Downscaling Climate Variables Downscaling:

1. Downscaling Climate Variables Downscaling: Inferring climate variations on smaller spatial/temporal scales than resolution of climate model/forecast 1Marina Timofeyeva, 2David Unger and 3Cecile Penland 1UCAR and NWS/NOAA 2NWS/NOAA 3OAR/NOAA Contributors: Robert Livezey and Rachael Craig NOAA NWS and OAR

2. Outline • Introduction: Local Climate Variables • Downscaling Seasonal Temperature Forecasts • Downscaling Seasonal Precipitation Forecast • Temporal Downscaling • Summary NOAA NWS and OAR

3. Introduction: Definitions Downscaling to a LocalClimateVariable: • Downscaling–inferring climate variations on smaller spatial/temporal scales than resolution of climate model/forecast • Local – points, station, small grid, etc. Key: higher resolution than the original variable used for downscaling • Climate – mean daily, weekly, monthly, seasonal (3-4 month) temperature, precipitation, wind fields, etc. • Variable – main object of interest: observation or forecast. Note climate variable is often considered in form of parameters of distribution NOAA NWS and OAR

4. Introduction: Climate Variables Standard Deviation of 500mb Geopotential height Anomalies in JFM Legend: Contours are every 10 m - > 45 m - > 75 m Slide courtesy: P.Sardeshmukh NOAA NWS and OAR

5. Introduction (cont.) Downscaling Methods: • Dynamical – applications are on meteorological scale, climate variables are estimated as averages of continuous model runs • Statistical – variable can be modeled at defined temporal scale, e.g. monthly, weekly, seasonal, etc,if predictability (deviation from observational noise and/or forecast skill) at such scale exists NOAA NWS and OAR

6. Introduction (cont.) Downscaling requirements: • Model Simplicity • Validity of Distribution • Existence of potential predictability NOAA NWS and OAR

7. Introduction: Assumptions Assumptions must be appropriate for the dynamical system being downscaled. Example: If the amplitude of a Rossby wave is normally distributed, the energy in that wave cannot be normally distributed. (In fact, it would be chi-squared.) NOAA NWS and OAR

8. Introduction: Source of Predictability Slide courtesy: P.Sardeshmukh NOAA NWS and OAR

9. Downscaling Temperature Forecasts Source for Downscaling: CPC forecasts Questions to be answered: • Why downscale? • What distribution is appropriate? • Is there potential predictability? • How do we do it? • What is the outcome? NOAA NWS and OAR

10. Downscaling Temperature Forecasts • Why downscale? NOAA NWS and OAR

11. Downscaling Temperature Forecasts When there is a climate signal, CPC has a reason to change the odds from climatological distribution NOAA NWS and OAR

12. Justification for Temperature PDF Example: One way dynamics affects probability: A temperature equation with cooling and heating: Also, let’s say that the heating Q has a Gaussian white noise component to it: Q = Qo +  Q NOAA NWS and OAR

13. Justification for Temperature PDF The pdf f(T) is described by the following equation: where  is essentially the variance of Q. This is the equation for a Gaussian distribution. Thus, Gaussian systems are equivalent in probability to linear dynamical systems. NOAA NWS and OAR

14. Downscaling Temperature Forecasts Predictability of The Downscaling Source : • Moderate to high national-scale skill confined to Fall/Winter strong ENSO years at short to medium leads • Otherwise, skill is primarily modest and level with lead (derived from biased climatologies, i.e. long-term trend) • Worst forecasts are for • Fall/Winter at short to medium leads in the absence of strong-ENSO • Summer/Fall at medium to long leads even for strong ENSOs: No remedy except to advance the science Heidke Skill Score Lead (month) Heidke Skill Score Lead (month) NOAA NWS and OAR

15. Downscaling Temperature Forecasts Predictability of the Downscaling Source – Map NOAA NWS and OAR

16. Downscaling Temperature Forecasts The CPC POE outlooks for each CD are used as downscaling source for station specific outlooks. Historical NCDC data (1959 to present) for station and CD are used in developing downscaling relations that, together with CPC operational forecasts, are used for station POE outlooks Observed T POF (%) Forecasted Temperature (°F) NOAA NWS and OAR

17. Downscaling Temperature Forecasts How CPC adjusts CD forecast distribution back towards climatology depending upon forecast skill. NOAA NWS and OAR

18. Downscaling Temperature Forecasts NOAA NWS and OAR

19. Downscaling Temperature Forecasts NOAA NWS and OAR

20. Downscaling Temperature Forecasts Adjustment of Intercept (ai) for local trend at the station is needed IF the trend over last 10 years is statistically significant: NOAA NWS and OAR

21. Downscaling Temperature Forecasts Δ(°F) NOAA NWS and OAR

22. Downscaling Temperature Forecasts Climatological Spread ρ (CD fcst/obs corr) Spread of Station Forecast Confident Prediction ri – Station/CD Correlation NOAA NWS and OAR

23. Downscaling Temperature Forecasts • Outcome – NWS Local Climate Product: • Outlook Graphics are dynamically generated for every location (1,141 sites; about 10 sites per WFO CWA) • Text interpretation of probability information for general public avoids use of very technical terms • Intuitive navigating options • Clickable maps for changing locations • Main menu and interactive (clickable) map and graphs NOAA NWS and OAR

