a. FSUnew cloud parameterization

Clouds can form at any layer of the model in this parameterization scheme. A threshold relative humidity, which varies with cloud height, determines the presence of cloud in a layer. If the mass-weighted relative humidity in a model layer exceeds the threshold relative humidity, then the cloud fraction in that layer is calculated from the following relation:

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where RH is the mass-weighted relative humidity of that layer and RH_c is the threshold relative humidity. Table 2 lists the values for RH_c for three different cloud types used in this model. This scheme also corrects the high cloud fraction from the information of convective precipitation amount using the following relation when the precipitation rate (P, mm) is nonzero:

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b. FSUold cloud parameterization

Similar to the FSUnew scheme, this scheme also used threshold relative humidity criteria to calculate cloud fraction in a model layer. However, FSUold differs from the FSUnew in the formulation of high clouds. FSUold did not implement the correction of the amount of high clouds from convective precipitation criteria. Moreover, FSUold used a different equation for the calculation of cloud fraction when relative humidity crosses the threshold

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where α is a proportionality factor, RH_c is the threshold relative humidity, and RH is the mass-weighted relative humidity in that layer. Table 3 provides the values of α and RH_c used by this parameterization scheme for three different could types.

c. NCAR–CCM3 cloud parameterization

This cloud parameterization scheme is adapted from NCAR–CCM3 model. This scheme is based on Slingo (1987) and used large-scale parameters, such as relative humidity and vertical stability, to calculate cloud fraction. Convective cloudiness is calculated from the mean convective motion in an atmospheric column. Stability of the atmospheric column is considered to be the criterion for determining the presence of layered clouds. Low clouds are allowed to present only if the vertical velocity is less than 50 hPa day⁻¹. Relative humidity criteria determine the presence of clouds associated with the low-level inversion.

d. Pleim–Xiu cloud parameterization

This parameterization scheme is based on Pleim and Xiu (1995) that, similar to the other three parameterization schemes, used relative humidity criteria for the calculation of cloud fraction. However, unlike other schemes, in this model the threshold relative humidity is a function of pressure of the layer:

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where P is pressure of the layer and P_s is surface pressure. In addition to that, in the nonconvective planetary boundary layer, the maximum relative humidity threshold is set to 0.90. Cloud fraction in a layer is derived from the mass-weighted relative humidity in that layer using Eq. (1), where the threshold relative humidity RH_c is derived from Eq. (4).

All of these schemes used large-scale parameters such as relative humidity, pressure, vertical stability, and CAPE to calculate cloud fraction diagnostically from large-scale parameters. Originally we intended to include a prognostic cloud scheme in our suite of models. The advantage of a prognostic cloud scheme is that it includes and predicts (as dependent variables) cloud fraction and the liquid water mixing ratio (e.g., Sundqvist 1978; Sundqvist et al. 1989); hence, there is a direct effect of cloud fraction on the convection and circulation in the model. However, in Krishnamurti et al. (2007) and Chakraborty et al. (2007) we have seen that large improvement can come for the modeling and forecasting of the diurnal change of different cloud types, radiation budget, and precipitation from the use of these simple diagnostic cloud schemes. Thus, we limited this study to the use of a suite of diagnostic cloud schemes.

a. Diurnal cycle of velocity potential

The diurnal cycle of velocity potential for the divergent component of winds at 200 hPa from ERA-40 datasets, and day 3 of forecasts of the four member models, their ensemble mean, the unified cloud scheme, and the superensemble are shown in Figs. 2 and 3 for the break and active monsoon periods, respectively. Also shown, at the top of the forecast panels within parentheses, is the pattern correlation (PC) of the forecasted fields to that of ERA-40. A spatial gradient in velocity potential signifies wind flow from its high value region to the low value region:

