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Using Synthetic Data to Test Downscaling Methods

This document by John Lanzante (GFDL/NOAA) explores innovative methods to test downscaling techniques through synthetic data generation. It outlines the importance of recruiting test subjects, applying downscaling methods, and analyzing the outcomes effectively. With realistic examples examining linearity, nonlinearity, and coastal errors, this work highlights the challenges faced when utilizing real-world data. Synthetic data emerges as a promising solution to overcome limited datasets, allowing for diverse testing scenarios to improve downscaling methods.

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Using Synthetic Data to Test Downscaling Methods

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  1. Using Synthetic Data to Test Downscaling Methods John Lanzante (GFDL/NOAA)

  2. CONCEPTS • Testing Downscaling: • Like Product Testing My Product 

  3. CONCEPTS STEP1:Recruit Test Subjects (Gather Data) STEP2:Feed Cereal For Several Decades (Apply Downscaling Method)

  4. CONCEPTS STEP3:How are subjects affected? How well did downscaling do? Not so clear – Need more subjects? Need more data? Real-world data may be limited? Can we generate synthetic data to fill the void?

  5. CONCEPTS STEP 4a:Snowmen most affected? Generate a new sample.

  6. CONCEPTS STEP 4b:Snow-women affected differently? Generate a new sample.

  7. REALISTIC EXAMPLES CASE 1 – Linearity: Simplest downscaling – linear regression

  8. REALISTIC EXAMPLES CASE 1 – Strong Nonlinearity: Simplest downscaling – linear regression

  9. REALISTIC EXAMPLES SUMMARY CASE 1 – Nonlinearity: Hard to test nonlinearity in real-world data ? (if we are just entering “non-linear regime”) Simulate various degrees of nonlinearity Compare linear & nonlinear downscaling methods Determine amount of degradation Determine time in future when degradation becomes “too large”

  10. REALISTIC EXAMPLES CASE 2 – Coastal Error: Downscaling error maximizes along coastline

  11. REALISTIC EXAMPLES CASE 2 – Coastal Error: Obs gridpoint  Entirely land Model gridpoint  Partly land, partly ocean

  12. REALISTIC EXAMPLES CASE 2 – Coastal Error: Land more detail (extremes) than Ocean (damped) Missing peaks & troughs unrecoverable

  13. REALISTIC EXAMPLES SUMMARY CASE 2 – Costal Error: Simulate land & ocean points Downscale land from mixture (land + sea) Vary the proportions of the mixture Is coastal effect due to mixture/mismatch?

  14. SYNTHETIC DATA MODEL One Particular Synthetic Data Model: O= Observations M= Model y= year d= day Red = free parameter (user selects the value) Oy d = Ōy + O’y d  Yearly mean + AR1 O’y d = rlag1 * O’y d-1 + ay d  AR1 fvar = varŌ / varO [ varO = varŌ + varO] My d = Oy d + by dcorr = correlation(O,M) a ~ N(0,vara) Proper choice of a & b b~ N(0,varb) yields desired rlag1 & corr

  15. SYNTHETIC DATA MODEL STEP 1: Generate Base Time Series rlag1 day-to-day persistence fvar interannual vs. day-to-day variability corr strength of relation: model vs. obs STEP 2: Historical Adjustment meanOBS characteristics of the distribution meanMODEL varOBS varMODEL STEP 3: Future Adjustment meanOBS characteristics of the distribution meanMODEL varOBS varMODEL

  16. SYNTHETIC DATA MODEL OUR APPLICATIONS OF THIS MODEL: Downscaling (just getting started) No results yet Applied successfully to several related issues (cross-validation, exceedance statistics, testing two distributions)

  17. SUMMARY REAL-WORLD COMPLICATIONS: Results may not be clear-cut: Sample size too small? Multiple factors may contribute? Some conditions more interesting? SOLUTION – GENERATE SYNTHETIC DATA: Advantages of Synthetic Data: Unlimited sample size (enhance signal/noise) Change one factor at a time Prescribe exact conditions Vary factor over a wide range (“turn the knob”) Can extend outside the range of historical data Turn knob “all the way” for unambiguous results

  18. A CAUTIONARY NOTE No “One Size Fits All”: No single “best” synthetic data model Must possess appropriate real-world characteristics Ability to vary the relevant factors Possible Models For Future Development: Skewed data (transform Gaussian data nonlinearly?) Precipitation (discrete Markov + bounded distribution?) Model occurrence & amount separately? Multivariate model?

  19. THE END

  20. REALISTIC EXAMPLES CASE 1 – Weak Nonlinearity: Simplest downscaling – linear regression

  21. SUPPLEMENTAL Causes of Nonlinearity? At highest T – model soil becomes excessively dry – T becomes excessive Other possibilities: Water Vapor, Clouds, Sea-Ice, etc.

  22. REALISTIC EXAMPLES CASE 2 – Coastal Error: Land  More extremes Ocean  Damped

  23. REALISTIC EXAMPLES CASE 2 – Coastal Error: X/Y Plot: Land (model) vs. Land (obs)

  24. REALISTIC EXAMPLES CASE 2 – Coastal Error: X/Y Plot: Ocean (model) vs. Land (obs)

  25. SYNTHETIC DATA MODEL STEP 4: Fit downscaling model to historical sample STEP 5: Test downscaling in historical & future samples OUR APPLICATIONS OF THIS MODEL: No results to show today Downscaling (just getting started) Guidance in the use of cross-validation Biases in exceedance statistics Testing difference between 2 distributions

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