Cross-spectral analysis on Net Ecosystem Exchange: Dominant timescale and correlations among key

ecosystem variables over the Ameriflux Harvard forest site

ATMO 529 class project

Koichi Sakaguchi

LTER photo galleryhttp://savanna.lternet.edu/gallery/albums.php

Objectives

1. 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 together

These knowledge will be helpful to infer important variables and processes that control ecosystem-level carbon cycle

Data 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 GCB

Data 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 positive

Methods

1. 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 NEE

I’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 series

Mean: -0.53 gC/m2/daySTD: 3.1 gC/m2/dayLag-1 autocorrelation: 0.88

Harmonic Analysis

For a particular frequency k, Ck2 / 2

represents the fraction of the variance explained at that frequency

From Hartmann’s note

€

Ck2 = (Ak + iBk )(Ak − iBk ) = Ak

2 + Bk2

“Spectral Power”

By using Fourier series in least-squares fit, we have

Power spectrum: NEE

341 ~ 409 days

178 ~ 194 days

No spectral averaging or smoothing

Red line : Red noise spectrum

Dashed line: statistically significant threshold with 90 & 95 % confidence

~90 days period

Power spectrum: NEE

341 ~ 409 days

178 ~ 194 days

Top: linear scaleBottom: semi-log plot(x-axis in log scale)

No spectral averaging or smoothing

Red line : Red noise spectrum

Dashed line: statistically significant threshold with 90 & 95 % confidence

~90 days period NEE varies largely in annual & seasonal scale… not too exciting

Look at NEE anomaly

Subtract 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 season

NEE anomaly power spectrum

Again most of the variance is in lower frequency.Annual ~ seasonal time scale still dominate!

Focused on lower frequencies

Top: linear scale, no smoothing

Bottom: linear scale, smoothed by 5-points running mean

NEE anomaly explained variances

1.2%

340~510

180~220

98~10549~51

45~45.5

1.3% 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,k

2 + Bx,k2

For two variables x(t), y(t), and their spectral power

€

Cy,k2 = (Ay,k + iBy,k )(Ay,k − iBy,k ) = Ay,k

2 + By,k2

“Cross spectrum” between x and y

From Stull, 1988

Example: NEE & air T

Intensity of in-phase signal ~ covariance

~ 90°-out-of-phase- kind-of covariance

~ Correlation

Phase difference

WHY?

Example: NEE & LH

~ Covariance

~ 90°-out-of-phase- kind-of covariance

~ Correlation

Phase difference

Tool for comparing different variables and for statistical significance

Conclusion•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 analysis

General statistics:

Row time series

Anomaly

variable mean std varlag1 auto-correlation

linear correlation with NEE

explained variance of

NEE

NEE -0.528 3.106 9.643 0.876

airT 8.421 9.295 86.405 0.945 -0.661 0.437

VPD 0.825 0.344 0.118 0.800 0.067 0.005

LH 35.931 36.466 1329.800 0.777 -0.771 0.594

SH 32.860 38.580 1488.400 0.586 -0.037 0.001

variable mean std varlag1 auto-correlation

linear correlation with NEE

explained variance of

NEE

NEE 0.000 1.478 2.186 0.507

airT 0.000 3.938 86.405 0.722 0.039 0.002

VPD 0.000 0.328 0.108 0.801 0.097 0.010

LH 0.000 21.369 456.650 0.414 -0.385 0.148

SH 0.000 29.896 893.792 0.373 -0.136 0.019

ReferencesBaldocchi, D.D, 2003. Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present, and future. Global Change Biology,9, p479-492

Mahecha, M.D., M.Reichstein, H.Lange, N.Carvalhais, C.Bernhofer, T.Grunwald, D.Papale, and G.Seufert, 2007. Characterizing ecosystem-atmosphere interactions from short to interannual time scales. Biogeosciences, 4, p743-758.

Stull, R.B. An introduction to Boundary Layer Meteorology, 1988. Kluwer Academic Press, MA, USA.