hour for the CMT experiments CMTEAR and CMTAWAY presented in section 4 and CMTFULL and CMTZERO discussed in section 3.
The total number of 850-hPa cyclonic vorticity maxima counted with magnitudes greater than 5.0 × 10−5 s−1 in the region 35°S–35°N for each 12-h forecast interval for the forecast experiments CMTAWAY and CMTNEAR, discussed in section 4, and the experiments CMTFULL and CMTZERO, discussed in section 3. Each vortex is binned as either forecasted early, on time, late, or a false alarm. The criterion for early and late is within 48 h of the analysis and within 4.0° of the analysis position.
