It is well known that ocean-atmosphere dynamic affects the weather conditions over the continents and the ocean itself.
The hydrologic cycle is driven by climatic parameters like precipitation, temperature, evaporation, winds and humidity.
Hence, the river's water discharges and lake water level variations are impelled by climatic conditions also. Lake Izabal
is the largest one in Guatemala; its main tributary is the Polochic River. Its level is related to the Polochic Rivers runoff
and therefore to the precipitation/evaporation over its catchment area. The Lake Izabal water level fluctuations are driven
by the annual cycle of rainy and dry seasons. In this study the ENVISAT RA-2 Geophysical Data Records orbits over the
lake, coupled with in-situ measurements are used in order to determine and characterize the lake level fluctuations. The
precipitation records over the lake's catchment area are also analyzed. In addition, some relationships of the lake level
interannual variations with the climate indexes of Southern Oscillation Index SOI and the Tropical North Atlantic NATL
were investigated. The main result is that the abrupt lake level rise in July 2006 is correlated to an abnormal precipitation
in June 2006. Theoretically, this was forced by "La Nina" Southern Oscillation events during early 2006.
The Cramer-Rao lower bound (CRLB) for the estimations of the cosine and sine amplitudes of multi-tone
sinusoidal model is derived and applied on TOPEX/Poseidon satellite altimetry data sets covering the Indian Ocean. The
CRLB depends on the variance of the White Gaussian Noise that it is computed by Modern Parametric Autoregressive
Adaptative Spectral Analysis. Determining CRLB parameters it is possible to establish the minimal error associated to
any model built to work in the study area what improves the intrinsic bias of the generated time series. The noise that
appears in the altimetric data depends strongly on the errors from the atmospheric and geophysical corrections, so the
role of the inverted barometer and tidal corrections are also analyzed. The results is summarized as: a) the spatial
structure of the order of the parametric model considering the application or not of the above corrections and its
relationship to the surface dynamical system of currents in Indian Ocean; b) the spatial structure of the variance of the
WGN in the area and its meaning; c) the CRLB for the Geoid's estimators and the CRLB for the estimators of the semiannual
and annual waves.
The radar altimeter data sets are used to study several dynamical characteristic of the World's Oceans because the artificial satellites have a global coverage. One of the most important applications is related to the Mean Sea Level changes. The authors take into account the TOPEX/Poseidon data for the Mediterranean Sea and the Iberian Atlantic in order to compute the trend of the Mean Sea Level by means of two different procedures: the linear regression and fractal geometry. The first one leads to very well known results but the errors in the estimation are quite large and the second leads to more reliable results.