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where V_h is the horizontal wind vector, ∇_h the horizontal gradient operator, and χ the velocity potential. In the ERA-40 data for the break monsoon [Figs. 2a(i) to 2a(iv)] a relative negative (compared to its surroundings) velocity potential is noticed over the South Asian monsoon region during 0000 and 0600 LST. This negative velocity potential peaks at 0600 LST over the northeastern parts of India with the diurnal magnitude of ∼10⁶ m² s⁻¹. During this time the value of velocity potential over the Arabian Sea and equatorial Indian Ocean is positive. This signifies a wind flow into the South Asian monsoon region from its surroundings at this pressure level. The situation reverses during 1200 and 1800 LST. Figures 2b–f show that the member models failed to forecast the phase, magnitude, and location of the high and low of velocity potential fields over this region. For example, at 1800 LST, all four models and their ensemble mean show a peak in velocity potential over the northwestern part of South Asia where a heat low prevails. This is in contrast to the observed high over northeast India where a monsoonal low is situated during this time of the year. The PC of most of the models and their ensemble mean with the observed counterpart is poor (ranges from −0.32 to 0.29). For the unified cloud scheme (Fig. 2g), the main improvement over the member models is noticed over the northeast Indian region where low (high) velocity potential during 0600 (1800) LST was successfully forecasted. Figure 2h shows that a superensemble could reasonably well predict the location and intensity of this diurnally varying high and low of velocity potential. The signature of a dipolelike structure with a minimum (maximum) over northeast India and a maximum (minimum) over the equatorial Indian Ocean at 0600 (1800) LST is present in this forecasts. The PCs for the superensemble and the unified scheme are higher compared to those of the member models and their ensemble mean during 0600 and 1800 LST.

During the active monsoon period (Fig. 3), the peak of the velocity potential over the Asian monsoon region occurs at 1800 LST, compared to 1200 LST for the break monsoon period (Figs. 2a and 3a, respectively). None of the member models show high skill in forecasting this phase of velocity potential at 200 hPa. In fact, all of these models and their ensemble mean show the peak at 0000 and 0600 LST, suggesting 6 to 12 h of phase error. The PC of the forecasted fields has improved with use of the unified scheme, but large phase errors remain over many regions during all four time slots of the day. It was possible to attain the highest PC with the superensemble forecast during 1800 LST (Fig. 3h) when the velocity potential reaches its peak. Comparing Figs. 3a and 3h we find that high values of velocity potential over the South Asian landmass are best captured by the superensemble methodology.

The above results show that there exists a diurnal mode of the 200-hPa velocity potential of the Asian summer monsoon in both the ERA-40 data and the model forecasts. At midnight and during early morning hours (0000 and 0600 LST) the velocity potential is smaller over the South Asian monsoon region when compared to its surroundings. At noon and during afternoon hours (1200 and 1800 LST) the situation reverses. This seesaw pattern in the diurnal cycle of velocity potential over the South Asian monsoon region (10°–30°N, 70°–100°E; labeled as IN in Fig. 4) and its surroundings (5°S–45°N, 50°–120°E minus the region IN; labeled as OUT in Fig. 4) is shown in Fig. 5 during day 3 of forecasts for the break and active monsoon periods. Over the region IN during break monsoon (Fig. 5a), the ERA-40 diurnal cycle shows negative velocity potential during 0000 and 0600 LST and positive velocity potential during other half of the day. The peak of ERA-40 data is at 1200 LST. Both the ensemble mean and the unified scheme show a nearly out of phase diurnal cycle over this region compared to ERA-40. The correlation coefficients (CCs) of the time series of ensemble mean and unified scheme with the ERA-40 datasets are −0.81 and −0.75, respectively, while that for the superensemble is 0.84. During active monsoon over the region IN (Fig. 5c), the peak in the velocity potential is at 1800 LST, as opposed to 1200 LST in the break monsoon. This is consistent with the results shown in Figs. 2 and 3. The amplitudes of the diurnal cycle from the ensemble mean and unified scheme are much higher compared to ERA-40, and the peak appears 6 h later (CCs are −0.73, −0.58, and 0.81 for the ensemble mean, unified scheme, and superensemble, respectively).

