Cross-spectral analysis on Net Ecosystem Exchange: Dominant timescale and correlations among key ecosystem variables over the Ameriflux Harvard forest siteObjectivesData descriptionSlide 4MethodsData preparationNEE time seriesHarmonic AnalysisPower spectrum: NEESlide 10Look at NEE anomalyNEE anomaly power spectrumNEE anomaly explained variancesCross-spectrum analysisExample: NEE & air TExample: NEE & LHConclusionFuture work (in one week)Supplemental material A Data for cross-spectrum analysisReferencesCross-spectral analysis on Net Ecosystem Exchange: Dominant timescale and correlations among key ecosystem variables over the Ameriflux Harvard forest siteATMO 529 class projectKoichi SakaguchiLTER photo galleryhttp://savanna.lternet.edu/gallery/albums.phpObjectives1. Find major frequencies (in days ~ inter-annual time scale) that explains large fraction of the variance in Net Ecosystem Exchange (CO2 flux)2. Find major frequencies in which NEE and another variable change togetherThese knowledge will be helpful to infer important variables and processes that control ecosystem-level carbon cycleData description• Time series measured at the Harvard forest, MA-Temperate deciduous forest-Annual precipitation:756-1469 mm-Mean air temperature 6.46 °C •Eddy covariance measurement-Covariance of vertical wind and temperature or mass concentration fluctuation = vertical fluxes-Daily average values from level 4 data for 10 years period (1992 ~ 2001) Good summary by Baldocchi, 2003 in GCBData description•Net Ecosystem Exchange (net CO2 flux between the atmosphere and land surface)http://www.atm.helsinki.fi/mikromet/NEE = - (photosynthesis - plant respiration - soil respiration)Sign convention : downward positiveMethods1. Spectrum analysis on ecosystem CO2 flux (Net Ecosystem Exchange) time series 2. Cross-spectrum analysis on NEE and other variables: - Surface air temperature - Vapor pressure deficit - Latent heat flux - Sensible heat flux to find timescales of high correlations (Spectral Coherence) with NEEI’m having a trouble with this !!!Data preparation1. Gap-filling: Gaps have to be filled for harmonic analysis (Discrete Fourier transforms)(Stull, 1988)!There are about 50 days of continuous gaps in daily average data in 1992. Mean values from other 9 years are placed on this period.2. Hanning window :Box car window is for amateurs!Fig. 6.15 in Hartmann’s note- decrease distortion in power spectrum from the side lobes.NEE time seriesMean: -0.53 gC/m2/daySTD: 3.1 gC/m2/dayLag-1 autocorrelation: 0.88Harmonic AnalysisFor a particular frequency k, Ck2 / 2 represents the fraction of the variance explained at that frequencyFrom Hartmann’s note€ Ck2= (Ak+ iBk)(Ak− iBk) = Ak2+ Bk2“Spectral Power”By using Fourier series in least-squares fit, we havePower spectrum: NEE341 ~ 409 days178 ~ 194 daysNo spectral averaging or smoothingRed line : Red noise spectrumDashed line: statistically significant threshold with 90 & 95 % confidence ~90 days periodPower spectrum: NEE341 ~ 409 days178 ~ 194 daysTop: linear scaleBottom: semi-log plot(x-axis in log scale) No spectral averaging or smoothingRed line : Red noise spectrumDashed line: statistically significant threshold with 90 & 95 % confidence ~90 days periodNEE varies largely in annual & seasonal scale… not too excitingLook at NEE anomalySubtract 10 years mean from each daily average value.Mean: 0 gC/m2/daySTD: 1.48 gC/m2/dayLag-1 autocorrelation: 0.51Large variation concentrated in growing seasonNEE anomaly power spectrumAgain most of the variance is in lower frequency.Annual ~ seasonal time scale still dominate!Focused on lower frequenciesTop: linear scale, no smoothingBottom: linear scale, smoothed by 5-points running meanNEE anomaly explained variances1.2%340~510180~22098~10549~5145~45.51.3% 0.8% 0.7% 0.2%Significant time scale (period in days) with 95% confidence% variance explained by each frequency range Similar magnitudes with SSA analysis on coniferous forest in Germany (Mahecha et al., 2007)Cross-spectrum analysisAnalyze the power spectrum of different variables together:See how they are related in different temporal scale (covariance explained at each frequency)Explained covariance at a particular frequency, k is related to:€ Cxy,k2=Ax,k+ iBx,k( )Ay,k− iBy,k( )2€ Cx,k2= (Ax,k+ iBx,k)(Ax,k− iBx,k) = Ax,k2+ Bx,k2For two variables x(t), y(t), and their spectral power€ Cy,k2= (Ay,k+ iBy,k)(Ay,k− iBy,k) = Ay,k2+ By,k2“Cross spectrum” between x and yFrom Stull, 1988Example: NEE & air TIntensity of in-phase signal ~ covariance~ 90°-out-of-phase- kind-of covariance~ CorrelationPhase differenceWHY?Example: NEE & LH~ Covariance~ 90°-out-of-phase- kind-of covariance~ CorrelationPhase differenceTool for comparing different variables and for statistical significanceConclusion•Processes in annual (340 ~ 400 days) and half-annual (178~194 days) time scale controls most of the variance of NEE•The variance of NEE anomaly are distributed more evenly, but still large fraction is associated with period greater than 20 days. Statistically significant periods are 340~510, 180~220, 98~105, and 49~51 days, together explains about 4% of the total variance of the anomaly.•It is demonstrated that NEE and surface air T (and LH) anomaly seem to be correlated in annual, half-annual, and 50 days periods, but statistical significance analysis needs further understanding of the speaker on cross-spectral analysis.Future work (in one week)•Spectral coherence analysis of NEE with other variables (85%)• Temporal correlation & cross-spectral analysis of observed NEE with modeled NEE by NCAR CLM3.5 (55%)•Similar analysis on other ecosystems - arid grass-shrub land & tropical forests (40%)•Temporal correlation & cross-spectral analysis of simulated NEE with other variables from model simulation (25%)•SSA analysis on the NEE (5%)The numbers in ( ) represents the probability of finishing before the write-up due date with 95% confidence.Supplemental material AData for cross-spectrum analysisGeneral statistics:Row time seriesAnomalyvariable meanstd varlag1 auto-correlationlinear correlation with NEEexplained variance of NEENEE -0.528 3.106 9.643 0.876airT 8.421 9.295 86.405 0.945 -0.661 0.437VPD 0.825 0.344 0.118 0.800 0.067 0.005LH 35.931 36.466 1329.800 0.777 -0.771 0.594SH 32.860 38.580 1488.400 0.586 -0.037 0.001variable meanstd varlag1 auto-correlationlinear correlation with NEEexplained variance of NEENEE 0.000 1.478