Global Warming and Recurrences of Anomalous Crop Productivity Years: Study Based on the Ensemble Sta

1
Global Warming and Recurrences of Anomalous Crop
Productivity Years Study Based on the Ensemble
Statistical Approach and IPCC Recommended
Scenarios

• Gennady V.Menzhulin and Artyem A.Pavlovsky
• Research Centre for Interdisciplinary
  Environmental Cooperation
• of Russian Academy of Sciences, St.-Petersburg,
  Russia
• 4th Management Committee Meeting - COST Action
  734 -
• Impact of Climate Change and Variability on
  European Agriculture
• Vienna, Austria
• 22-23 October 2007

2
Purposes of Research

• - To develop the methodology of crop
  productivity statistical models derivation based
  on the regression ensemble approach.
• - To design the multifactor regression models of
  the productivity annual anomalies for winter,
  spring and Durum wheat in US grain production
  zone and winter and spring wheat over the
  European Russia and new Independent European
  States.
• - To calculate the forecasting estimates of
  possible changes in recurrence of crop
  productivity anomalous years used seven model
  global warming scenarios IPCC recommended.

3
Agricultural Regions Investigated
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US Winter Wheat
Soft Red Winter
Hard Red Winter
Hard Winter
Soft Winter
5
US Spring Wheat
Hard Red Spring
Durum
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Winter Wheat in the Former USSR
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Spring Wheat in the Former USSR
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Input Wheat Production and Area Information
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Example on Wheat Productivity Data for Some
Regions of the Former USSR (cent./ha)
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Initial Data on US Wheat Production and Areas
(Winter Wheat, Allen, Kansas)
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Year-to-Year Changes of Winter Wheat Productivity
and their Trend Lines in Some Russian Regions
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Year-to-Year Changes of Winter Wheat Productivity
and their Trend Lines in Some US Counties
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On the Quality of Initial Agricultural
Information
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Examples of Winter Wheat Productivity Data
Presented in the Former USSR Statistical
Yearbooks
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Time Series of US Spring Wheat Production and
Areas
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Processing of Initial Agricultural Information
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Ensemble of Trend Lines of Productivity Used in
Research

• Polynomial among annual points trend lines
• Yp1a0p1a1p1i
• Yp2a0p2a1p2ia2p2i2
• Yp3a0p3a1p3ia2p3i2a3p3i3
• Yp4a0p4a1p4ia2p4i2a3p4i3a4p4i4
• Yp5a0p5a1p5ia2p5i2a3p5i3a4p5i4a5p5i5
• Yp6a0p6a1p6ia2p6i2a3p6i3a4p6i4a5p6i5a6p6i6
• Yp7a0p7a1p7ia2p7i2a3p7i3a4p7i4a5p7i5a6p7i6
  a7p7i7
• Yp8a0p8a1p8ia2p8i2a3p8i3a4p8i4a5p8i5a6p8i6
  a7p8i7a8p8i8

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Ensemble of Trend Lines of Productivity Used in
Research

• Exponential among annual points trend lines
• Ye1exp(a0e1a1e1i)
• Ye2exp(a0e2a1e2ia2e2i2)
• Ye3exp(a0e3a1e3ia2e3i2a3e3i3)
• Ye4exp(a0e4a1e4ia2e4i2a3e4i3a4e4i4)
• Ye5exp(a0e5a1e5ia2e5i2a3e5i3a4e5i4a5e5i5)
• Ye6exp(a0e6a1e6ia2e6i2a3e6i3a4e6i4a5e6i5a6e
  6i6)
• Ye7exp(a0e7a1e7ia2e7i2a3e7i3a4e7i4a5e7i5a6e
  7i6a7e7i7)
• Ye8exp(a0e8a1e8ia2e8i2a3e8i3a4e8i4a5e8i5a6e
  8i6a7e8i7a8e8i8)
• Logistical trend lines
• Yl 1/alblexp(-?li)

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Examples of Wheat Productivity Among Dots
Trend Lines
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Initial Indicators of Productivity Anomaly
Relative (Normalized) Productivity

• ?k(i) yk(i)-Yk(i) / Yk(i)
• ?k(i) yk(i) / Yk(i).
• Yk - trend lines
• k - type of the trend line
• i - year

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Examples of ?-Indicator Year-to-Year Changes
(Lugansk, Ukraine, Spring Wheat)
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Potential (Maximal) Productivity Over Dots
Trend Line

• Ym??,k(i) Yk(i) 1?k(best year)
• Ym??,k maximal productivity trend conformed to
  the among year-to-year points
  trend-line Yk..
• ?k(best year) relative deviation of real
  productivity from the among year-to-year
  points trend line in the year of the
  best agrometeorological conditions.
• i year.

