Spatiotemporal Regime of Climate & Streamflow in the US Great Lakes Basin

Transcription

1 Spatiotemporal Regime of Climate & Streamflow in the US Great Lakes Basin Boris Shmagin & Carol Johnston, South Dakota State University, Nir Y. Krakauer, City College of New York

2 Introduction

3 Five main regions & streamflow regimes

4 Introduction

5 Multivariate empirical data & philosophy of analysis {Q * } A factor is a portion of a quantity, usually an integer or polynomial that, when multiplied by other factors, gives the entire quantity. The determination of factors is called factorization (or sometimes "factoring"). It is usually desired to break factors down into the smallest possible pieces so that no factor is itself factorable. Factor analysis allows the determination of common axes influencing sets of independent measured sets. It is "the granddaddy of multivariate techniques (Gould 996, pp. 4-4) & was invented by Spearman. The main applications of factor analytic techniques are: () to reduce the number of variables and () to detect structure in the relationships between variables, that is to classify variables. (From: Wolfram MathWorld)

6 The explanation for regime of streamflow has to be found

7 The boundaries are administrative

8 The explanation for regime of streamflow has to be found Consideration of the Great Lakes region as uniform in joint boundaries is the common approach

9 Report from USGS

10 Historical changes were presented month by month

11 Topics Introduction: The explanation for regime of streamflow has to be found (presented earlier) Regime of climate characteristics (air temperature & precipitations) Scale in Regime what is it? The model Results for discussion

12 {P 5*65 } {T 5*98 } Data for characteristics of climate regime

13 Air temperatures '988-89' '9-' '94-5' '98-9' '9-' '96-7' '9-' '98-9' '9-' '96-7' '94-4' '944-45' '948-49' '95-5' '956-57' '964-65' '968-69' '97-7' '976-77' '98-8' '984-85' Factor Scores '99-9' '-' '4-5' Factor Linear (Factor ) Poly. (Factor ) Factor Linear (Factor ) Poly. (Factor ) Hydrological year '9-' '94-5' '98-9' '9-' '96-7' '9-' '98-9' '9-' '96-7' '94-4' '944-45' '948-49' '95-5' '956-57' '964-65' '968-69' '97-7' '976-77' '98-8' '984-85' '988-89' '99-9' '-' '4-5' Hydrological year Factor Scores '9-' '94-5' '98-9' '9-' '96-7' '9-' '98-9' '9-' '96-7' '94-4' '944-45' '948-49' '95-5' '956-57' '964-65' '968-69' '97-7' '976-77' '98-8' '984-85' '988-89' '99-9' '-' '4-5' {T 5*98 } Factor Linear (Factor ) Poly. (Factor ) Hydrological year Factor Scores

14 Precipitation, annual sum Precipitation, annual sum Factor 5 Linear (Factor 5) Poly. (Factor 5). Factor Linear (Factor ) Poly. (Factor ) '9-' '94-5' '98-9' '9-' '96-7' '9-' '98-9' '9-' '96-7' '94-4' '944-45' '948-49' '95-5' '956-57' '964-65' '968-69' '97-7' '976-77' '98-8' '984-85' '988-89' '99-9' '-' '4-5' '9-' '94-5' '98-9' '9-' '96-7' '9-' '98-9' '9-' '96-7' '94-4' '944-45' '948-49' '95-5' '956-57' '964-65' '968-69' '97-7' '976-77' '98-8' '984-85' '988-89' '99-9' '-' '4-5' {T 5*65 } Factor Linear (Factor ) Poly. (Factor ). Factor 4 Linear (Factor 4) Poly. (Factor 4) Factor Linear (Factor ) Poly. (Factor ) '9-' '94-5' '98-9' '9-' '96-7' '9-' '98-9' '9-' '96-7' '94-4' '944-45' '948-49' '95-5' '956-57' '964-65' '968-69' '97-7' '976-77' '98-8' '984-85' '988-89' '99-9' '-' '4-5' '9-' '94-5' '98-9' '9-' '96-7' '9-' '98-9' '9-' '96-7' '94-4' '944-45' '948-49' '95-5' '956-57' '964-65' '968-69' '97-7' '976-77' '98-8' '984-85' '988-89' '99-9' '-' '4-5' '9-' '94-5' '98-9' '9-' '96-7' '9-' '98-9' '9-' '96-7' '94-4' '944-45' '948-49' '95-5' '956-57' '964-65' '968-69' '97-7' '976-77' '98-8' '984-85' '988-89' '99-9' '-' '4-5'

