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

Abstract

Abstract. 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.

A general approach for evaluating of the coverage, resolution, and representation of streamflow monitoring networks

“…Spatial gaps in monitoring networks have been described variously as deficiencies in network coverage (e.g., Ning & Chang, 2003 ; Thornton et al, 2022 ), density (e.g., Coulibaly et al, 2013 ), or representation (e.g., Laize, 2004 , DeWeber et al, 2014 ). Indeed, even the objective of maximizing temporal streamflow information acquired from a monitoring network (Alfonso et al, 2010 ; Caselton & Husain, 1980 ; Foroozand & Weijs, 2021 ) can be viewed as maximizing network coverage of entropy of a temporal variable. In this case, the incremental value for a site is the conditional entropy of its streamflow over time given the joint entropy of streamflow across all other sites in the network.…”

“…Heuristic valuation of explanatory and response factors is frequently used for network design (Burn & Golter, 1991 ; Chang & Lin, 2014 ; Lanfear, 2005 ; Strobl et al, 2006 ). Alternatively, a network can be designed to maximize the information acquired by monitoring (Caselton & Husain, 1980 ; Foroozand & Weijs, 2021 ; Krstanovic & Singh, 1992 ; Mishra & Coulibaly, 2010 ) or minimize the sample error of a model calibrated with that information (Fiering, 1965 ; Kiang et al, 2013 ; Marcus et al, 2003 ; Moss & Karlinger, 1974 ; Tasker & Stedinger, 1989 ). In all of these cases, network evaluation is conditioned on a weighting system, a single hydrologic variable, or a particular model.…”

Selection of Optimal Palmer Predictors for Increasing the Predictability of the Danube Discharge: New Findings Based on Information Theory and Partial Wavelet Coherence Analysis

“…The concept of Shannon’s information entropy (1948) [ 16 ], which is very widely used in hydrology [ 2 , 9 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 ], was also applied in the present work.…”

“…Relatively recent investigations [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ] provide us with a series of analysis procedures that elucidate the intrinsic transition between the states of a natural phenomenon subject to disturbing causes. Therefore, we were able to decipher them to an extent.…”