In the current study, we have presented a systematic analysis of the diurnal cycle of rainfall over the Indian region using satellite observations, and evaluated the ability of the Weather Research and Forecasting Model (WRF) to simulate some of the salient features of the observed diurnal characteristics of rainfall. Using high resolution simulations, we also investigate the underlying mechanisms of some of the observed diurnal signatures of rainfall. Using the Tropical Rain-fall Measuring Mission (TRMM) 3-hourly, 0.25 ×0.25 degree 3B42 rainfall product for nine years (1999-2007), we extract the finer spatial structure of the diurnal scale signature of Indian summer monsoon rainfall. Using harmonic analysis, we construct a signal corresponding to diurnal and sub-diurnal variability. Subsequently, the 3-hourly time-period or the octet of rain-fall peak for this filtered signal, referred to as the “peak octet,” is estimated with care taken to eliminate spurious peaks arising out of Gibbs oscillations. Our analysis suggests that over the Bay of Bengal, there are three distinct modes of the peak octet of diurnal rainfall corresponding to 1130, 1430 and 1730 IST, from north central to south Bay. This finding could be seen to be consistent with southward propagation of the diurnal rainfall pattern reported by earlier studies. Over the Arabian sea, there is a spatially coherent pattern in the mode of the peak octet (1430 IST), in a region where it rains for more than 30% of the time. In the equatorial Indian Ocean, while most of the western part shows a late night/early morning peak, the eastern part does not show a spatially coherent pattern in the mode of the peak octet, owing to the occurrence of a dual maxima (early morning and early/late afternoon). The Himalayan foothills were found to have a mode of peak octet corresponding to 0230 IST, whereas over the Burmese mountains and the Western Ghats (west coast of India) the rainfall peaks during late afternoon/early evening (1430-1730 IST). This implies that the phase of the diurnal cycle over inland orography (e.g., Himalayas) is significantly different from coastal orography (e.g., Western Ghats). We also find that over the Gangetic plains, the peak octet is around 1430 IST, a few hours earlier compared to the typical early evening maxima over land. The second part of our study involves evaluating the ability of the Weather Research and Fore-casting Model (WRF) to simulate the observed diurnal rainfall characteristics. It also includes conducting high resolution simulations to explore the underlying physical mechanisms of the observed diurnal signatures of rainfall. The model (at 54km resolution) is integrated for the month of July 2006 since this period was particularly favourable for the study of diurnal cycle. We first evaluate the sensitivity of the model to the prescribed sea surface temperature (SST) by using two different SST datasets, namely Final Analyses (FNL) and Real-time Global (RTG). The overall performance of RTG SST was found to be better than FNL, and hence it was used for further model simulations. Next, we investigated the impact of different parameterisations (convective, microphysical, boundary layer, radiation and land surface) on the simulation of diurnal cycle of rainfall. Following this sensitivity study, we identified the suite of physical parameterisations in the model that “best” reproduces the observed diurnal characteristics of Indian monsoon rainfall. The “best” model configuration was used to conduct two nested simulations with one-way, three-level nesting (54-18-6km) over central India and Bay of Bengal. While the 54km and 18km simulations were conducted for July 2006, the 6km simulation was carried out for the period 18-24 July 2006. This period was chosen for our study since it is composed of an active period (19-21 July 2006), followed by a break period (22-24 July 2006). At 6km grid-spacing the model is able to realistically simulate the active and break phases in rainfall. During the chosen active phase, we find that the observed rainfall over central India tends to reach a maximum in the late night/early morning hours. This is in contrast to the observed climatological diurnal maxima of late evening hours. Interestingly, the 6km simulation for the active phase is able to reproduce this late night/early morning maxima. Upon further analysis, we find that this is because of the strong moisture convergence at the mid-troposphere during 2030-2330 IST, leading to the rainfall peak seen during 2330-0230 IST. Based on our analysis, we conclude that during both active and break phases of summer monsoon, mid-level moisture convergence seems to be one of the primary factors governing the phase of the diurnal cycle of rainfall. Over the Bay of Bengal, the 6km model simulation is in very good agreement with observations, particularly during the active phase. The southward propagation observed during 19-20 July 2006, which was not captured by the coarse resolution simulation (54km), is exceedingly well captured by the 6km simulation. The positive anomalies in specific humidity attain a maxima during 2030-0230 IST in the north and during 0830-1430 IST in the south. This confirms the role of moisture convergence in the southward propagation of rainfall. Equally importantly we find that while low level moisture convergence is dominant in the north Bay, it is the mid-level moisture convergence that is predominant in the south Bay.