15 The typical stations Explained Variability by Factor in Precip. [%] Explained Variability by Factor in Temp. [%] No of COOP station Factor Loading of station in Precip. Factor Loading of station Temp. I - 4 I I.86 I.89 II - II II.8 II.9 III III.8 IV - III IV.77 III -.86 V V.55

16 Station, air temperatures Station, air temperatures T 4 (8*,) Factor Linear (Factor ) Poly. (Factor ).. Ann [F] Linear (Ann [F]) Poly. (Ann [F]) '5-6' '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' Factor Linear (Factor ) Poly. (Factor ) Factor Linear (Factor ) Poly. (Factor ) '5-6' '5-6' '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '5-6' '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' Jan Ann [F] Dec Nov Jun Aug Sep Mar Apr Feb Oct May Jul Expl.Var Prp.Totl Jul May Mar Apr Feb Jan Dec Nov Aug Jun Sep Oct Expl.Var Prp.Totl Factor Factor Factor Factor Factor Factor Factor Factor Factor 4 Linear (Factor 4) Poly. (Factor 4) '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '5-6'

17 Station, precipitations Station, precipitations P 4 (8*,) Ann sum [in] Linear (Ann sum [in]) Poly. (Ann sum [in]) Factor Factor Factor Factor 4 Factor 5 Sep.79 Oct.66 Ann [in] Nov.68.8 Dec.6 Jun.5 -. May.7 Apr.7 Aug.8 Feb.7 Mar.7 Jul Jan Expl.Var Prp.Totl '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '5-6' Factor Linear (Factor ) Poly. (Factor ). Factor 4 Linear (Factor 4) Poly. (Factor 4) Factor 5 Linear (Factor 5) Poly. (Factor 5) '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '5-6' Factor Linear (Factor ) Poly. (Factor ) 4. Factor Linear (Factor ) Poly. (Factor ) '5-6' '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '5-6' '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '5-6' '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '5-6'

18 Station, precipitations Station, precipitations '888-89' '897-98' '96-7' '95-6' '9-4' '94-4' '95-5' '969-7' '978-79' '987-88' '5-6' Ann sum [in] Linear (Ann sum [in]) Poly. (Ann sum [in]) P 4 (8*,) P 4 (8*,) '86-7' '84-4' '858-59' '874-75' '89-9' '96-7' '9-' '98-9' '954-55' '97-7' '986-87' '-' Use of longer time series changes the trend Ann [in] Linear (Ann [in]) Poly. (Ann [in])

19 Analyzing precipitation from Analyzing precipitation from USGS FACTOR Linear (FACTOR ) Poly. (FACTOR ) FACTOR4 Linear (FACTOR4 ) Poly. (FACTOR4 ) FACTOR Linear (FACTOR ) Poly. (FACTOR ) Factor Scores FACTOR Linear (FACTOR ) Poly. (FACTOR ) year Factor Scores Factor Scores Factor Scores year - - Data for 95 5 were collected & passed for analysis by Glenn Hodgkins from USGS) FACTOR6 Linear (FACTOR6 ) Poly. (FACTOR6 ) {P 9*4 } FACTOR7 Linear (FACTOR7 ) Poly. (FACTOR7 ) - year FACTOR5 Linear (FACTOR5 ) Poly. (FACTOR5 ) Factor Scores Factor Scores Factor Scores year year year year

