1. 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

2. Background – Soil moisture dynamics and climate n 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.

3. Background – Soil moisture dynamics and climate n Hence climate anomalies can be ‘‘sustained’’ through land surface feedbacks primarily because they can ‘‘feed off’’ on this long-term memory.

4. Experimental Results Canonical findings across experiments are: 1)The amplitude of soil moisture variations decreases with soil depth. 2)Soil moisture ‘memory’ across various geographic regions increases for dryer states when compared to wetter conditions. 3)Soil moisture is generally in-phase with precipitation at long-time scales but can be out-of-phase for short time scales. Robock et al.,2000

5. 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.

6. Precipitation Transpiration Evaporation Drainage Through-fall Soil Porosity Root- Depth R L Dimensionless

7. 4 rods per ring 1998-2005 – 8 years of 30 min. data

8. P i ~ 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 ~ P i -Interception ~ 768 mm y -1 = P(t) ET/Through-fall ~ 85% L(t) ET

9. Modeling Soil Moisture Dynamics: ET-s relationship ET/ET max S 1.0 0 Linear Model Nonlinear Model Uniform Model from Porporato et al. (2004)

10. Models for Soil Moisture Dynamics

11. Spectral Analysis of Soil Moisture Soil moisture spectrum E s (f) Fourier-Transform:

12. Phase Shifts (from Katul et al., 2007) (1) By increasing the rooting zone depth (d r ), 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 ET max, rainfall and soil moisture become out-of- phase. Consistent with linear phase shift analyses reported by Amenu et al. [2005] (Illinois Climate Network stations).

13. Precipitation Evapotranspiration Soil moisture Duke Forest Experiment – 8 years of 30-min. Data

15. Unbounded variance as f  0 or time  Random Force Langevin e.g. Langevin Equation: dx/dt = v [random] Unbounded trajectories.

16. ET max varies with time only S ET/ET m

17. Summary and Conclusions Simplified hydrologic balance suggests that for white-noise precipitation, soil moisture becomes red (decaying as f -2 ). Analytical model for memory

18. Summary and Conclusions If soil moisture memory (here ~ 45 days) is >> 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.

19. Summary and Conclusions n Simplified analytical model predicts that reduced ETmax results in (1) ‘longer’ soil moisture memory and (2) out-of-phase relationship between rainfall and soil moisture variations.

20. 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, 5024–5045. 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, doi:10.1029/2006WR005356 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, 1138–1140 Porporato, A., E. Daly, and I. Rodriguez-Iturbe (2004), Soil water balance and ecosystem response to climate change, Am. Nat., 164, 625–632. Robock et al. (2000), The global soil moisture bank, Bulletin of the American Meteorological Society, 81, 1281-1299.

21. Variable Interception and ETmax LAInThrough-fall