Over the outer region (OUT; right panels of Fig. 5) a distinct peak in the ERA-40 datasets is noticed at 0600 LST during the active monsoon. However, the amplitude of the diurnal variation is much less during the break monsoon. Over this region, the member models (represented by their ensemble mean) and the unified scheme perform slightly better than over the inner region. During the break period, the ensemble mean shows higher velocity potential during 0600 and 1200 LST and lower values during 0000 and 1800 LST. The CC of the time series of the ensemble mean with ERA-40 is 0.07. The unified scheme performs better than the ensemble mean (CC = 0.34). The superensemble forecasts are very close to those of ERA-40 with a maximum at 0600 LST and minimum at 1800 LST (CC = 0.87). During the active period, both the ensemble mean and the unified scheme show peak at 1200 LST, 6 h later than in the ERA-40 dataset. It was possible to predict this phase of the diurnal cycle of velocity potential at 200 hPa by the superensemble during day 3 of the forecasts (CC = 0.97).

This shows that the seesaw pattern in the diurnal cycle of velocity potential at 200 hPa over the South Asian monsoon region and its surroundings was better predicted by the superensemble during both break and active monsoon periods. The member models and the unified scheme performed poorly over the monsoon domain, but the unified scheme did reasonably better over the surrounding regions. This high and low in velocity potential sets up a gradient that reverses its sign during the day and night hours. The corresponding circulation pattern is illustrated by the arrows in Fig. 4.

b. Diurnal cycle of horizontal winds

The diurnal cycle (at 0600 and 1800 LST for clarity) of the horizontal wind vector at 200 hPa from ERA-40, the ensemble mean of four member models, the unified scheme, and the superensemble are shown in Fig. 6 during the break monsoon period. The divergence of the horizontal wind is indicated in the background as shaded (divergent region) and contour (convergent region). Over the northern parts of India, the Tibetan Plateau, and Southeast Asia, major regions of convergence are noticed during early morning hours (Fig. 6a). Winds from the surroundings rush toward this region at late night and early morning hours. The situation reverses during 1800 LST (Fig. 6b). The convergent regions at 0600 LST become divergent regions at 1800 LST, and wind flows out of this region. For the ensemble mean there is no clear convergent region at 0600 LST over the Tibetan Plateau (Fig. 6c). A shallow convergent region is noticed over central India, far south of that of the observed. The corresponding wind pattern is also affected by this southward-shifted convergent region. The PC of the divergence field for the ensemble mean with that of ERA-40 is 0.07. The unified cloud scheme performed better than the ensemble mean in the location of the convergence (0600 LST) and divergence (1800 LST) fields (Figs. 6e,f), which are shifted slightly northward closer to the ERA-40 fields. The location of divergence and convergence over Southeast Asia is also captured by the unified scheme (PC = 0.12). The superensemble shows the best forecast of the horizontal wind vector at this level. Over the Tibetan Plateau, a major region of convergence at 0600 LST and divergence at 1800 LST is forecasted reasonably. Also, regions of divergence (convergence) over the equatorial Indian Ocean at 0600 (1800) LST are captured by the superensemble. The PC of this forecast with ERA-40 is 0.31. Note here that, although the superensemble forecast is better than other forecast products, the superensemble could not capture some of the features of the diurnal cycle of the Asian monsoon circulation.

The corresponding diurnal cycle of vector wind at 925 hPa is shown in Fig. 7. Vectors with large amplitude of diurnal variation are noticed near the coasts. This is indicative of a clear land–sea contrast at this pressure level. The amplitude of this variation is about 3–4 m s⁻¹. During daytime the land heats up faster than the ocean. This forms a thermal-low pressure that drives the sea breeze toward the land in the afternoon hours. This is evident in the ERA-40 data at 1800 LST (Fig. 7b). However, at night the land cools faster than the oceans and a land breeze blows from the land to the ocean during early morning hours (Fig. 7a). This relative warming/cooling of land and ocean during day and night hours and the corresponding diurnal cycle of wind flow is present in the forecasts from the ensemble mean, unified scheme, and superensemble (Fig. 7c–h). However, the superensemble forecasts are better compared to the other two products. This is evident in the PC of the divergent field (PCs are 0.44, 0.47, and 0.82 for the ensemble mean, unified scheme, and superensemble, respectively).

