Design of Experiment and Assessing Interactions within Atmospheric Processes

1
Design of Experiment and Assessing Interactions
within Atmospheric Processes

• Dev Niyogi
• North Carolina State University
• Email dev_niyogi_at_ncsu.edu

2
Human thinking islogical , sequential, and
linearReal world isConvulated, Non-linear,
and Interactive
3
Some References

• Mesoscale Meteorological Modeling, Roger Pielke
  Sr., Second Edition. (blue.atmos.colostate.edu)
• Box, Hunter and Hunter, Design of Experiment,
  1987
• Stein and Alpert, Factor Separation Analysis, J.
  Atmos. Sci. 1993
• Alpert et al., How good are sensitivity studies?,
  J. Atmos. Sci. 1995
• Henderson- Sellers, A fractional factorial
  approach, J. Climate, 1993
• Niyogi et al. 1995, Env. Mod. Assess, Statistical
  Dynamical Experiments
• Niyogi et al. 1999 Uncertainty in initial
  specification- hierarchy Boun. Layer Meteorol.
• Niyogi et al. 2002 Land surface response-
  midlatitudes and tropics, J. Hydromet
• (www4.ncsu.edu/dsniyogi)

4
Sensitivity Analysis
5
Sensitivity Analysis

• Inherent component of model studies
• Both observational as well as numerical modeling
  studies rely on sensitivity analysis
• Approach Change a variable see the effect on
  the outcome

6
Sensitivity Analysis

• Objective
• Understand the cause effect relationship
• Understand the relative importance of the
  different processes affecting the outcome
• Develop focused efforts on improving input for
  critical variables (GIGO)
• Develop if then scenarios for policy makers
  socioeconomic analyses,
• Evaluate models

7
OAT Analysis

• Inherent component of model studies
• Both observational as well as numerical modeling
  studies rely on sensitivity analysis
• Approach Change a variable see the effect on
  the outcome

8
One at A Time Analysis
9
One at A Time Analysis
10
Another Example OAT Analysis
11
Summary of OAT Analysis

• - Linear results
• Interactions need to be extracted in a ad-hoc
  manner / subjectively
• Results state what is happening and not how it
  is happening in the analysis

12
Sensitivity Analysis using Observations
13
Sensitivity Analysis using Observations

• Needs careful planning (several known and unknown
  feedbacks possible)
• Effects cannot be switched off reliably (unlike
  in a model)
• Modeling OAT sensitivities could be used for
  developing trends and extrapolations
• Observational OAT can be largely used for
  hypothesis tests (too many factors too much
  noise)
• KISS (Keep it Simple Stupid) syndrome can be boon
  and a bane (too much confounding and original
  results may be lost)

14
Sensitivity Analysis using Observations

• Either Absent / Present scenarios tested
• Cloud cover and no clouds
• Irrigation and no irrigation
• Fertilizer and no fertilizer
• Or High / Low scenarios tested
• High soil moisture and low soil moisture
• Ambient CO2 and Doubled CO2

15
High soil moisture
Low Soil Moisture
LESS DIFFUSE
Measure the environment below the two
experimental domains and evaluate the outcome
(temperature, crop yield, photosynthesis, )
16

• Ambient versus doubled CO2 levels

Measure the environment below the two
experimental domains and evaluate the outcome
(temperature, crop yield, photosynthesis, )
17
Example of a field sensitivity study Field
Measurements at NCSU to assess diffuse radiation
feedback Does increase in diffuse radiation
fraction help crop yield?
18
MORE DIFFUSE
LESS DIFFUSE
Measure the environment below the two
experimental domains and evaluate the outcome
(temperature, crop yield, photosynthesis, )
19
Comparison of OAT in models and in field

• Models High Diffuse - gt more photosynthesis
• Observations High diffuse -gt less temperatures
  -gt more shade on crops -gt leaf geometry changes
  -gt large fluctuations

20
Clustering and Cleaning eventually gets the right
results from observations always an element of
uncertainty that results could have gone other
way too in some scenarios. Q Should the
observations be relied on for testing models? (of
course yes but dont use observations as the
truth!)
21
(No Transcript)
22
Diffuse radiation effect under cloudy conditions
Diffuse radiation effect under non-cloudy
conditions
23
Clustering and Synthesis of Sensitivity
Experimentation Data Interpretation
High LAI case
Observations and Models need to go hand in hand
to help develop the understand (dont treat
observations alone as the truth)
Low LAI case
24
Too many model evaluation studies particularly
for synthesizing processes rely overtly on
observations Observations are essential for
model testing and evaluation But observations are
also chaotic QUESTION OBSERVATIONS Know the
uncertainty associated with the
measurements Models need not agree with all
observations to be good Models give time
dependent ensemble output observations at a
given time are just that- observation at that
point and/or time Even observations have
feedbacks embedded which have not been
traditionally extracted
25
No I am not a modeler! Models do not represent
the reality but neither do observations unless
they are clearly synthesized. Need to synthesize
results (observations and model output) in a
nonlinear / feedback and interaction
perspective
26
Modeling Analysis
27
(No Transcript)
28
Feedbacks and Interactions
29
Feedbacks and Interactions