20 Scale in Regime what is this? * Streamflow * Precipitation * Upper Peninsula (UP) of Michigan

21 Regimes of annual stream runoff scale in research: GL & UP MI MN UP MI UP MI LP MI NY Regions for GL (956( ) OH

22 Annual Runoff 4 - F II Annual Runoff F I 4 7 Annual Runoff F YII cfs 8 5 cfs 4 cfs cfs F Water year F Water year (X(X (X #S $ &V xz (X (X(X &V 4 (X &V #S 6 5 (X (X(X &V 6 5 (X #S#S (X #S # $ &V&V &V &V 6 5 $ #S#S S xz 7 $ #S#S &V xz (X #S $ #S #S #S (X (X xz $ #S#S &V 78 7 &V &V &V xz #S #S $ #S (X $$ #S $ xz &V xz F 7 'W 9 'W xzxz 9 $ xz $ #S &V xz $ %U (X &V %U (X $ %U &V 'W 'W 'W'W &V 57 F 5 &V (X &V xz $ (X 49 %U %U 5 5 %U 5 %U 5 %U (X F 5 xz Annual Runoff 86 - F Y Water year cfs F Annual Runoff 85 - F IY 9 %U Water year cfs 96 'W 'W #S 987 Annual Runoff 79 - F III 9 (X 87 xz 4 $ 'W %U 'W xz $ 'W'W 98 #S 'W F Water year 99 #S 'W cfs Annual Runoff F YI Water year Water year Factor Loadings for US territory & annual discharge for typical watersheds

23 Precipitation from Global grid Time series gathered in initial matrix: {P 8*9 } P 8,i Lat ( o N) \ Lon ( o W)

24 , , FACTOR Linear (FACTOR ) Poly. (FACTOR ) Factor Scores FACTOR Linear (FACTOR ) Poly. (FACTOR ) FACTOR Linear (FACTOR ) Poly. (FACTOR ) year year Factor Scores year Factor Scores FACTOR4 Linear (FACTOR4 ) Poly. (FACTOR4 ) year FACTOR5 Linear (FACTOR5 ) Poly. (FACTOR5 ) Factor Scores Factor Scores year FACTOR7 Linear (FACTOR7 ) Poly. (FACTOR7 ) FACTOR6 Linear (FACTOR6 ) Poly. (FACTOR6 ) Factor Scores year Factor Scores year Precipitation

25 Data from cooperative stations for UP MI Picture: Location & elevation of 44 meteorological cooperative stations with annual sum of total monthly snowfall & monthly air temperature On April 8, (

26 Annual snowfall as traditional map & as structure from initial matrix: T (95 TS98.88 TS9.8 TS Fact Fact Fact TS TS (95-4*8) 4*8) FACTOR Year TS TS TS47.8 TS TS TS TS TS TS TS TS Expl.Var Prp.Totl Picture: FACTOR FACTOR Year Year

27 Annual & seasonal regime as a structure for monthly Scatterplot (Spreadsheet7 v*5c) FACTOR = *x FACTOR = *x+.6*x^ FACTOR = Spline air temperature (UP MI) FACTOR MT 78 FACTOR = *x FA CTOR = *x +.*x^ FACTOR = Spline Year MT 78 FACTOR4 = *x FACTOR4 = *x+.4*x^ FACTOR4 = Spline MT 98 FACTOR = *x FACTOR = *x-. *x^ FACTOR = Spline 4 Scatterplot (Spreadsheet7 v*5c) FACTOR = *x FACTOR = *x+.*x^ FACTOR = Spline FACTOR FACTOR4 FACTOR FACTOR YEAR MT 78 FACTOR = *x FACTOR = *x+.4*x^ FACTOR = Spline MT FACTOR YEAR = *x FACTOR = *x-.7*x^ FACTOR = Spline FACTOR YEAR YEAR MT 78 FACTOR5 = *x FACTOR5 = *x+.*x^ FACTOR5 = Spline FACTOR5 - - Fact Fact Fact Fact 4 Fact 5 - JAN YEAR FEB.75 MAR.4.57 APR.9.64 MAY.8 JUN.8.66 JUL.5.5 AUG.8 SEP.55 OCT.75 NOV.5.54 DEC.87 Expl.Var Prp.Totl FACTOR YEAR MT 98 FACTOR = *x FACTOR = *x+.*x^ FACTOR = Spline MT MT 98 FACTOR4 = *x FACTOR = *x FACTOR4 = *x-.9*x^ FACTOR = *x+.*x^ YEAR FACTOR = Spline FACTOR4 = Spline MT 98 FACTOR5 YEAR = *x FACTOR5 = *x+.7*x^ -. FACTOR5 = Spline YEAR.5 FACTOR FACTOR YEAR FACTOR4 FACTOR Year Fac Fac Fac Fac 4 Fac 5 JAN.86 FEB.75.8 MAR.6.7 APR.78 MAY.69 JUN.57.5 JUL.6.4 AUG SEP.7 OCT NOV DEC.9.8 Expl.Var Prp.Totl

