Slide 1

Slide 2

Design of Experiment and Assessing Interactions within Atmospheric Processes Dev Niyogi North Carolina State University Email: dev_niyogi@ncsu.edu

Slide 3

Human thinking is logical, sequential, and linear Real world is Convulated, Non-linear, and Interactive

Slide 4

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

Slide 5

Sensitivity Analysis Sensitivity Analysis

Slide 6

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

Slide 7

Sensitivity Analysis Sensitivity Analysis ObjectiveObjective 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

Slide 8

OAT Analysis OAT Analysis Inherent component of model studiesInherent component of model studies Both observational as well as numerical modeling studies rely on sensitivity analysisBoth observational as well as numerical modeling studies rely on sensitivity analysis Approach Change a variable see the effect on the outcomeApproach Change a variable see the effect on the outcome

Slide 9

One at A Time Analysis One at A Time Analysis

Slide 10

Slide 11

Another Example OAT Analysis Another Example OAT Analysis

Slide 12

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

Slide 13

Sensitivity Analysis using Observations

Slide 14

-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)

Slide 15

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

Slide 16

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

Slide 17

Ambient versus doubled CO2 levels

Slide 18

Example of a field sensitivity study Field Measurements at NCSU to assess diffuse radiation feedback Does increase in diffuse radiation fraction help crop yield?

Slide 19

MORE DIFFUSE LESS DIFFUSE Measure the environment below the two experimental domains and evaluate the outcome (temperature, crop yield, photosynthesis, )

Slide 20

Comparison of OAT in models and in field Comparison of OAT in models and in field Models High Diffuse - > more photosynthesisModels High Diffuse - > more photosynthesis Observations High diffuse -> less temperatures -> more shade on crops -> leaf geometry changes -> large fluctuationsObservations High diffuse -> less temperatures -> more shade on crops -> leaf geometry changes -> large fluctuations

Slide 21

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!)

Slide 22

Slide 23

Diffuse radiation effect under cloudy conditions Diffuse radiation effect under non- cloudy conditions

Slide 24

Clustering and Synthesis of Sensitivity Experimentation Data Interpretation Low LAI case High LAI case Observations and Models need to go hand in hand to help develop the understand (dont treat observations alone as the truth)

Slide 25

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

Slide 26

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

Slide 27

Modeling Analysis

Slide 28

Slide 29

Feedbacks and Interactions Feedbacks and Interactions

Slide 30

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

Slide 31

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

Slide 32

Interactions ExamplesExamples Medicine and Prescription Drug Use Drug A will lead to helping relieve headacheDrug A will lead to helping relieve headache Drug A taken while taking Drug B will cause nauseaDrug A taken while taking Drug B will cause nausea Drug A taken with coffee can cause marked improvementDrug 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

Slide 33

Feedbacks and Interactions Surface Energy Balance & EvapotranspirationSurface Energy Balance & Evapotranspiration Rn = Etr + Shf + storage; Etr = Eg+TrRn = Etr + Shf + storage; Etr = Eg+Tr Gradients in Surface FluxesGradients in Surface Fluxes Non-classical CirculationNon-classical Circulation Convection and Cumulus FormationConvection and Cumulus Formation Precipitation and Land Use ChangePrecipitation and Land Use Change Regional Climate ChangeRegional Climate Change

Slide 34

Slide 35

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(CO2:SM) = F12 - (F1+F2) - Fo

Slide 36

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

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

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

Slide 43

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

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

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

Slide 49

Slide 50

Slide 51

Analysis of Variance

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Why land surface changes in tropics matter? The answer could be in the soil moisture availability

Slide 57

Relevance of the results to Biosphere Atmosphere Interaction studies Process - based analysis of the physical parameterizations for every vegetation - typeProcess - based analysis of the physical parameterizations for every vegetation - type Extracted direct as well as interactive feedbacksExtracted 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)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 changesPrevious 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 statusCO2 doubling effects should not be discussed without considering soil moisture status

Slide 58

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

Slide 59

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

Slide 60

Differential Vegetation Characteristics based SGS heterogeneity consideration For the example considered (C3 and C4 grassland)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)Results are from a One - At - Time (OAT) approach (without interactions)

Slide 61

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

Slide 62

Slide 63

Slide 64

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 DVCFacSep 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)Interaction term do not show expected compensation (SHF and LHF main effects could be inversely linked but the interactions could be directly related)

Slide 65

Slide 66

Slide 67

Differential Vegetation Characteristics based SGS heterogeneity consideration Are all the interactions similarly important?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 CO 2 doubling on such a DVC based SGS heterogeneity?What is the effect of CO 2 doubling on such a DVC based SGS heterogeneity?

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Differential Vegetation Characteristics based SGS heterogeneity consideration Numerous conditions of C3 - C4 like DVC interaction analyzed under varying soil moisture, CO 2, and soil texture conditionsNumerous conditions of C3 - C4 like DVC interaction analyzed under varying soil moisture, CO 2, 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)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 CO 2 conditions (and when resources are not limiting), and significantly persist otherwise.DVC errors were reduced under doubling of CO 2 conditions (and when resources are not limiting), and significantly persist otherwise. Anomaly results (CO 2 doubling exercises need to be re-evaluatedAnomaly results (CO 2 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.Simple area - averaging is not adequate and may lead to incorrect delineation of carbon source - sinks as well as moisture budget.

Slide 73

Slide 74

Slide 75

Slide 76

Variation of the effective variables based on the C3 C4 area averaging and explicit interaction consideration.

Slide 77

(a) Area - Averaged, and (b) Interaction effect (~ 20 % of the direct effect)

Slide 78

Effective Parameter / relations for C3 - C4 like DVC based SGS heterogeneity Rs eff = a 3.C3 + a 4.C4 + max {0.35(a 3.C3), 1.5(a 4.C4)} An eff = a 3 C3 + a 4 C4 max{0.5(a 3.C3), 0.25(a 4.C4)} Etr eff = a 3.C3 + a 4.C4 max{0.33(a 3.C3), 0.2(a 4.C4)} LHF eff = a 3.C3 + a 4.C4 max{0.25(a 3.C3), 0.15(a 4.C4)} SHF eff = a 3.C3 + a 4.C4 + max{0.2(a 3.C3), 0.3(a 4.C4)}

Slide 79

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

Slide 80

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

Slide 81

Slide 82

Slide 83

Slide 84

Slide 85

Slide 86

Slide 87