The convergence (divergence) of wind at 200 hPa during early morning (afternoon) hours (Fig. 6) and the opposite wind direction near the surface (Fig. 7) indicates a three-dimensional circulation that diurnally overturns in the spatial scale of the Asian summer monsoon. Similar circulation patterns were noticed in the active monsoon period as well (not shown). The following section presents the signature of this three-dimensional flow in the vertical velocity field.

c. Diurnal cycle of vertical velocity

The diurnal cycle of vertical pressure velocity at eight different pressure levels over the South Asian monsoon region (IN) and its surroundings (OUT) from ERA-40, the ensemble mean of the member models, the unified scheme, and the superensemble are shown in Figs. 8 and 9 during break and active monsoon periods, respectively, for day-3 forecasts. In the upper levels (200, 300, and 400 hPa) a downward motion (positive pressure velocity) is noticed over the South Asian monsoon region in the ERA-40 datasets at midnight and in the early morning hours during the break monsoon (Fig. 8). The vertical velocity is mostly upward over the surrounding region during this time. This is consistent with the convergence of winds at 200 hPa noticed in Figs. 2 and 6. At noon and during afternoon hours, upward motion prevails over the South Asian monsoon region and downward motion prevails over the surroundings in the upper levels. This is also consistent with the divergent circulation at 200 hPa during the afternoon hours noticed in Figs. 2 and 6. This characteristic of the diurnal mode of vertical pressure velocity is poorly captured by the ensemble mean and the unified scheme. Forecasts from both of these schemes are phase shifted by 6 h too late. However, the amplitude of this diurnal mode is somewhat better for the unified scheme compared to the ensemble mean. This improvement is evident in the rms errors shown inside the respective forecast panels. The rms error of the diurnal cycle is minimum for the superensemble forecasts. The superensemble successfully captured the phase and amplitude of the diurnal cycle of vertical velocity over both these regions at upper levels.

The diurnal cycle is not very strong at 500 hPa, although it carried the same sign of the upper levels. From Fig. 8 it is clear that this is the level of transition in the characteristics of the diurnal cycle. At 600- and 700-hPa levels over the South Asian monsoon region, upward motion is noticed at 0600 and 1200 LST and downward motion at 0000 and 1800 LST. The sign of vertical velocity is completely opposite in the outer domain. Both the ensemble mean and unified scheme completely missed this phase of the vertical velocity at the 600- and 700-hPa levels. The phase and amplitude of the superensemble forecasts are very close to the ERA-40 datasets.

The ERA-40 data showed a weak diurnal variation at 850- and 925-hPa levels. The phase of this variation is very similar over the South Asian monsoon region and its surroundings with downward motion at midnight and during early morning hours and upward motion at noon and during afternoon hours. The ensemble mean and the unified scheme show a large amplitude of diurnal variation at these pressure levels and had the highest rms errors. Forecasts from the superensemble are very close to that of ERA-40. Rms errors from the superensemble are almost one order of magnitude less compared to the other two forecasts.

The active monsoon shows a similar signature of the diurnal cycle of vertical pressure velocity (Fig. 9). However, the amplitude of the oscillation is higher, particularly in the middle and lower troposphere. At 925 hPa, a distinct peak of the diurnal cycle over IN is noticed at 1800–0000 LST, which is very weak during the break monsoon period. The peak is at 0600 LST over the outer region at this pressure level. The amplitude of this diurnal oscillation increases with height and reaches a maximum at 700 hPa in the ERA-40 datasets. Above 500 hPa, the peak of vertical pressure velocity occurs at 0600 LST, 6 h later compared to the lower levels. The South Asian monsoon region (IN) and its surroundings (OUT) are out of phase at every pressure level from the surface up to 200 hPa. Figure 9 shows that the ensemble mean and the unified scheme predicted a very weak diurnal cycle in the upper levels and a stronger diurnal cycle in the lower levels compared to the ERA-40-based estimates. The out of phase relationship between the inner and outer regions is also not captured by these simulations. As a result, the rms errors of the forecasted fields are high from these simulations. It was possible to reduce this error with use of the superensemble at all pressure levels. The superensemble could realistically capture the out of phase relationship of pressure velocity between the regions IN and OUT. The peak over the inner region during 0000 LST below 500 hPa and during 0600 LST above 400 hPa is forecasted reasonably by the superensemble. Overall, the reduction in rms errors is 2 to 3 times compared to the ensemble mean and the unified scheme.

