ENVIRONMENT AND ENERGY

Summary

The Earth is a dynamic system, various physical processes lead to deformations of the Earths surface or mass transport in its interior. Quantifying the changes with the help of measurements is a key task of geodesy, for instance to make signals attributed to climate change visible. For this, reference systems and reference surfaces are required. E.g. sea level rise refers to the so called Mean Sea Surface (MSS), or the geoid as an equipotential surface is required to show mass transport. The reference surfaces can be determined from hundreds of million measurements collected by satellites. Due to the characteristics of the collected data and the complexity of the surfaces, high performance computing is required for the numerical analysis.

Project Description

Introduction and Context

The project is focused on the computation of reference surfaces which are required to quantify temporal changes in the Earth system. Various physical processes lead to mass transport in the Earth system or to a deformation of the Earths’ surface. These changes can be either numerically modeled based on physical laws, e.g. the ocean circulation by oceanographic models, or – as targeted in geodesy – measured. These measurements can then be either used to calibrate or validate the physical models or to identify unknown signals or confirm expected signals.

For deformation studies or mass transport studies, the gravity field of the Earth plays an important role. By definition of physical heights, no water flows between points of same height. Due to an irregular distribution of materials of various density in the Earths’ interior, the gravitational attraction is varying. Therefore, an equipotential surface has a very irregular shape. Its accurate knowledge is required for the definition of height systems and to monitor mass transport relative to the a long term mean. From the static gravity field, the so called geoid can be derived, which shows the deviation of the equipotential surface from a kind of best fit ellipsoid (see Fig. 1). The variations are in the order of ±100 meter. Whereas the dominant features are well known, the fine scale variations are not globally known with the required precision (centimeter level). Therefore dedicated satellite gravity field missions were developed to measure the gravity field from space. With the help of the granted computing time, global gravity field models from satellite missions were computed.

To study sea level rise, a long term Mean Sea Surface (MSS) is required to quantify the changes with respect to the mean. The MSS is the second reference surface studied within the project. A global MSS product is depicted in Fig. 2. It is determined from temporally and spatially averaged Sea Surface Height (SSH) measurements taken by radar altimetry satellites since decades. Although its computations seems simple – averaging the measured heights in space and time – the computation is challenging as the data sampling is very irregular in the spatial as well as the time domain. Within the project, a continuous representation of the MSS is proposed, co-estimating the spatio-temporal changes.

Comparing the geoid in Fig. 1 and the MSS in Fig. 2 over the ocean, both reference surfaces seem to correspond. But, when taking the difference and applying some smoothing the third reference surface of interest results, the so called Mean Dynamic ocean Topography (MDT, see Fig. 3). Assuming the Earth in rest and no forces acting on the ocean, it is obvious that the ocean water masses would adjust to the geoid (no water flows). But due to variations in temperature, salinity and forces like winds, the MSS deviates from the geoid. This deviation is defined as the MDT and can be linked to the steady-state ocean circulation. The currents are proportional to the gradient of MDT. Within the project, an approach is developed to jointly estimate both, the geoid and the MDT from SSH and complementary measurements for regional analysis.

Due to a huge number of measurements (hundreds of millions) analyzed, the data characteristics, and a large number of parameters (hundreds of thousands) required to describe the reference surfaces, the applied approaches are computationally challenging and require the use of high performance computing resources.

Approach for Spatio-Temporal Mean Sea Surface Estimation

Although the MSS is ‚just‘ the temporal average of the instantaneous SSH measurements the computation is challenging. This is strongly related to the sampling of the altimetry missions: this are either exact repeat missions, which revisit the same ground location after a few days (10 to 30 days) or geodetic missions with a repeat cycle above a year. Whereas the first have a coarse spatial resolution (80 to 300 km cross track), the later have a cross track spacing of just few kilometers (see Fig. 4). Consequently, for the estimation of an MSS both mission types have to be jointly analyzed over a period of decades. As the number of missions varies over the analysis period, spatial and temporal sampling is inhomogeneous, such that aliasing occurs. Therefore the temporal ocean variability has to be accounted for.

Within the project, a one step procedure is developed, jointly estimating a high resolution MSS parameterized by finite elements and a lower resolution spatio-temporal model for the ocean variability. With the help of the computing time  granted in the project, the approach was successfully implemented and tested for regional MSS determination [1, 2].