We study the space-time characteristics of global tropical rainfall. The data used is from the Tropical Rainfall Measuring Mission (TRMM) and spans the years 2000-2009. Using anomaly fields constructed by removing a single mean and by subtracting the climatology of the ten year dataset, we extract the dominant modes of variability of tropical rainfall from an Empirical Orthogonal Function (EOF) analysis. To our knowledge, this is the first attempt at applying the EOF formal-ism to high spatio-temporal resolution global tropical rainfall. Spatial patterns and temporal indices obtained from the EOF analysis with single annual mean removed show large scale patterns associated with the seasonal cycle. Even though the seasonal cycle is dominant, the principal component (PC) time series show fluctuations at subseasonal scales. When the climatological mean is removed, spatial patterns of the dominant modes resemble features associated with tropical intraseasonal variability (ISV). Correspondingly, the signature of a seasonal cycle is relatively suppressed, and the PCs have prominent fluctuations at subseasonal scales. The significance of the leading EOFs is demonstrated by means of a novel ratio plot of the variance captured by the leading EOFs to the variance in the data. This shows that, in regions of high variability (which go hand in hand with high rainfall), the EOF/PC pairs capture a fair amount of the variance (up to 20% for the first EOF/PC pair) in the data. We then pursue an EOF analysis of the finest data resolution available. In particular, we per-form a regional analysis (a global analysis is beyond our present computational resources) of the tropics with 0.25◦×0.25◦, 3-hourly data. The regions we focus on are the Indian region, the Maritime Continent and South America. The spatial patterns obtained reveal a rich hierarchical structure to the leading modes of variability in these regions. Similarly, the PCs associated with these leading spatial modes show variability all the way from 90 days to the diurnal scale. With the results from EOF analysis in hand, we quantify the multiscale spatio-temporal structures encountered in our study. In particular, we examine the power spectra of the PCs and EOFs. A robust feature of the space and time spectra is the distribution of energy or variance across a range of scales. On the temporal front, aside from a seasonal and diurnal peaks, the variance scales as a power-law from a few days to the 90 day period. Similarly, below the planetary scale, from approximately 5000 km to 200 km the spatial spectrum also follows a power-law. Therefore, when trying to understand the variability of tropical rainfall, all scales are important, and it is difficult to justify a focus on isolated space and time scales.

The fine-scale structure of global (30N-30S) tropical rainfall is characterised using 13 years (1998-2010) of 3-hourly and daily, 0.25-degree Tropical Rainfall Measuring Mission (TRMM) 3B42 rainfall product. At the outset, the dominant timescales present in rainfall are identified. Specifically, the Fourier spectrum (in time) is estimated in two ways (a) spectrum of spatially averaged (SoSA) rainfall; and (b) spatial average of the spectrum (SAoS) of rainfall at each grid point. This procedure is applied on rainfall at the 3-hourly and daily temporal resolutions. Both estimates of the spectrum show the presence of a very strong seasonal cycle. But, at subseasonal timescales, the two methods of estimating spectrum show a marked difference in daily rainfall. Specifically, with SoSA the variability peaks at a subseasonal timescale of around 5 days, with a possible secondary peak around 30-40 days (mostly in the southern tropics). With SAoS, the variability is distributed across a range of timescales, from 2 days to 90 days. However, with finer resolution (3-hourly) observations, it is seen that (besides the seasonal cycle) both methods agree and yield a dominant diurnal scale. Along with other subseasonal scales, the contribution and geographical distribution of diurnal scale variability is estimated and shown to be highly significant. Given its large contribution to the variability of tropical rainfall, the diurnal cycle is extracted by means of a Fourier-based filtering and analysed. The diurnal rainfall anomaly is constructed by eliminating all timescales larger than 1 day. Following this, taking care to avoid spurious peaks associated with Gibbs oscillations, the time of day (called the peak octet) when the diurnal anomaly is largest is identified. The peak octet is estimated for each location in the global tropics. This is repeated for 13 years, and the resulting mode of the time of maximum rainfall is established. It is seen that (i) most land regions receive rainfall during the late afternoon/early evening hours; (ii) rainfall over open oceans lack a dominant diurnal signature with a possible combination of early morning and afternoon showers; (iii) coastal regions show a clear south/southwest propagation in the mode of the peak octet of rainfall. In addition to being a comprehensive documentation of the diurnal cycle at very fine scales, the results serve as a critical test for the validation of theoretical and numerical models of global tropical rainfall.