Dan's Assignment 13

“Constraints of Satellite Derived CO2 on Carbon Sources and Sinks,” Ph.D. Thesis by Yogesh Kumar Tiwari
http://www.earthsystemschool.mpg.de/fileadmin/user_upload/Documents/Theses/Thesis_IMPRS_Tiwari.pdf

Reviewed by Dan Knights, 12/4/2007

In choosing a Ph.D. thesis to review, I decided to look outside Computer Science to explore potentials for collaboration. I am interested in the study of Earth's climate and the process of global climate change and control, so I decided to read, “Constraints of Satellite Derived CO2 on Carbon Sources and Sinks,” by Yogesh Kumar Tiwari at the Max-Planck Institute for Biogeochemistry, because it seems to have potential for a computer science application.

The objective of Tiwari's thesis is to evaluate the accuracy of novel techniques for locating sources and sinks for carbon on the planet Earth, which is sometimes referred to as the, “CO2 Transport Inverse Problem”. He begins by making the case for the need to locate these sources and sinks. Specifically, he gives these examples: (1) Increase in temperature can increase soil respiration rates, which decreases the soil's ability to store carbon. (2) Increases in carbon dioxide concentrations can increase plant photosynthesis, but decreased rainfall can decrease photosynthesis. The former will increase plant sequestering of carbon, the latter will decrease it. Such contrasting behavior necessitates careful and fine-grained monitoring of CO2 emissions. The better we know the sources, the better we can understand the process and how to control it.

Tiwari also points to the need to monitor CO2 emissions on the international level for enforcement of laws and treaties, such as the Kyoto Protocol, a CO2-reduction agreement signed by 174 countries as of November, 2007.

The main problem confronted by Tiwari in his thesis is really an optimization and search problem. The ultimate goal is to monitor changes in CO2 in as fine-grained a manner as possible, so as to associate changes with specific sites around the planet. Tiwari formulates this problem as follows.

Let f represent the “fluxes” or changes in the CO2 emissions at each measurement cite, and let C represent the observed carbon measurements at over 100 sites around the world. The actual regional fluxes, f, are transformed as they are transported through the atmosphere to the measurement sites for observation (C). Let T represent the transition matrix that transforms the fluxes into the observations. The the problem is stated simply as solving the equation C = Tf + C0 for f, where C0 represents the “initial concentration at the beginning of the simulation period.”

The issue that the CO2 research community hopes to overcome is that the matrix T has dimensions on the order of [the # of observation sites] × [the # of fluxes]. Since the number of observation sites is relatively small, and the # of fluxes in the model can be very large (spread throughout the world, and varying through time), the above equation presents a highly under-determined system. There have been, however, recent increases in the potential number of CO2 measurement localities through the use of recently launched satellite tools, for example, the Atmospheric Infrared Sounder (AIRS) currently flown on a NASA satellite. Tiwari uses two models of CO2 transport, LMDZ and TM3, coupled with specific ground-based CO2 readings for certain areas, to generate predicted observations. He then compares these predictions to the observations made by AIRS.

What Tiwari found was that the AIRS measurements matched well with certain predictions in the model, but had some discontinuity and time lag with others. Also, because of the, “dilution of surface sources and sinks” as the CO2 mixes with other gases in the troposphere, satellite observations are highly sensitive to systematic measurement errors.

By reading Tiwari's thesis from a Computer Science/Machine Learning perspective, I saw several potential areas for interdisciplinary collaboration. Firstly, there seems to be a need for systematically adapting the time-varying data to account for the lag in observations, which could perhaps be enhanced with dynamic time warping (DTW). Also, the system is inherently chaotic, but is an n-dimensional state space being projected to 1-dimensional time series. There are techniques in non-linear dynamics that can estimate the “degree of chaos” in a system, such as finding the Lyapunov exponent. Perhaps a post-analysis of the predictive models can be compared to the observed data to compare their Lyapunov exponents, or other measures of chaos. This may provide an additional modality for validation. Thirdly, it seems that if the satellite data is found to be inaccurate due to certain systematic measurement errors, it seems possible that a machine learning approach could be beneficial. If a neural net or some Bayesian network learning model were to use large amounts of satellite observation data matched with and aggregate of real ground data and with a mixture of several predictive models as a training set, it seems possible that the learning model could account for systematic error and even error introduced by the predictive models. The meaningful output of the observation data would be enhanced by the “interpreted” output given by the learning model.

Last modified 4 December 2007 at 8:55 am by danknights