On January 29-30, 2008 a squall line of thunderstorms moved through the Ohio Valley resulting in four deaths and one injury. Such events highlight the importance of accurate forecasting for public safety. Mesoscale Modeling plays an important role in any forecast of a potential squall line. The focus of this study was to examine the performance of several parameterization scheme combinations in the Weather Research and Forecasting Model version three (WRF) as they related to this event. These examinations included cloud microphysics (WRF Single-Moment 3-class, 6-class, and Goddard), cumulus parameterization (Kain-Fritsch and Bets-Miller-Janjic) and planetary boundary layer schemes (Yonsei-University and Mellor-Yamada-Janjic). A total of 12 WRF simulations were conducted for all potential scheme combinations. Data from the WRF simulations for several locations in south central Kentucky were analyzed and compared using Kentucky Mesonet observations for four locations: Bowling Green, Russellville, Murray and Liberty, KY. A fine model resolution of 1 km was used over these locations. Coarser resolutions of 3 km and 9 km were used on the outer two domains, which encompassed the Ohio and Tennessee Valleys. The model simulation performance was assessed using established statistical measures for the above four locations and by visually comparing the North American Regional Reanalysis dataset (NARR) along with modeled simulations. The most satisfactory scheme combination was the WRF Single-Moment 3-class Microphysics scheme, Kain-Fritsch cumulus parameterization scheme and Yonsei University scheme for the planetary boundary layer. The planetary boundary layer schemes were noted to have the greatest influence in determining the most satisfactory model simulations. There was limited influence from different selections of microphysics and cumulus parameterization schemes. The preferred physics parameters from these simulations were then used in six additional simulations to analyze the affect different initialization data sets have with regards to model output. Data sets used in these simulations were the Final Operational Analysis global data, North American Regional Reanalysis (3 and 6 hour) and the North American Mesoscale Model at 1, 3 and 6 hour timesteps, for a total of six simulations. More timesteps or an increase in model resolution did not materially improve the model performance.

Time splitting is a numerical procedure used in solution of partial differential equations whose solutions allow multiple time scales. Numerical schemes are split for handling the stiffness in equations, i.e. when there are multiple time scales with a few time scales being smaller than the others. When there are such terms with smaller time scales, due to the Courant number restriction, the computational cost becomes high if these terms are treated explicitly. In the present work a nonlinear advective equation is solved numerically using different techniques based on a generalised framework for splitting methods. The nonlinear advective equation was chosen because it has an analytical solution making comparisons with numerical schemes amenable and also because its nonlinearity mimics the equations encountered in atmospheric modelling. Using the nonlinear advective equation as a test bed, an analysis of the splitting methods and their influence on the split solutions has been made. An understanding of influence of splitting schemes requires knowledge of behaviour of unsplit schemes beforehand. Hence a study on unsplit methods has also been made. In the present work, using the nonlinear advective equation, it shown that the three time level schemes have high phase errors and underestimate energy (even though they have a higher order of accuracy in time). It is also found that the leap-frog method, which is used widely in atmospheric modelling, is the worst among examined unsplit methods. The semi implicit method, again a popular splitting method with atmospheric modellers is the worst among examined split methods. Three time-level schemes also need explicit filtering to remove the computational mode. This filtering can have a significant impact on the obtained numerical solutions, and hence three-time level schemes appear to be unattractive in the context of the nonlinear convective equation. Based on this experience, splitting methods for the two-time level schemes is proposed. These schemes realistically capture the phase and energy of the nonlinear advective equation.