The abstract The abstract as word cloud. as word cloud. Picture created on Picture created on www.Wordle.netwww.Wordle.net

Uncertainty for TimeUncertainty for Time––Spatial Hydrological Structures Spatial Hydrological Structures in the Upper Missouri River Basin: in the Upper Missouri River Basin: the Use of Statistical Learningthe Use of Statistical Learning

CUAHSI 3rd Biennial Colloquium on Hydrologic Science & Engineering

Boulder, Colorado. July 16-18, 2012

Boris A. ShmaginBoris A. Shmagin & Carol A. Johnston& Carol A. JohnstonSouth Dakota State University Brookings, SD 57007, U. S. A.South Dakota State University Brookings, SD 57007, U. S. A.

AbstractAbstractThe concept of uncertainty must be considered in order to The concept of uncertainty must be considered in order to

study, describe, assess and communicate the risk associated study, describe, assess and communicate the risk associated with hydrologic events such as flooding or drought. The need forwith hydrologic events such as flooding or drought. The need fora general theory of uncertainty was introduced by Lofty Zadeh a general theory of uncertainty was introduced by Lofty Zadeh in 2005. Zadeh considered the uncertainty as a property of in 2005. Zadeh considered the uncertainty as a property of information and used the human languageinformation and used the human language’’s property & functions s property & functions to explain his improvement of mathematical modeling (fuzzy to explain his improvement of mathematical modeling (fuzzy logic) for complex system. To move from the uncertainty as logic) for complex system. To move from the uncertainty as property for informational exchange in engineering systems property for informational exchange in engineering systems (Zadeh, 2005) & mathematical theories (Dubois & Prade, 2009) (Zadeh, 2005) & mathematical theories (Dubois & Prade, 2009) to the uncertainty for hydrological events, the uncertainty mustto the uncertainty for hydrological events, the uncertainty mustto be considered as a part of human (scientific) knowledge & to be considered as a part of human (scientific) knowledge & communication. communication.

Knowledge about natural systems such as watersheds may be Knowledge about natural systems such as watersheds may be obtained only by the analysis of empirical data (instrumental obtained only by the analysis of empirical data (instrumental observations). The source for uncertainty in the interaction in observations). The source for uncertainty in the interaction in systems must be traced in the chain: researcher systems must be traced in the chain: researcher –– modeler modeler (model maker) (model maker) –– stakeholder; those systems must be defined stakeholder; those systems must be defined with processes taking place in relation to the watershed:with processes taking place in relation to the watershed:

** [researcher [researcher -- object (natural as watershed & engineering object (natural as watershed & engineering as dam, levies)] result of interaction => [data]; as dam, levies)] result of interaction => [data];

* * [data [data –– model maker] result of modeling => [hydrologic model maker] result of modeling => [hydrologic structures]; structures];

* * [modeler [modeler –– stakeholder or scholar] result of interaction => stakeholder or scholar] result of interaction => [new knowledge].[new knowledge].

Uncertainty starts from the research task unveiled by the Uncertainty starts from the research task unveiled by the researcher & then to be traced with the changes of our researcher & then to be traced with the changes of our knowledge in every of those double interactions. In other words,knowledge in every of those double interactions. In other words,scientist working in hydrology has to define & handle the scientist working in hydrology has to define & handle the uncertainty & communicate the knowledge about timeuncertainty & communicate the knowledge about time--spatial spatial variability of the hydrologic events. For connections in the variability of the hydrologic events. For connections in the beginning & the end [researcher beginning & the end [researcher –– object] & [results object] & [results ––stakeholder] concepts & approaches have to be developed. For stakeholder] concepts & approaches have to be developed. For the central part of this chain: [object the central part of this chain: [object –– data data –– model model –– results], results], --mathematical models are in use. mathematical models are in use.

