Scaling and Analysis of Long Time Series of Soil Moisture Content

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Scaling and Analysis of Long Time Series of Soil
Moisture Content

• By
• Gabriel Katul
• Nicholas School of the Environment and Earth
  Sciences,
• Duke University

NSF Workshop Data-Model Assimilation in Ecology
Techniques and Applications Norman, Oklahoma,
October 22-24, 2007
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Background Soil moisture dynamics and climate

• Because of storage effects within the soil pores,
  the dynamics of soil moisture posses a memory
  that is often considerably longer than the
  integral timescale of many atmospheric processes.

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Background Soil moisture dynamics and climate

• Hence climate anomalies can be sustained
  through land surface feedbacks primarily because
  they can feed off on this long-term memory.

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Experimental Results
Robock et al.,2000

• Canonical findings across experiments are
• The amplitude of soil moisture variations
  decreases with soil depth.
• Soil moisture memory across various geographic
  regions increases for dryer states when compared
  to wetter conditions.
• Soil moisture is generally in-phase with
  precipitation at long-time scales but can be
  out-of-phase for short time scales.

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Objective

• A simplified analytical theory that predicts the
  spectrum (and phase) of soil moisture content at
  time-scales ranging from minutes to inter-annual.
  
• Focus on a case study in which 8 years of
  30-minute spatially and depth - averaged soil
  moisture time series is available along with
  precipitation, throughfall, and eddy-covariance
  based evapotranspiration.

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Precipitation
Transpiration
Through-fall
Evaporation
Root- Depth RL
Soil Porosity
Drainage
Dimensionless
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1998-2005 8 years of 30 min. data
4 rods per ring
8
Pi 1280 mm y-1
Measured Interception 40 of P 512 mm y-1
See data below ET 650 mm y-1
Measured by EC Through-fall Pi-Interception
768 mm y-1 P(t) ET/Through-fall 85
L(t) ET
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Modeling Soil Moisture Dynamics ET-s
relationship
ET/ETmax
Uniform Model
1.0
Nonlinear Model
Linear Model
1.0
S
0
from Porporato et al. (2004)
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Models for Soil Moisture Dynamics
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Spectral Analysis of Soil Moisture
Fourier-Transform
Soil moisture spectrum Es(f)
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Phase Shifts (from Katul et al., 2007)

• By increasing the rooting zone depth (dr), the
  rainfall and soil moisture variability become
  increasingly out-of-phase.
• (2) for long time scales (e.g., decadal), f?0
  and soil moisture and rainfall variability become
  in-phase with each.
• (3) Lowering ETmax, rainfall and soil moisture
  become out-of-phase.
• Consistent with linear phase shift analyses
  reported by Amenu et al. 2005 (Illinois Climate
  Network stations).

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Duke Forest Experiment 8 years of 30-min. Data
Evapotranspiration
Precipitation
Soil moisture
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(No Transcript)
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Random Force
Langevin
Unbounded variance as f?0 or time?
e.g. Langevin Equation dx/dt v
random Unbounded trajectories.
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ET max varies with time only
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Summary and Conclusions

• Simplified hydrologic balance suggests that for
  white-noise precipitation, soil moisture becomes
  red (decaying as f-2).

• Analytical model for memory

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Summary and Conclusions

• If soil moisture memory (here 45 days) is
• gtgt 12 hours, then diurnal dynamics of
• soil moisture do not contribute much
• to the overall variance.

• 45 day memory is much larger than those of many
  atmospheric processes. Hence, climate anomalies
  can be sustained through land-surface feedbacks
  primarily because they can feed-off on this
  long-memory.

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Summary and Conclusions

• Simplified analytical model predicts that reduced
  ETmax results in
• longer soil moisture memory and
• out-of-phase relationship between rainfall and
  soil moisture variations.

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References

• Amenu, G. G., P. Kumar, and X. Z. Liang (2005),
  Interannual variability of deep-layer hydrologic
  memory and mechanisms of its influence on surface
  energy fluxes, J. Clim., 18, 50245045.
• Katul, G. G., A. Porporato, E. Daly, A. C. Oishi,
  H.-S. Kim, P. C. Stoy, J.-Y. Juang, and M. B.
  Siqueira (2007), On the spectrum of soil moisture
  from hourly to interannual scales, Water Resour.
  Res., 43, W05428, doi10.1029/2006WR005356
• Koster, R. D., and M. J. Suarez (2001), Soil
  moisture memory in climate models, J.
  Hydrometeorol., 2, 558 570.
• Koster, R. D., et al. (2004), Regions of strong
  coupling between soil moisture and precipitation,
  Science, 305, 11381140
• Porporato, A., E. Daly, and I. Rodriguez-Iturbe
  (2004), Soil water balance and ecosystem response
  to climate change, Am. Nat., 164, 625632.
• Robock et al. (2000), The global soil moisture
  bank, Bulletin of the American Meteorological
  Society, 81, 1281-1299.

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Variable Interception and ETmax
LAIn
Through-fall