Objective functions for information-theoretical monitoring network design: what is “optimal”?

This paper concerns the problem of optimal monitoring network layout using information-theoretical methods. Numerous different objectives based on information measures have been proposed in recent literature, often focusing simultaneously on maximum information and minimum dependence between the chosen locations for data collection stations. We discuss these objective functions and conclude that a single-objective optimization of joint entropy suffices to maximize the collection of information for a given number of stations. We argue that the widespread notion of minimizing redundancy, or dependence between monitored signals, as a secondary objective is not desirable and has no intrinsic justification. The negative effect of redundancy on total collected information is already accounted for in joint entropy, which measures total information net of any redundancies. In fact, for two networks of equal joint entropy, the one with a higher amount of redundant information should be preferred for reasons of robustness against failure. In attaining the maximum joint entropy objective, we investigate exhaustive optimization, a more computationally tractable greedy approach that adds one station at a time, and we introduce the “greedy drop” approach, where the full set of stations is reduced one at a time. We show that no greedy approach can exist that is guaranteed to reach the global optimum.

Objective functions for information-theoretical monitoring network design: what is optimal?

This paper concerns the problem of optimal monitoring network lay- out using information-theoretical methods. Numerous different objectives based on information measures have been proposed in recent literature, often focusing simultaneously on maximum information and minimum dependence between the chosen locations for data collection. We discuss these objective functions and conclude that a single objective optimization of joint entropy suffices to maximize the collection of information for a given number of sensors. Minimum dependence is a secondary objective that automatically follows from the first, but has no intrinsic justification. In fact, for two networks of equal joint entropy, one with a higher amount of redundant information should be preferred for reasons of robustness against failure. In attaining the maximum joint entropy objective, we investigate exhaustive optimization, a more computationally tractable greedy approach that adds one station at a time, and we introduce the greedy drop approach, where the full set of sensors is reduced one at a time. We show that only exhaustive optimization will give true optimum. The arguments are illustrated by a comparative case study.

Tracking bits of information through forecasting systems: from source to decision

<p>Probabilistic forecasts are essential for good decision making, because they communicate the forecaster's best attempt at representation of both information available and the remaining uncertainty of a variable of interest. The amount of information provided, which can be measured in bits using information theory, would then be a natural measure of success for the forecast in a verification exercise. On the other hand, it may seem rational to tune the forecasting system to provide maximum value to users. Somewhat counter-intuitively, there are arguments against tuning for maximum value. When the design of the forecasting system also includes the choice of the sources of information, monitoring network optimization becomes part of the problem to solve.  <br>In this presentation, we give a brief overview of the different roles information theory can have in these different aspects of probabilistic forecasting. These roles range from analysis of predictability, model selection, forecast verification, monitoring network design, and data assimilation by ensemble weighting. Using the same theoretical framework for all these aspects has the advantage that some connections can be made that may eventually lead to a more unified perspective on forecasting. </p>

Ground-based CO2 monitoring network design over India to constrain the regional terrestrial fluxes

<p>The present study aims to design an optimal CO<sub>2</sub> monitoring network over India to better constrain the Indian terrestrial surface fluxes using Lagrangian Particle Dispersion Model FLEXPART and Bayesian inversion methods. Prior and posterior cost functions are calculated using potential emission sensitivity from FLEXPART, prior flux uncertainties from CASA-GFED biosphere fluxes and CDIAC fossil fuel fluxes, and assumed uniform observational uncertainty of 2 ppm. A total of 73 regular grid cells are identified over the Indian land mass in 2°x2° latitude by longitude resolution assuming each cell can hold a potential site. Further, using incremental optimization methodology, the effectiveness of CO<sub>2</sub> observations from these locations to reduce the Indian terrestrial flux uncertainty is quantified. The study is carried out in three parts. Firstly, we evaluated the existing stations over India in terms of reduction in uncertainty brought out by them in the surface flux estimation over the Indian landmass. This provides a unique opportunity for the representative stations to restart the observational programs based on their role in the flux estimation. In second part, we devised a methodology to design an extended network by adding a few more potential stations to the existing stations. Thirdly, we identified a completely new set of optimal stations for measuring atmospheric CO<sub>2</sub> over India, which do not have any liabilities of pre-existing stations. The study depicts that the existing stations could bring down the uncertainty in the range of 18% to 36%. Among the existing stations, Kharagpur, Sagar, Shadnagar, Kodaikanal and Pondicherry are the best stations, which are indeed adding value to the CO<sub>2</sub> flux inversions by reducing the uncertainty in the range of 4% to 13%. Addition of five new stations to the base network formed an extended network, which could reduce the uncertainty by an additional 15% for all the seasons reaching up to 45%. The new stations are mainly located over the east and north-east India with few exceptions during post-monsoon where stations are identified over the west and south India as well. The study identified 12 stations for each season and formed a ‘new network’ that could achieve the equivalent uncertainty reduction as compared with the 14 stations in the ‘extended network’. From this, an ‘optimal network’ and the best network consisting of 17 stations were identified that could best represent flux scenario and transport over India in all the four seasons. In northeast India, flux uncertainty is quite large, also the prevailing westerly wind in most parts of the year contributes to the surface CO<sub>2</sub> signature of India to that location, demanding requirement of CO<sub>2 </sub>observations throughout the year. The study highlights a major zone of CO<sub>2</sub> ‘observational void’ that exists in potential locations near east and northeast parts of India. Immediate requirement of CO<sub>2</sub> monitoring initiative in these areas is highly recommended.</p>