The goal of the poster presentation is to illustrate the The goal of the poster presentation is to illustrate the uncertainty uncertainty –– knowledge relationship & modification during knowledge relationship & modification during hydrological study of Upper Missouri River Basin (UMRB) with hydrological study of Upper Missouri River Basin (UMRB) with the application of statistical learning. Statistical learning the application of statistical learning. Statistical learning ((VapnikVapnik, 1998) is based on statistical techniques (empirical , 1998) is based on statistical techniques (empirical principal components, linear multiprincipal components, linear multi--regressions, simplified Fourier regressions, simplified Fourier analysis, shifts), & allows quantification of: analysis, shifts), & allows quantification of:

(1)(1) the multidimensional timethe multidimensional time--spatial variability of spatial variability of hydrological events in the UMRB as hydrological structures;hydrological events in the UMRB as hydrological structures;

(2)(2) the the ““recoveryrecovery”” of regionalization & seasonality of river of regionalization & seasonality of river discharge in UMRB;discharge in UMRB;

(3)(3) the variability of time series in the form of hydrological the variability of time series in the form of hydrological structures with oscillations & seasonality.structures with oscillations & seasonality.

The definition & properties of coordinate systems aid The definition & properties of coordinate systems aid visualization of the uncertainty concept of hydrological events visualization of the uncertainty concept of hydrological events in in a given river watershed. The models affiliated with different a given river watershed. The models affiliated with different coordinate systems in the UMRB reflect 30% coordinate systems in the UMRB reflect 30% -- 78% of 78% of variability of existed empirical data. Those characteristics of variability of existed empirical data. Those characteristics of mathematical models (reflected variability, number of factors & mathematical models (reflected variability, number of factors & others) may be used to establish hydrology & then bring the others) may be used to establish hydrology & then bring the concept of the knowledge & uncertainty to stakeholders & concept of the knowledge & uncertainty to stakeholders & scholars. Definition of the uncertainty for hydrological events scholars. Definition of the uncertainty for hydrological events based on the use of statistical learning opens the way for a based on the use of statistical learning opens the way for a variety of disciplines for the development of an artificial variety of disciplines for the development of an artificial intelligence approach to analyze the interaction of hydrologicalintelligence approach to analyze the interaction of hydrologicalevents, engineering installations, & social systems in the UMRB,events, engineering installations, & social systems in the UMRB,including the concepts of risk assessment.including the concepts of risk assessment.

ReferencesReferencesBeven, K. (2007). Towards integrated environmental models oBeven, K. (2007). Towards integrated environmental models of f

everywhere: uncertainty, data & everywhere: uncertainty, data & modellingmodelling as a learning process. as a learning process. Hydrology & Earth System Sciences, 11(1), 460Hydrology & Earth System Sciences, 11(1), 460--467. 467.

BudescuBudescu, D. V., , D. V., BroomellBroomell, S., & , S., & PorPor, H., H.--H. (2009). Improving H. (2009). Improving communication of uncertainty in the reports of the intergovernmecommunication of uncertainty in the reports of the intergovernmental ntal panel on climate change. Psychological science, 20(3), 299panel on climate change. Psychological science, 20(3), 299--308. 308.

Dubois, D. & H. Prade (1988) Possibility Theory, New York: Dubois, D. & H. Prade (1988) Possibility Theory, New York: Plenum Plenum Hall, J., & Anderson, M. (2002). Handling uncertainty in exHall, J., & Anderson, M. (2002). Handling uncertainty in extreme or treme or

unrepeatable hydrological processes? The need for an alternativeunrepeatable hydrological processes? The need for an alternativeparadigm. Hydrological Processes, 16(9), 1867paradigm. Hydrological Processes, 16(9), 1867--1870. 1870.

PappenbergerPappenberger, F., & Beven, K. J. (2006). Ignorance is bliss: Or seven , F., & Beven, K. J. (2006). Ignorance is bliss: Or seven reasons not to use uncertainty analysis. Water Res. Res., 42(5),reasons not to use uncertainty analysis. Water Res. Res., 42(5), 11--8. 8.