Therefore, the three-dimensional structure of the diurnal overturning of the Asian summer monsoon is evident in the upper-level (Figs. 2, 3 and 6) and near-surface (Fig. 7) horizontal winds and in the vertical velocity fields (Fig. 8 and 9). There is a large difference (6–12 h) in phase of the diurnal cycle of vertical velocity near the surface and in the upper levels during both active and break periods. This is maintained by the out-of-phase diurnal mode in vertical velocity over the South Asian monsoon region and its surroundings.

d. Diurnal cycle of clouds and precipitation

The diurnal cycle of high clouds from ISCCP satellite-based estimates, the ensemble mean of the four models, the unified cloud scheme, and the superensemble are shown in Fig. 10 for day-5 forecasts separately over the land and ocean areas of 10°–30°N, 70°–100°E. Also shown, inside the respective forecast panels, are the rms errors of the forecasts of the total diurnal cycle in percent. Over the land parts of this region during the break monsoon (Fig. 10a), the ISCCPbased estimates show the phase of the diurnal cycle at 2100 LST with an amplitude of about 6%. The ensemble mean of the models show a very weak diurnal variation of high clouds over land. The amplitude of this variation is less than 25% of that of the ISCCP-based estimates. However, the ensemble mean of the models correctly captured the phase of the diurnal cycle. The rms error of the ensemble mean is 3.6%. On the other hand, both the unified scheme and the superensemble forecasted the phase and amplitude of the diurnal cycle reasonably well. The rms errors for these forecast schemes are 0.2% and 0.4%, respectively.

Over the ocean parts of the South Asian monsoon domain during the break period (Fig. 10b), high clouds from ISCCP datasets show the peak at 1800–2100 LST. The amplitude of this diurnal variation is about 2%, lower than that over land (6%). The unified cloud scheme and the superensemble showed phase errors of 3–6 h over this region. The rms error of the total diurnal cycle for both these forecasts is 1.9%. Although the ensemble forecast carries a lower rms error, its diurnal cycle is 180° out of phase compared to the ISCCP datasets. Comparing Figs. 10a and 10b, one can state that the ensemble mean forecasts completely missed the land–ocean contrast in amplitude of the diurnal cycle of high clouds. In the ISCCP data, land has a higher amplitude compared to over the oceans. However, the ensemble mean shows almost similar amplitude over both oceans and land.

The active period (Figs. 10c and 10d) is characterized by a higher amplitude of diurnal variation over both land and ocean. However, while the phase over land remains the same (at 2100 LST), the phase over ocean is 3–6 h earlier during the active monsoon period than in the break monsoon period. Both the unified cloud scheme and the superensemble were able to realistically capture this phase of the diurnal cycle of high clouds over land and ocean. The phase from ensemble mean forecasts is during the morning hours over both land and oceans. Moreover, over land the diurnal variation is very weak (amplitude ∼1% compared to 8% in the ISCCP estimates). The rms errors of the forecasts were reduced by the unified scheme and the superensemble.

The diurnal cycle of low clouds over land parts of the South Asian monsoon domain, on the other hand, had a phase at 1200 LST during both break and active periods (Figs. 11a and 11c), 9 h earlier than the peak in high clouds (Figs. 10a and 10c). The amplitude of the diurnal cycle is about 7%. The ensemble mean of the four cloud schemes failed to forecast this phase and amplitude of the diurnal cycle of low clouds during day 5. The ensemble mean forecasts showed a weak diurnal variation with amplitude of around 1% and phase at 0600 LST. It was possible to correct this huge error in the member models with use of the unified cloud scheme and the multimodel superensemble. The rms error of the entire diurnal cycle were reduced to below 2% by these products as opposed to more than 4.5% in the ensemble mean forecasts.