24. Downscaling Precipitation Forecasts Source for Downscaling: CPC forecasts Questions to be answered: • Why downscale? –discussed in previous section • What distribution is appropriate? • Is there potential predictability? • How do we do it? • What is the outcome? – discussed in previous section NOAA NWS and OAR

25. Mean = 60.7 St.Dev.= 13.6 Median = 59.5 Mode = 52.0 Skewness = 0.225 Kurt = -0.526 Downscaling Precipitation Forecasts Temperature is a normally distributed variable, therefore the downscaling method based on regression can provide good estimates Precipitation (right chart) is too skewed for normal distribution. The regression would require a transformation of this variable. Compositing can be used for Precipitation forecasts because it does not employ regression analysis. Mean = 0.30 St. Dev.= 0.38 Median = 0.19 Mode = 0.01 Skewness = 3.11 Kurtosis = 14.67 NOT a good fit NOAA NWS and OAR

26. Downscaling Precipitation Forecast Distributions of seasonal precipitation totals are too skewed NOAA NWS and OAR

27. Downscaling Precipitation Forecast Is there Potential Predictability in CPC Precipitation Forecasts? • Useable national-scale skill entirely confined to Fall/Winter strong ENSO years in short to medium leads • Otherwise skill is statistically indistinguishable from zero Heidke Skill Score Lead (month) Heidke Skill Score Lead (month) NOAA NWS and OAR

28. Downscaling Precipitation Forecast Predictability of CPC Precipitation Forecasts NOAA NWS and OAR

29. Downscaling Precipitation Forecast • Which distribution is an appropriate assumption for precipitation? • Data: 1960 – 2003 3 month (DJF, …OND) total precipitation for 87 locations in NWS WR • Kolmogorov-Smirnoff GOF test of Distributions: Normal, Lognormal and Gamma • Mapping CPC forecast potential predictability on fit of an assumed distribution NOAA NWS and OAR

30. Downscaling Precipitation Forecast Which distribution is an appropriate assumption for precipitation? NOAA NWS and OAR

31. Downscaling Precipitation Forecast • What does it mean? • Linear regression cannot be used because distribution assumptions, used by regression tests, are not met in many cases • Several alternatives: • Variable transformation, e.g. sqrt, ln, etc. • Normal Quantile transformation • Special Case, zero precipitation amounts, require the use of two model forecast systems: • forecast probability of precipitation chance and • forecast probability of precipitation amount NOAA NWS and OAR

32. Downscaling Precipitation Forecast Warning : To apply a nonlinear transformation we must ensure a straightforward procedure to transform the downscaled predictions back to physical units. For example, log transformation has a relationship between parameters in transformed (α,β) and untransformed (μ,σ) domains (Aitchison and Brown, 1957): NOAA NWS and OAR

33. Downscaling Precipitation Forecast Parameters of the linear regression are quantiles of standard normal distribution NOAA NWS and OAR

34. Disaggregation - Seasonal to Monthly Temporal Downscaling • Regression and Average of 3 estimates • Simultaneous spatial and temporal downscaling possible • Tm- = bs- Ts- + as- ; S- = m-2,m-1,m, R=Lower • Tm0 = bs0 Ts0 + as0 ; S0 = m-1,m,m+1, R=Best • Tm+ = bs+ Ts+ + as+ ; S+ = m ,m+1,m+2, R=Lower Tm= (Tm- + Tm0 +Tm+ )/3 FMA JFM MAM + + M = 3 NOAA NWS and OAR

35. CRPS Skill Scores: Temperature Skill .10 .05 .01 FD CD 3-Mo 1-Month Lead, All initial times 1-Mo NOAA NWS and OAR

36. Downscaling Other than Seasonal Climate Variables • Alternative – Statistical downscaling of variables representing stochastic structure of climate variables at finer than seasonal scale. • Example - statistical downscaling model is linked with a GCM by using most predictable fields (e.g., SST, Wind fields) as forcing. Downscaling model is a correlation model between variables derived from the GCM fields and variables representing stochastic structure of local climate variables NOAA NWS and OAR

37. Downscaling Other than Seasonal Climate Variables • Stochastic structure variables of temperature – Insolation term (T, A and phase), AR terms (Φ) and white noise term (ε): β Temperature (ºC) α Insolation (Watts/m2) TMN PHASE days NOAA NWS and OAR

38. Lessons learned • Keep your model simple and your assumptions in mind • To have good downscaling results, the original prediction skills must be good. • The statistics between large and small scales must be robust and appropriate. NOAA NWS and OAR

39. Additional Thoughts • Models which don’t represent the current climate well cannot be credibly downscaled statistically • for even the current climate with methods based only on observations • for the current climate with methods based on model corrections if either (a) the model is missing important variability or (b) observational data are limited • Models of future climate downscaled statistically is problematic because climate change is inherently a non-stationary process • Nested or linked model downscaling implies major technical challenges as well as assumptions about scale interactions if attempted for future climates (possible solution is global high-resolution models) NOAA NWS and OAR