This paper contributes to the reproduction of the limited fine timescale rainfall time series from the abundant daily rainfall time series. It provides a copula based daily rainfall disaggregation model to predict the total wet period's duration (L) for given daily rainfall amount (R). Transition probabilities, parameterised by L, are used to aid the assignment of daily storm profile (DSP) type to R. A wet(1)-dry(0) alternation sub-model is used to generate a 1-0 binary chain of total duration D and consistent with variable L. Carefully designed rules are followed to select an observed scaled DSP from the Australian capital cities located in different climatic regions. Multiplication of the scaled DSP proportions by R gives the storm profile for the wet day. Finally, the storm profile start time is randomly sampled from the available time of the wet day or as determined by the DSP type. Application of the developed model to the Australia capital cities' daily rainfall time series has reproduced gross statistics of the rainfall time series very well at all aggregation levels down to 6 minutes. There is a very high potential for widespread application of the presented model throughout Australia and abroad, in particular where fine timescale rainfall data are limited. Further research is required to regionalise the model parameters outside the capital cities.