28 Air temperature - observed Model for simplified Fourier analysis: Where are: values & model K π X t = X + Ai cos ( t ϕi ) + Z i= T i t X t observation, X mean for the interval of observations, A i amplitude, Ti period, ϕ i phase of i-cosinusoid, Z t difference between observation & model. The equation quotients are calculated separately for each selected period & for all periods together under the condition of minimization of the random part, No T- period [year] A-amplitude [F] ϕ -phase F '888-89' '898-99' '98-9' '98-9' '98-9' '98-9' Model '948-49' '958-59' '968-69' '978-79' Hydr. year 4 T ann '988-89' '998-99' 8-9' '8-9' '8-9'

29 Scale for time series Scale for time series '86-7' '88-9' '85-5' '86-6' '874-75' '886-87' '898-99' '9-' '9-' '94-5' '946-47' '958-59' '97-7' '98-8' '994-95' in '6-7' '8-9' '-' '998-99' '888-89' '898-99' '98-9' '98-9' '98-9' '98-9' '948-49' '958-59' '968-69' '978-79' '988-89' F 8-9' '8-9' '8-9' No T- period [year] A-amplitude [F] ϕ -phase Model 4 T ann Hydr. year Model 4 prec ann sum Hydr. year

30 The Model

31 The System Model of Geosphere Vertical slice of the Geographical Sphere with two independent elements: System of Anthropological Geography (S AG ) & System of Physical Geography (S FG ). Arrows indicate vertical and horizontal components of matter, energy and information circulating (after Krcho, 978)

32 System Model for Landscape Each of these components may be characterized by matrix of input {Wi}, matrix of output {Qi}, & matrix of states {Hi}. System of Physical Geography Sphere (S FG ) with five independent elements: a - atmosphere, a - hydrosphere, a - lithosphere, a 4 - pedosphere, a 5 -biosphere.

33 Multidimensional structure of relations R ij The number of characteristics for elements of landscape and watershed is unlimited but for stable landscape the set of watersheds or stations with data allows to obtain statistical description of connections. {Ri} is a matrix of relations between parts of landscape. Entering the codes and numbers for initial matrix {X n*p } we open the way to recovery connections those exist in landscape Axis for hydrological space factors (principal components) of initial data matrixes {X n*p }, allow consider {Ri} as a time spatial structure.

34 Discover of invisible structure by system analysis

35 Results for discussion System model applied to landscape allows to formulate research tasks, develop methods of analysis, & present results as a map Hydrological object has a scaled time-spatial structure of interaction (straight & feedback connections) with other components of landscape (air, rocks & sediments, soil, plants & animals) The complex multidimensional structure of time spatial regime for regional hydrosphere was described for U. S. part of Great Lake watershed The entire set of empirical data was used Results may be used for improvement of observational net & in applications

36 Questions? Lake Superior, /8/9 : pm Scientific research completed on a base of authors donated time