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.

Near-surface soil moisture is a key state variable of the hydrologic cycle and plays a significant role in the global water and energy balance by affecting several hydrological, ecological, meteorological, geomorphologic, and other natural processes in the land-atmosphere continuum. Presence of soil moisture in the root zone is vital for the crop and plant life cycle. Soil moisture distribution is highly non-linear across time and space. Various geophysical factors (e.g., soil properties, topography, vegetation, and weather/climate) and their interactions control the spatio-temporal evolution of soil moisture at various scales. Understanding these interactions is crucial for the characterization of soil moisture dynamics occurring in the vadose zone. This dissertation focuses on understanding the spatio-temporal variability of near-surface soil moisture and the associated physical control(s) across varying measurement support (point-scale and passive microwave airborne/satellite remote sensing footprint-scale), spatial extents (field-, watershed-, and regional-scale), and changing hydro-climates. Various analysis techniques (e.g., time stability, geostatistics, Empirical Orthogonal Function, and Singular Value Decomposition) have been employed to characterize near-surface soil moisture variability and the role of contributing physical control(s) across space and time. Findings of this study can be helpful in several hydrological research/applications, such as, validation/calibration and downscaling of remote sensing data products, planning and designing effective soil moisture monitoring networks and field campaigns, improving performance of soil moisture retrieval algorithm, flood/drought prediction, climate forecast modeling, and agricultural management practices.

The dynamics captured in the ocean surface current data provided by satellite altimetry has been a subject of debate since the past decade. In particular, the contribution of surface and interior dynamics to altimetry remains unclear. One avenue to settling this issue is to compare the turbulence (for example, the nature of spectra and interscale fluxes) captured by altimetry to theories of two-dimensional, surface and interior quasigeostrophic turbulence. In this thesis, we focus on mesoscales (i.e., scales of the order of few hundred kms) that are well resolved by altimetry data. Aspects of two dimensional, three dimensional, geotropic and surface quasigeostrophic turbulence are revisited and compared with the observations. Specifically, we compute kinetic energy (KE) spectra and fluxes in five geographical regions (all over the globe) using 21 years of 0.25◦resolution daily data as provided by the AVISO project. We report a strong forward cascade of KE at small scales (accompanied by a spectral scaling of the form k−3) and a robust inverse cascade at larger scales. Further, we show that the small diver-gent part in horizontal velocity data drives the strong forward flux of KE. Indeed, on considering only the non-divergent part of the flow, in accord with incompressible two-dimensional turbulence, the inverse cascade is unaffected, but the forward transfer becomes very weak and the spectral slopes over this range of scales tend to a relatively steeper k−3.5scaling. We note that our results do not agree with interior first bar clinic mode quasigeostrophic (incorrect strength of forward flux) or surface-quasigeostrophic (incorrect spectral slopes) turbulence. Rather, the results are compatible with rotating shallow water and rotating stratified Boussinesq models in which condition of geostrophic balance is dominant but the divergence of horizontal velocity field is not exactly zero. Having seen the “mean” picture of fluxes and spectra from altimetry, in the second part of the thesis we investigate the variability of these entities. In particular, we employ Empirical Or-thogonal Function (EOF) analysis and focus on the variability in the spectral flux. Remarkably, over the entire globe, irrespective of the region under consideration, we see that the first two EOFs explain a large part of the variability in flux anomalies. The geometry of these modes is distinct, the first represents a single signed transfer across scales (i.e. large to small or small to large depending on the sign of the associated principal component), while the second is a mixed mode in that it exhibits a forward/inverse transfer at large/small scales.

Fahrbahnunebenheiten und Gleislagestörungen können als Repräsentanten schwach stationärer Prozesse aufgefasst werden. Die Beschreibung der Qualitätsklassen von Fahrwegen erfolgt konventionell über die Spektraldichte (Leistungsdichte). Ausgehend von der Spektraldichte-Beschreibung wird die Generierung synthetischer Fahrwegstörungen für die numerische Simulation von Fahrzeugen als Mehrkörpersystem mit den Mitteln der Fourieranalyse und mit Hilfe von Wavelets untersucht. / Road unevenness and track irregularities can be considered as realisations of weakly stationary stochastic processes. A description of track quality levels is given by the (power)spectral density of the related process. Here, the synthesis of track irregularities for a given spectral density using fourier series and wavelets is considered.

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Fahrbahnunebenheiten und Gleislagestörungen können als Repräsentanten schwach stationärer Prozesse aufgefasst werden. Die Beschreibung der Qualitätsklassen von Fahrwegen erfolgt konventionell über die Spektraldichte (Leistungsdichte). Ausgehend von der Spektraldichte-Beschreibung wird die Generierung synthetischer Fahrwegstörungen für die numerische Simulation von Fahrzeugen als Mehrkörpersystem mit den Mitteln der Fourieranalyse und mit Hilfe von Wavelets untersucht. / Road unevenness and track irregularities can be considered as realisations of weakly stationary stochastic processes. A description of track quality levels is given by the (power)spectral density of the related process. Here, the synthesis of track irregularities for a given spectral density using fourier series and wavelets is considered.