• Feedback processes are a result of cause and
  effect.
• That is, one follows the other in a time
  sequential manner
• The processes could be coupled as well as
  uncoupled
• A -gt B -gt C
• A-gt B -gt C -gta -gt b -gt c

30
Feedbacks and Interactions

• Interactions, on the other hand, implies
  concurrence.
• There is no cause and effect associated with the
  interactions and a simultaneous effect is
  associated.
• A -gt B -gt C and D

31
Interactions

• Examples
• Medicine and Prescription Drug Use
• Drug A will lead to helping relieve headache
• Drug A taken while taking Drug B will cause
  nausea
• Drug A taken with coffee can cause marked
  improvement
• Nutrition and Health
• Results show wine is good for health add to your
  diet
• red wine is better
• true for people exercising
• Same effect as grape juice
• Wine is not necessary, take out of your diet
• All are examples of real-life interactions
  occurring which need to be resolved

32
Feedbacks and Interactions

• Surface Energy Balance Evapotranspiration
• Rn Etr Shf storage Etr EgTr
• Gradients in Surface Fluxes
• Non-classical Circulation
• Convection and Cumulus Formation
• Precipitation and Land Use Change
• Regional Climate Change

33
(No Transcript)
34
Factor Separation (FacSep) Analysis (Stein and
Alpert, 1993 Alpert et al. 1995 J. Atmos.
Sci.) Interaction Explicit Analysis of
effect of simultaneous soil moisture
and CO2 changes on terrestrial feedback

• Eo Fo f CO2 - , Moist -
• F1 f CO2 , Moist -
• F2 f CO2 - , Moist
• F12 f CO2 , Moist
• E(CO2) F1 - Eo
• E(SM) F2 - Eo
• E(CO2SM) F12 - (F1F2) - Fo

35
FacSep results can be interpreted and analyzed
using either time series tools or other
traditional descriptive statistics routinely used
in One at A Time Sensitivity Analysis
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40

41
Feedbacks and Interactions

• Full Factorial (2n) I.e. 8 combns for 3 factors
  16 for 4 32 for 5 etc.
• At three settings (low, medium, and high) this
  will be 3n I.e. 27 for 3 factors, 64 for 4
  factors etc.
• Solution?
• Fractional Factorial Approach (statistical
  design)
• Some confounding (all interactions / combinations
  not resolved)
• Several design matrices routinely available
  (statistics texts, software packages, internet,
  )

42
Fractional Factorial Designs

• Resolution 5 all main effects and two-factor
  interactions resolved (FF0516)
• Resolution 4 some two factor Xns retained
  (FF0616)
• Resolution 3 Screening type interactions may
  not be resolved (FF0508)
• Nonlinear response surface (fc0318)
• Effect Main Effect Interaction
• Main effect plots -gt Pareto plot -gt Interaction
  plots-gt normal plots / active contrast / gambler
  plots -gt diagnosis of feedbacks and interactions

43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
47
Summary of OAT Analysis

• - Linear results
• Interactions need to be extracted in a ad-hoc
  manner / subjectively
• Results state what is happening and not how it
  is happening in the analysis

48
(No Transcript)
49
(No Transcript)
50
Analysis of Variance
51
(No Transcript)
52
(No Transcript)
53
(No Transcript)
54
(No Transcript)
55
Why land surface changes in tropics
matter?The answer could be in the soil moisture
availability
56
Relevance of the results to Biosphere Atmosphere
Interaction studies

• Process - based analysis of the physical
  parameterizations for every vegetation - type
• Extracted direct as well as interactive feedbacks
  
• Interaction effects can be equated to the
  indirect effects of CO2 doubling (though not
  causally, often as empirical corrections)
• Previous studies suggested, CO2 doubling will
  affect C3 vegetation and may not affect C4. This
  may be true only for the direct effects but
  considering interactions, both C3 and C4
  vegetation appears to be significantly affected
  by CO2 changes
• CO2 doubling effects should not be discussed
  without considering soil moisture status