Low clouds over the ocean parts of the South Asian monsoon region also showed a peak at 1200 LST during both break and active periods (Figs. 11b and 11d). When compared to the phase of high clouds, this is about 9 h earlier during the break period and 3 h earlier during the active period. However, the ensemble mean of the models showed the peak of high and low clouds at the same time. The unified scheme and the superensemble correctly predicted both phase and amplitude of the diurnal variation of low cloud over the ocean. The rms error of the total diurnal cycle from the ensemble mean, unified scheme, and superensemble forecasts are, respectively, 2.5%, 1.0%, and 0.6% during the monsoon break, and 1.9%, 1.0%, and 0.3% during the active monsoon period.

The diurnal cycle of precipitation over South Asia (10°–30°N, 70°–100°E) during the break and active periods is shown in Fig. 12 from TRMM-based estimates, the ensemble mean of the member models, the unified scheme, and the superensemble. Over the land parts, TRMM data shows a peak at around 2100 LST during the break period and at 1800–2100 LST during the active period. The phase of this variation is captured by the ensemble mean, albeit an underestimation in the amplitude of diurnal variation during both break and active periods. The unified cloud scheme slightly overestimates the amplitude during both break and active periods. The superensemble forecasts were better than the ensemble mean and the unified scheme, especially when monsoon is active over this region.

Over the ocean parts, the difference in diurnal amplitude for the active and break monsoon is large. While the diurnal cycle of the monsoon break shows an amplitude below 0.2 mm h⁻¹, it is more than 0.5 mm h⁻¹ during the active monsoon. However, the phase during both of these extreme precipitation periods is at 0900 LST. All three forecasts overestimate the amplitude during the monsoon break and underestimate it during the active monsoon. However, the superensemble forecast is closer to the TRMM datasets, particularly during the active season. Note that the peak of precipitation over the ocean occurred about 6–9 h earlier than the high clouds, which is in accordance with the observation by Tian et al. (2004). Owing to a large phase error for the ensemble mean in forecasting the diurnal cycle of high clouds over ocean, the aforementioned phase difference between precipitation and high clouds is absent in the ensemble mean forecasts. Both the unified cloud scheme and the superensemble are consistent in capturing this difference in the phase of the diurnal cycle precipitation and high clouds.

e. Relative distribution of diurnal phase of precipitation during a day

Relative occurrences (in %) of the phase of diurnal precipitation during different hours of a day at various precipitation ranges over the land and ocean areas of the South Asian monsoon region for the entire 47 days of day 5 forecasts (20 July–5 September 2000) are shown in Fig. 13. At first, the hour corresponding to the peak of precipitation during each day (i.e., diurnal phase) was calculated and grouped into different bins according to the total precipitation on that day. The bin intervals were <10, 10–25, 25–45, 45–70, 70–100, and >100 mm day⁻¹. Now, the relative occurrences of peak hour of precipitation were obtained by dividing the number of days at every 3 h by the total number of days at that bin. We have included all 47 days of the forecasts (instead of two separate 10-day periods for the break and active monsoon periods) to obtain a complete picture at all precipitation ranges. The results show that over land for the TRMM dataset the peak in precipitation occurred mainly during afternoon hours (1500–2100 LST) when total precipitation on that day is below 70 mm. However, for precipitation exceeding 70 mm day⁻¹, the peak in precipitation shifts to late night/early morning hours (0000–0600 LST). The ensemble mean and the unified scheme showed a delayed phase in occurrences (by about 3 h) for both light and heavy precipitation. The superensemble showed correct phase for low to moderate precipitation (<25 mm day⁻¹). However, two distinctly different preferred times of the phase are forecasted for moderate to heavy precipitation ranges (25–100 mm day⁻¹), one being in the afternoon hours and another during early morning hours (0300–0600 LST). While the afternoon hour peak agreed with the TRMM data, the TRMM does not show a very clear peak in the late night hours for this range of precipitation. For very heavy precipitation (>100 mm day⁻¹), the observed (TRMM) peak during 0000–0600 h is reasonably captured by the superensemble. The overall pattern of the superensemble forecasts (PC = 0.72) improved compared to the ensemble mean (PC = 0.54) and the unified schemes (PC = 0.53). Using a Student’s t test, it was found that this improvement is significant at the 95% level when compared to the ensemble mean.

