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The structure and climatology of the monsoon low-level jet (MLLJ) is studied based on dynamically downscaled simulations over a 37-year period (1980-2016) using the Weather Research Forecasting (WRF) model. The simulations are conducted by adopting a continuous initialization method with daily re-initializations using ERA-Interim data as initial and boundary conditions. Validation of the downscaled fields with radiosonde data shows that the model has reasonable skill in reproducing MLLJ characteristics. Analysis of the simulations suggests that the MLLJ exhibits systematic diurnal variation: maximum winds of the synoptically induced large-scale monsoon jet occur during the daytime, and the orographic channelled winds through the mountains of East Africa, Hejaz, and Western Ghats in the night-time. These diurnal changes in monsoon winds modulate the moisture convergence process and the associated evolution of rainfall over India. Seasonal and monthly climatology of monsoon winds shows that the model accurately reproduces the spatial pattern of winds and slightly overestimates (2-3 m/s) the mean monthly winds over the Bay of Bengal and Arabian Seas. Analysis of wind variability and the trends using 37 years simulations suggests that the MLLJ exhibits an increasing trend in wind speed on both seasonal and monthly scales, except for August which shows a decreasing trend. The weakening of the MLLJ in August has a profound influence on the number of monsoon depressions forming over the Bay of Bengal (which are decreasing), and on the number of break days (which are increasing) and associated precipitation reduction over the central Indian region.