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Example of Potential Productivity Over Dots
Trend Line (Allen, Kansas, winter wheat)
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Productivity Indicators

• Relative (normalized) productivity
• ?k(i) y(i)-Yk(i)/ Yk(i)
• Relative (normalized) productivity losses
• ?k(i)100 Ymax,k y(i)/ Ymax,k
• k 1,2,3,8
  polynomial trends,
• k 9,10,1116
  exponential trends.
• Ym??,k k- type of
  potential productivity trend line.
• Totally in the research 32 types of trend line
  are used.

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Example of Year-to-Year Changes of the Relative
Productivity Losses (Allen, Kansas, winter wheat)
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Initial Meteorological Information
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Three Examples of Trend Lines for Meteorological
Factors (April, Rawlins, Kansas)
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Meteorological Predictors

• Five polynomial trend lines of Tmean, Tmax, Tmin
  and P.
• Relative temperatures and precipitation using as
  the predictors
• tmean,k (i) Tmean (i) Ttrmean,k (i) /
  Ttrmean,k (i)
• tmax,k (i) Tmax (i) Ttrmax,k (i) /
  Ttrmax,k (i)
• tmin,k(i) Tmin (i) Ttrmin,k (i) /
  Ttrmin,k (i)
• pk (i) P(i) Ptrk (i) / Ptr k (i).
• k1,2,3,4,5 trend type,
• i1,2,3n - months of vegetation season,
• (5 trends 8-11 months) series of each
  type of predictor.

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Three Examples of Meteorological Predictors
Series(relative mean temperature, April,
Rawlins, Kansas)
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Development of Crop Productivity Regression Models
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Selection of Predictants Based on the Technique
of Direct Exhausting Among All Possible
Multifactor Regressions

• For each agricultural region were constructed
• Predictants 32 (?, ?).
• Predictors on
• Temperature 60 (tmean, tmax, tmin)
• Precipitation 60 (p).
• Total amount of regressions used in exhaustion
  methods for each agricultural region
• Two-factors (36x35/2!)x(60x60)x32 72576000
• Three-factors (36x35x34/3!)x(60x60)x32
  411264000
• Four-factors (36x35x34x33/4!)x(60x60)x32
  3392928000
• Five-factors (36x35x34x33x32/5!)x(60x60)x32
  21714739200
• Six-factors (36x35x34x33x32x31/6!)x(60x60
  )x32 112192819200
• Total for one region more 137 billions.
• Total for 318 former USSR and US regions more
  42 trillions.

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Predictant Selection Technique Using the
Empirical Index I of Multiple Correlation

• For each agricultural region (67 of the Fformer
  USSR and 241 for the US counties) for all wheat
  cultivars in the former USSR (winter and spring
  wheat) and USA (winter, spring, and Durum wheat)
  the three-dimensional matrix of empirical index
  of multiple correlation was calculated
• Ijkl sqrt ? corr2(yjk ,tmin,jl) corr2(yjk
  ,tmax,jl) corr2(yjk ,pjl)
• i
• y predictants ?, ?..
• tmin, tmax, p predictors.
• i month of vegetation season.
• j number of region (67 241).
• k predictant type, k 1 8, 9 16, 17
  24, 25 32 .
• l type of temperature predictor, l
  1,2,3,4,5 (five polynomial trend lines).
• m type of precipitation predictor, m
  1,2,3,4,5 (five polynomial trend line).
• Total amount of I index , using for exhausting
  technique for best predictant for each
  administrative unit of the former USSR and USA
  put together 800 (32?5?5).

