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R. Reichle 1 * and C. Draper 1,2 With contributions from:

AMSR-E Technical Interchange Meeting Oxnard, CA Sep 4-5, 2013 Soil moisture retrievals from AMSR-E and ASCAT: Error estimates and data assimilation. R. Reichle 1 * and C. Draper 1,2 With contributions from: G. De Lannoy, R. de Jeu, Q. Liu, V. Naeimi, R. Parinussa, W. Wagner.

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R. Reichle 1 * and C. Draper 1,2 With contributions from:

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  1. AMSR-E Technical Interchange Meeting Oxnard, CA Sep 4-5, 2013 Soil moisture retrievals from AMSR-E and ASCAT: Error estimates and data assimilation R. Reichle1* and C. Draper1,2 With contributions from: G. De Lannoy, R. de Jeu, Q. Liu, V. Naeimi, R. Parinussa, W. Wagner 1NASA/GSFC, Greenbelt, MD, USA 2Universities Space Research Association, Columbia, MD, USA *Email: Rolf.Reichle@nasa.gov

  2. Motivation • Root Mean Square Error (RMSE) needed • to validate against mission target accuracies, and • to specify observation error for data assimilation. • Difficulty: No recognized soil moisture truth at large scales. RMSE traditionally from validation against in situ observations: • Point-scale (e.g., SCAN): Representativity errors when comparing against satellite estimates. • Footprint-scale (e.g., USDA ARS): Limited spatial coverage.

  3. Outline Error estimates for soil moisture retrievals Triple collocation Error propagation Soil moisture data assimilation

  4. Approach How can we estimate RMSE in satellite soil moisture retrievals? • Two methods: • Triple collocation • Error propagation through remote sensing retrieval algorithms • Two remotely sensed soil moisture datasets: • AMSR-E (X-band) Land Parameter Retrieval Model (de Jeu and Owe, 2003) • ASCAT C-band TUWien empirical change detection (Wagner et al., 1999) • Experiment details: • Jan 2007 - Oct 2011 • North American domain

  5. Triple Collocation Triple Collocation (TC) is a method to estimate RMS errors. TC requires three independent estimates. NOTE: 1.) TC cannot provide absolute RMS errors because it does not estimate the bias. 2.) For soil moisture, we found TC to work only for “anomalies” from the seasonal cycle. 3.) TC is sensitive to the climatology of the chosen reference data set.

  6. Triple Collocation • Surface soil moisture datasets: • (converted to anomalies from the mean seasonal cycle) • θ(A): ASCAT • θ(L): AMSR-E LPRM • θ(C): Catchment model • Additive random error model (θ = truth, < ϵ(X) >= 0) • θ(A) = α(θ + ϵ(A)) • θ(L) = λ(θ + ϵ(L)) • θ(C) = γ(θ + ϵ(C)) • α, λ, γ are calibration constants • (rescale to account for systematic differences in variability between datasets) • Stoffelen(1998), Scipal et al. (2008), Miralles et al. (2010)

  7. Triple Collocation • Set θ(A) as the reference dataset (α=1)  subscript “A” for estimated calibration constants and estimated errors. • Solve for calibration: • λA ≈ < θ(L) θ(C) > / < θ(A) θ(C) > • γA ≈ < θ(L) θ(C) > / < θ(A) θ(L) > • Solve for ϵ2 = (RMSETC)2: • ϵA2(A) ≈ < (θ(A) – θ(L)/λA) · (θ(A) – θ(C)/γA) > • ϵA2(L) ≈ < (θ(L)/λA – θ(A) ) · (θ(L)/λA – θ(C)/γA) > • ϵA2(C) ≈ < (θ(C)/γA – θ(A) ) · (θ(C)/γA – θ(L)/λA) > • Assumption: • Errors are not correlated with each other, nor with the true state.

  8. Interpretation of large-scale soil moisture RMSE RMSE(X)2 = var(X) + var(true) – 2 Rsqrt( var(X) var(true)) + bias2 • “Because vartrue differs from place to place […] a single global RMSE target may not be appropriate.” (Entekhabi et al., 2010). • At the global scale, we do not know vartrue (or even the mean): • Information on agreement is in time series correlation coefficient R. • Comparing soil moisture data sets using TC requires rescaling them to match the climatology of a reference data set. • RMSETC estimates will depend on the climatology of the chosen reference data set.

  9. Triple Collocation Variability (anomalies) RMSE of ASCAT (anom) ASCAT [Ref dataset = ASCAT] [Ref dataset = AMSR-E] AMSR-E/LPRM [Ref dataset = GEOS-5] GEOS-5

  10. RMSE and Fractional RMSE (fRMSE) Spatial differences in variability introduce nonlinearities: the ratio (and ranking!) of the domain-average RMSETC in m3m-3 depends on the selected reference: Solution: Report errors as fractional RMSE: fRMSE = RMSEX(X) / var(X)

  11. Triple Collocation Variability (anomalies) RMSE of ASCAT (anom) Fractional RMSE ASCAT ASCAT [Ref dataset = ASCAT] [Ref dataset = AMSR-E] AMSR-E/LPRM AMSR-E/LPRM Estimated RMSE reflects variability of reference product. Use fractional RMSE instead. [Ref dataset = GEOS-5] GEOS-5 Draper et al. 2013, RSE, in press