PidgeonPidgeon, N., & , N., & FischhoffFischhoff, B. (2011). The role of social & decision , B. (2011). The role of social & decision sciences in communicating uncertain climate risks. Nature Climatsciences in communicating uncertain climate risks. Nature Climate e Change, 1(1), 35Change, 1(1), 35--41. 41.

VapnikVapnik V. N. 1998 Statistical Learning TheoryV. N. 1998 Statistical Learning Theory””.. Wiley,Wiley, New York.New York.Zadeh, L. (2005). Toward a generalized theory of uncertaintZadeh, L. (2005). Toward a generalized theory of uncertainty (GTU) y (GTU)

-- an outline. Information Sciences, 172(1an outline. Information Sciences, 172(1--2), 12), 1--40. 40.

Communication Communication of the results of the results Object Object –– Data Data –– Models Models –– Results Results

Engagement Engagement with the objectwith the object

Researcher Researcher –– Modeler Modeler –– Stakeholder Stakeholder

Statistical Learning: Statistical Learning: SummarySummary

““1. With the appearance of computers the concept of natural 1. With the appearance of computers the concept of natural science, its methodology & philosophy started a process of a science, its methodology & philosophy started a process of a

paradigmparadigm change: change: The concepts, methodology, & philosophy of a The concepts, methodology, & philosophy of a Simple WorldSimple World

move to very different concepts, philosophy & methodology of a move to very different concepts, philosophy & methodology of a Complex WorldComplex World..

2. In such changes an important role belongs to the 2. In such changes an important role belongs to the mathematical facts that were discovered by analyzing the mathematical facts that were discovered by analyzing the

““Drosophila flyDrosophila fly”” of cognitive science the of cognitive science the ““Pattern recognition Pattern recognition problemproblem”” & attempts to obtain their philosophical & attempts to obtain their philosophical

interpretation.interpretation.3. The results of these analyzes lead to methods that go 3. The results of these analyzes lead to methods that go

beyond the classical concept of science: creating generative beyond the classical concept of science: creating generative models of events & models of events & explainabilityexplainability of obtained rules. of obtained rules.

4. The new paradigm introduces direct search for solution 4. The new paradigm introduces direct search for solution ((transductivetransductive inference, instead of inductive), the meditative inference, instead of inductive), the meditative

principle of decision making, & a unity of two languages for principle of decision making, & a unity of two languages for pattern description: technical (rational) & holistic (irrationalpattern description: technical (rational) & holistic (irrational). ).

This leads to the convergence of the exact science with This leads to the convergence of the exact science with humanities.humanities.

5. The main difference between the new paradigm 5. The main difference between the new paradigm (developed in the computer era) & the classical one (developed in the computer era) & the classical one (developed before the computer era) is the claim:(developed before the computer era) is the claim:

To guarantee the success of inference one needs to control the To guarantee the success of inference one needs to control the complexity of algorithms for inference rather than complexity complexity of algorithms for inference rather than complexity

of the function that these algorithms produce. of the function that these algorithms produce. Algorithms with low complexity can create a complex function Algorithms with low complexity can create a complex function

which will generalize well.which will generalize well.””From From VapnikVapnik’’ss presentation: presentation:

Empirical Inference Science, 2006Empirical Inference Science, 2006

The abstract as word clouds. The abstract as word clouds. Pictures created on Pictures created on

www.Wordle.netwww.Wordle.netIdeal (math) axis (from Merriam Ideal (math) axis (from Merriam -- Webster):Webster):

aa :: a straight line about which a body or a geometric figure rotatesa straight line about which a body or a geometric figure rotates or may be supposed to rotateor may be supposed to rotatebb :: a straight line with respect to which a body or figure is symmeta straight line with respect to which a body or figure is symmetrical rical —— called also called also axis of symmetryaxis of symmetry

cc :: a straight line that bisects at right angles a system of parallea straight line that bisects at right angles a system of parallel chords of a curve & divides the curve into two symmetrical parl chords of a curve & divides the curve into two symmetrical partstsdd :: one of the reference lines of a coordinate system math technologone of the reference lines of a coordinate system math technological (engineering) scientificical (engineering) scientific