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On the Comparison of Direct Exhausting Technique
(left) and Method Based on Index of Multiple
Correlation I (right)(Spring Wheat, Belgorod)
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Linear Regression of Productivity Indicators on
Meteorological Factors
?, ? Productivity indicators (relative
productivity or losses). tmin,a, tmin,ß, p?
minimal, maximal temperature and precipitation
indicators in a, ß, ? months
respectively. ? (with subscripts) coefficients
of regression.
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Statistical Characteristics of Regression Models
of Spring Wheat Productivity in Some Former USSR
Regions (Students statistical criteria
parameters are in the predictor cells)
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Model Reproduction of Historical Year-to-Year
Relative Losses of Wheat Productivity (white
dots real data, red dots model)
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Model Reproduction of Historical Year-to-Year
Relative Anomalies of Wheat Productivity(white
dots real data, red dots model)
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Model Reproduction of Historical Year-to-Year
Relative Losses of Wheat Productivity (white
dots real data, red dots model)
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Model Reproduction of Historical Year-to-Year
Relative Anomalies of Wheat Productivity (white
dots real data, red dots model)
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Forecasting Meteorological Information
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Climate Change Scenarios Used in the Research
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Scenarios of the Greenhouse Gases Emission and
the World Development
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GCMs Gridpoints on the Former USSR European
and the US Territories
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The FUSSR Regions Corresponding to GCMs
Gridpoints(ECHAM4/OPYC3)
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CCSR/NIES
The FUSSR Regions Corresponding to GCMs
Gridpoints
CSIRO(Mk2)
CGCM2
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GFDL(R30)
The FUSSR Regions Corresponding to GCMs
Gridpoints
NCAR-DOE(PCM)
HadCM3
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US Counties Corresponding to GCMs Gridpoints
(ECHAM4/OPYC3)
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CCSR/NIES
US Counties Corresponding to GCMs Gridpoints
CGCM2
CSIRO(Mk2)
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GFDL(R30)
US Counties Corresponding to GCMs Gridpoints
HadCM3
NCAR-DOE(PCM)
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To the Problem of Statistical Stationary Series
Derivation of Forecasted Climate Parameters
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Forecasted Year-to-Year Changes of Meteorological
Parameters in the Next 50 Years (Russia,
Yaroslavl region)
Monthly mean air temperature
Total monthly precipitation
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To the Construction of Statistical Stationary
Series for Forecasted Meteorological Parameters
(HadCM3, precipitation, Sedgwick, Kansas)
? min?abs(si-swn,i) (used as indicator) si
fraction of the total deviation,
cumulatively fallen on fluctuations with
the frequencies less than i, swn,i the
same for the white noise.
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Forecasted Estimates of the Wheat Productivity
Anomalies Recurrences
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Forecasted Year-to-Year Changes of the Relative
Productivity Losses in 20072050 (Russia,
Bashkortostan, winter wheat)
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Forecasted Temporal Dynamics of the Relative
Productivity Losses in 20072050 (11-year
smoothed averaged figures)
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Forecasted Temporal Dynamics of the Relative
Productivity Losses in 20072050 (11-year
smoothed averaged figures)
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Forecasted Dynamics of Relative Productivity
Losses (Russia, Belgorod, spring wheat)
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Forecasted Dynamics of Relative Productivity
Losses in Three Kansas Counties (ECHAM4, winter
wheat)
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Forecasted Dynamics of Relative Productivity
Losses (winter wheat, Idaho, Idaho)
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Forecasted Dynamics of Relative Productivity
Losses (Sioux, North Dakota, spring wheat)
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Historical and Forecasted Dynamics of Relative
Productivity Losses
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Main Conclusions
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• The long term series of crop productivity data
  collected at present comprise the valuable
  material for developing the accurate and
  statistical reliable regression models of crops
  productivity indicators dependencies on
  meteorological factors. They would be
  successfully used in the investigations of
  climate change impact on agriculture especially
  for future crop productivity anomalies
  recurrences.
• Using of statistical modelling technique based
  on the selection of the most reliable and
  accurate statistical model among the ensemble of
  all possible multifactor regression gives the
  possibility to refuse the many a prior
  prerequisites offered the sources of
  uncertainties in forecasting estimates.
  Regression models designed using such technique
  with respect to the accuracy surpass
  significantly before used models based on a
  priori subjectively selected inflexible
  predictors and predictants.
• At present some model climate change scenarios
  are able to provide the enough conforming of
  their estimates of regional future changes in
  meteorological factors that appear in the certain
  one-type forecasting estimates of crop
  productivity anomalies dynamics in next 50 years
  in different regions. The analysis of such
  conformities carrying out using the set of
  climate changes scenarios of the 4th generation
  is very actual.

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Many Thanks for Your Attention!