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# Graphical models and climate networks

I just bumped into this interesting webpage:

This project uses Bayesian networks to study how climate patterns influence each other. It sounds really interesting, and more truly "network-theoretic" than just computing an "average link strength" between lots of nodes.

Abstract: This project seeks to recover cause-effect relationships from observational/reanalysis data using graphical models. We have applied causal discovery methods, particularly constraint-based structure learning to understanding the dynamical interactions among four prominent modes of atmospheric low-frequency variability in boreal winter including the Western Pacific Oscillation (WPO), Eastern Pacific Oscillation (EPO), Pacific North America Pattern (PNA) and North Atlantic Oscillation (NAO). The role of ENSO in these interactions is also examined. The results are shown as static and temporal independence graphs also known as Bayesian Networks. Ongoing efforts include the construction of a new type of climate network based on cause-effect-relation (information flow) in the atmosphere.

A summary graph showing the causal-relationship among WPO, EPO, NAO and PNA. Arrows indicate the direction of information flow and numbers correspond to the time-lag in days. (Ebert-Uphoff and Deng 2012a)

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1.
edited July 2014

This is another paper by those guys. I like the idea of thinking about information flow.

Abstract - In this paper we introduce a new type of climate network based on temporal probabilistic graphical models. This new method is able to distinguish between direct and indirect connections and thus can eliminate indirect connections in the network. Furthermore, while correlation-based climate networks focus on similarity between nodes, this new method provides an alternative viewpoint by focusing on information flow within the network over time. We build a prototype of this new network utilizing daily values of 500 mb geopotential height over the entire globe during the period 1948 to 2011. The basic network features are presented and compared between boreal winter and summer in terms of intra-location properties that measure local memory at a grid point and inter-location properties that quantify remote impact of a grid point. Results suggest that synoptic-scale, sub-weekly disturbances act as the main information carrier in this network and their intrinsic timescale limits the extent to which a grid point can influence its nearby locations. The frequent passage of these disturbances over storm track regions also uniquely determines the timescale of height fluctuations thus local memory at a grid point. The poleward retreat of synoptic-scale disturbances in boreal summer is largely responsible for a corresponding poleward shift of local maxima in local memory and remote impact, which is most evident in the North Pacific sector. For the NH as a whole, both local memory and remote impact strengthen from winter to summer leading to intensified information flow and more tightly-coupled network nodes during the latter period.

Comment Source:This is another paper by those guys. I like the idea of thinking about information flow. * Imme Ebert-Uphoff and Yi Deng, [A new type of climate network based on probabilistic graphical models: Results of boreal winter versus summer](http://deng.eas.gatech.edu/sites/default/files/files/Ebert-Uphoff_Deng_2012_ClimateNetwork.pdf), _Geophysical Research Letters_ **39**(2012) L19701. > **Abstract** - In this paper we introduce a new type of climate network based on temporal probabilistic graphical models. This new method is able to distinguish between direct and indirect connections and thus can eliminate indirect connections in the network. Furthermore, while correlation-based climate networks focus on similarity between nodes, this new method provides an alternative viewpoint by focusing on information flow within the network over time. We build a prototype of this new network utilizing daily values of 500 mb geopotential height over the entire globe during the period 1948 to 2011. The basic network features are presented and compared between boreal winter and summer in terms of intra-location properties that measure local memory at a grid point and inter-location properties that quantify remote impact of a grid point. Results suggest that synoptic-scale, sub-weekly disturbances act as the main information carrier in this network and their intrinsic timescale limits the extent to which a grid point can influence its nearby locations. The frequent passage of these disturbances over storm track regions also uniquely determines the timescale of height fluctuations thus local memory at a grid point. The poleward retreat of synoptic-scale disturbances in boreal summer is largely responsible for a corresponding poleward shift of local maxima in local memory and remote impact, which is most evident in the North Pacific sector. For the NH as a whole, both local memory and remote impact strengthen from winter to summer leading to intensified information flow and more tightly-coupled network nodes during the latter period.
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2.
edited July 2014

Hello John

I studied this paper last evening and looked at the software they used (TETRAD). I could tell you that the results of the paper could not easily be replicated due to many variations of possibilities for both usage of data as well as the software input data.

You might know that the software TETRAD does not do bi-directional edges (per user manual)! I have no idea how they got the bi-directional edges in the diagrams they posted in their websites. Also TETRAD only does Linear Transformations from node to node (per user manual).

I could also report that this approach requires very large computing no lesser than machine learning.

They have used a new approach that differs from the known Machine Learning SIMILARITY algorithms mentioned in the beginning of the paper, given the fact that the latter performs magnificently in many disciplines of science, I wondered why.

But I love the network approach with weights associated to each edge.

However I am thinking of another/additional approach to their network i.e replace the network by its edge-adjacency matrix which will be super large (NO PROBLEM for GPU servers). Then assign a positive probability for flow of some weather condition from i-node to j-node and place that probability into entry i,j in adjacency matrix, making sure the matrix is stochastic. Note that the i,j entry may not be same as j, i .

Then we study the matrix-POWERS of the adjacency matrix to simulate the flow of information for weather condition. The infinite power in particular will show us a STABLE condition where stochastic matrix stays the same as its powers. If the original matrix is not stochastic the infinite power might not have a limit i.e. an unstable orbit of some kind.

In addition to the Correlation/Covariance let's take the above adjacency matrices (for different times or places on the planet) and find their commutator and take the matrix norm of it:

||AB - BA||

This would then give us another measure of tangled-ness of the weather systems.

Or going really wild... take the Log[A] and Log[B] and compute the BCH[A,B] i.e. Baker–Campbell–Hausdorff formula up to some number of terms down the bracket series . (guess from whom I learned this)

Dara

Comment Source:Hello John I studied this paper last evening and looked at the software they used (TETRAD). I could tell you that the results of the paper could not easily be replicated due to many variations of possibilities for both usage of data as well as the software input data. You might know that the software TETRAD does not do bi-directional edges (per user manual)! I have no idea how they got the bi-directional edges in the diagrams they posted in their websites. Also TETRAD only does Linear Transformations from node to node (per user manual). I could also report that this approach requires very large computing no lesser than machine learning. They have used a new approach that differs from the known Machine Learning SIMILARITY algorithms mentioned in the beginning of the paper, given the fact that the latter performs magnificently in many disciplines of science, I wondered why. But I love the network approach with weights associated to each edge. However I am thinking of another/additional approach to their network i.e replace the network by its edge-adjacency matrix which will be super large (NO PROBLEM for GPU servers). Then assign a positive probability for flow of some weather condition from i-node to j-node and place that probability into entry i,j in adjacency matrix, making sure the matrix is stochastic. Note that the i,j entry may not be same as j, i . Then we study the matrix-POWERS of the adjacency matrix to simulate the flow of information for weather condition. The infinite power in particular will show us a STABLE condition where stochastic matrix stays the same as its powers. If the original matrix is not stochastic the infinite power might not have a limit i.e. an unstable orbit of some kind. In addition to the Correlation/Covariance let's take the above adjacency matrices (for different times or places on the planet) and find their commutator and take the matrix norm of it: ||AB - BA|| This would then give us another measure of tangled-ness of the weather systems. Or going really wild... take the Log[A] and Log[B] and compute the BCH[A,B] i.e. Baker–Campbell–Hausdorff formula up to some number of terms down the bracket series . (guess from whom I learned this) Dara