  12. Triple Collocation ASCAT fRMSETC AMSR-E fRMSETC Width of 90% confidence interval for ASCAT fRMSETC Width of 90% confidence interval for AMSR-E fRMSETC Uncertainty estimates indicate where fRMSETC is reliable. Draper et al. 2013, RSE, in press

  13. Triple Collocation fRMSETC estimates can provide insights into relative skill. Consistent with expectations. Draper et al. 2013, RSE, in press

  14. Triple Collocation Assumptions Draper et al. 2013, RSE, in press Assumption: Errors not correlated across datasets and with the truth. Check by adding a 4th dataset (in situ). In situ “errors” are not small! (scale mismatch, sensor issues,...) • fRMSETC is reasonably insensitive to choice of data triplet. • Residual differences between fRMSETC estimates are related to error correlations between data products.

  15. Triple Collocation Assumptions Previous finding holds only if using anomalies from the mean seasonal cycle!

  16. Outline Error estimates for soil moisture retrievals Triple collocation Error propagation Soil moisture data assimilation

  17. Error propagation • Propagate expected errors in input observations and parameters through the soil moisture retrieval model: • ASCAT (Naeimi et al. 2007) • LPRM (Parinussa et al. 2011) • Used average of the error time series at each location. • Assumed to represent errors in the soil moisture anomalies.

  18. Triple Collocation (TC) and Error Propagation (EP) ASCAT fRMSETC AMSR-E fRMSETC ASCAT fRMSEEP AMSR-E fRMSEEP TC and EP yield reasonably consistent fRMSE patterns. Draper et al. 2013, RSE, in press

  19. Triple Collocation • fRMSETC is consistent with: • fRMSE from error propagation • expectations (vegetation classes) Draper et al. 2013, RSE, in press

  20. Outline Error estimates for soil moisture retrievals Triple collocation Error propagation Soil moisture data assimilation

  21. Improvements from data assimilation Skill increases significantly through data assimilation. Similar improvements from AMSR-E/LPRM and ASCAT. Metric: Anom. time series corr. coeff. Anomalies ≡ mean seasonal cycle removed Validated with in situ data Draper et al. (2012), GRL, doi:10.1029/2011GL050655.

  22. Improvements from data assimilation Skill increases significantly through data assimilation. Similar improvements from AMSR-E/LPRM and ASCAT. Consistent with similar skill levels for the AMSR-E and ASCAT retrievals themselves…. …except for terrain with high topographic complexity (TC>10%). Draper et al. (2012), GRL, doi:10.1029/2011GL050655.

  23. Improvements from data assimilation Root zone soil moisture skill improvement from assimilation over model (ΔR) Synthetic experiment As long as (obs skill − model skill) > −0.2, assimilation improved the model skill. Draper et al. (2012), GRL, doi:10.1029/2011GL050655. Reichle et al. (2008), GRL, doi:10.1029/2007GL031986.

  24. Conclusions (1/4) • Both triple collocation and error propagation can estimate spatial patterns in the fRMSE. • Good agreement with each other, and with expectations (based on vegetation, known problems) • Triple collocation is believed to provide correct magnitude, and method is robust (dependent on careful selection of data sets, use of anomalies from the seasonal mean)

  25. Conclusions (2/4) • How should we evaluate remotely sensed soil moisture globally? • Substantial spatial variation in RMSE and fRMSE across North America • Evaluation based on handful of in situ sites may not represent global accuracy • Triple collocation or error propagation could provide a useful complement • It is unclear how current RMSE target accuracies can be interpreted globally • Selection of reference determines magnitude of RMSE (and domain-average RMSE has non-linear dependence on reference) • Uniform RMSE target over large domain not sensible • Need alternative metrics (fRMSE, or see Crow et al. (2010), Entekhabi et al. (2010))

  26. Conclusions (3/4) • Data assimilation: • Assimilation of soil moisture retrievals improves model estimates of surface and root zone soil moisture. • AMSR-E and ASCAT retrievals have comparable skill and yield similar improvements after data assimilation. • Improvements can be realized even when the retrievals are (somewhat) less skillful than the model estimates.

  27. Conclusions (4/4) • How should we specify soil moisture observation error variances for data assimilation? • Usually specified as a constant in the observation climatology. • Uniform error variance not sensible, and resulting spatial patterns do not resemble other estimates. • Use a uniform fRMSE, or spatial maps from triple collocation or error propagation (latter gives temporal variability).

  28. Thank you for your attention. Questions? References: Draper, C. S., R. H. Reichle, R. de Jeu, V. Naeimi, R. Parinussa, and W. Wagner (2013), Estimating root mean square errors in remotely sensed soil moisture over continental scale domains, Remote Sensing of Environment, in press. Draper, C. S., R. H. Reichle, G. J. M. De Lannoy, and Q. Liu (2012), Assimilation of passive and active microwave soil moisture retrievals, Geophysical Research Letters, 39, L04401, doi:10.1029/2011GL050655.

  29. Back-Up Slides

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