57

• Carbon Assimilation Rates are intrinsically
  linked with soil moisture availability
• Used coupled GEM based outcome over all the nine
  SiB2 vegetation types to prove the hypothesis
• landscape can be a source / sink depending on the
  soil moisture status
• Need to consider interactions explicitly while
  analyzing Biosphere Atmosphere Interactions

58
Hydrological Carbon Feedbacks CO2 issues need
implicit hydrological considerations

• e.g. Ball Berry carbon assimilation /
  transpiration model
• Gs (m . An / Cs . RHs ) b
• m, b - specie specific constants
• An - Net Assimilation
• Cs - CO2 at leaf surface
• RHs - humidity at leaf surface
• Carbon Assimilation is linked with transpiration
  (which is linked with surface energy balance, and
  so on)
• Possible to scale carbon effects via hydrological
  considerations

59
Differential Vegetation Characteristics based SGS
heterogeneity consideration

• For the example considered (C3 and C4 grassland)
• Air temperature and SHF related impacts were
  minimal
• Transpiration and LHF effects were significantly
  affected
• Largest errors could be in carbon budget or
  environmental (air pollution, hydrometeorological)
  studies
• Results are from a One - At - Time (OAT) approach
  (without interactions)

60
C3 - C4 Interactions

• Use Factor Separation approach (Stein and
  Alpert, 1993) for CO2 (present day, doubled),
  soil moisture (wet, dry), soil texture (clay,
  loam), and vegetation type (C3, C4) changes

61
(No Transcript)
62
(No Transcript)
63
Differential Vegetation Characteristics based SGS
heterogeneity consideration

• FacSep study identified two as well as higher
  order interactions are significantly active with
  C3 - C4 vegetation based DVC
• Interaction term do not show expected
  compensation (SHF and LHF main effects could be
  inversely linked but the interactions could be
  directly related)

64
(No Transcript)
65
(No Transcript)
66
Differential Vegetation Characteristics based SGS
heterogeneity consideration

• Are all the interactions similarly important?
• Need to identify statistically significant
  interactions
• Fractional Factorial Analysis performed for 12-h
  averaged (day time) coupled GEM outcome
• What is the effect of CO2 doubling on such a DVC
  based SGS heterogeneity?

67
(No Transcript)
68
(No Transcript)
69
(No Transcript)
70
(No Transcript)
71
Differential Vegetation Characteristics based SGS
heterogeneity consideration

• Numerous conditions of C3 - C4 like DVC
  interaction analyzed under varying soil moisture,
  CO2, and soil texture conditions
• Analysis confirms interactions are an important
  component of the carbon budget (not simply
  addition as often perceived, but also need to
  consider higher order terms to identify missing
  components)
• DVC errors were reduced under doubling of CO2
  conditions (and when resources are not limiting),
  and significantly persist otherwise.
• Anomaly results (CO2 doubling exercises need to
  be re-evaluated
• Simple area - averaging is not adequate and may
  lead to incorrect delineation of carbon source -
  sinks as well as moisture budget.

72
(No Transcript)
73
(No Transcript)
74
(No Transcript)
75
Variation of the effective variables based on
the C3 C4 area averaging and explicit
interaction consideration.
76
(a) Area - Averaged, and (b) Interaction effect
( 20 of the direct effect)
77
Effective Parameter / relations for C3 - C4
like DVC based SGS heterogeneity

• Rseff a3.C3 a4.C4 max 0.35(a3.C3),
  1.5(a4.C4)
• Aneff a3C3 a4C4 max0.5(a3.C3),
  0.25(a4.C4)
• Etreff a3.C3 a4.C4 max0.33(a3.C3),
  0.2(a4.C4)
• LHFeff a3.C3 a4.C4 max0.25(a3.C3),
  0.15(a4.C4)
• SHFeff a3.C3 a4.C4 max0.2(a3.C3),
  0.3(a4.C4)

78
Future Directions

• Interactions are dominant in atmospheric
  processes
• Methods are still evolving to extract and analyze
  them
• Two of the popular methods Fractional Factorial
  and Factor Separation appear promising
• Fractional Factor Separation also evolving
• Results function of sampling?
• Need for using these observations in field
  experiments and then for parameterization testing
• Question Observations..

79
Brain Storming Exercise

• Develop an interaction explicit scenario which
  you think is not well understood?
• Describe how interaction explicit approaches may
  help explain the feedbacks and interactions

80
(No Transcript)
81
(No Transcript)
82
(No Transcript)
83
(No Transcript)
84
(No Transcript)
85
(No Transcript)
86
(No Transcript)