Over the ocean parts of the South Asian monsoon domain, in the TRMM datasets, the preferred phase of the diurnal precipitation is at 1200–1500 LST for low to moderate precipitation and in the early morning hours for heavy precipitation (Fig. 13e). However, these peaks were not as distinct as is noticed over land. This suggests that over oceans the chance of peak precipitation at various thresholds is distributed more evenly during all hours of the day. The ensemble mean and the unified schemes could not forecast these phases at various thresholds (PCs are 0.50 and 0.21, respectively). The peaks were more distinct for the superensemble forecasts, but were at correct hours for all precipitation thresholds. The PC of the forecast is improved for the superensemble (0.69) compared to the other two products. Similar to over the land region, this improvement in the forecasted PC is significant at the 95% level compared to the ensemble mean.

f. Contribution of the diurnal mode to the kinetic energy of the monsoon circulation

Figure 14a illustrates the contribution to the generation of kinetic energy from the diurnal mode during the break monsoon period. Here these results are tropospheric integrals from the surface to the 100-hPa level and cover the monsoon domain between 10° and 30°N, 70° and 100°E. The units are joules per second. These are composites over a 10-day period, 23 July–1 August 2000 from ERA-40 and day 5 of the forecasts from the ensemble mean, the unified scheme, and the superensemble. The important result is a net positive contribution for the integral

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for the diurnal mode, where R is gas constant for air, P is pressure, and ω′ and T ′ are the diurnal component of vertical pressure velocity and air temperature: ∫_m[ ] dm represents the mass-weighted integral

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where g is acceleration due to gravity, x and y represent longitude and latitude directions respectively, and P is the pressure. This positive contribution of the diurnal mode is clearly seen in the observed estimates and the superensemble forecasts. The ensemble mean and the unified scheme fail to capture this feature. The important implications of this result are as follows: Each day this diurnal mode is providing energy for driving the monsoon via the thermally direct diurnal vertical circulations. The daily averaged magnitude of that energy transfer for the diurnal to the monsoon scale is of the order of 10¹² J s⁻¹. Having the same positive sign every day makes this effect quite large accumulatively over a monsoon season.

Figure 14b illustrates the contributions to the local change of total kinetic energy for the same period for ERA-40, the ensemble mean, the unified scheme, and the superensemble over the same monsoon domain. This is expressed by

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where K is the kinetic energy. These results for a 10-day average depend strongly on the prevailing monsoon phenomenology of that period. This change of total kinetic energy is of the order of 10¹³ J s⁻¹ and is one order of magnitude larger than the diurnal change. This change, on an hour by hour basis, shows a net positive growth of total kinetic energy from the observed estimates (7.3 × 10¹³ J s⁻¹) and the multimodel superensemble (1.7 × 10¹³ J s⁻¹). The ensemble mean (−1.2 × 10¹³ J s⁻¹) and the unified model (−3.7 × 10¹³ J s⁻¹) do not show a positive contribution during this period. In terms of rms error, both the unified scheme and the superensemble showed higher skills compared to the ensemble mean forecasts. Note that the change in energy of the diurnal cycle over the Asian monsoon region is of the order of 10¹² J s⁻¹, and rate of change of kinetic energy over the same domain is of the order of 10¹³ J s⁻¹. Therefore, it appears that the diurnal change contributes roughly 10% to the total change of kinetic energy of the Asian summer monsoon. Similar results were found during the active monsoon period (not shown). Because of the steady contribution of the diurnal change this is an important aspect of the monsoon.