1. Improving Diameter Growth Prediction of Douglas-fir in Eastern Washington State, U.S.A. by Incorporating Precipitation and Temperature Andrew D. Hill, Ph.D. University of Washington College of Forest Resources

2. Rationale for Study Older methods need improvement Old assumptions no longer valid Forest Service said we should –Gave us money –Gave us data Older research said we could

3. Literature Douglass (1909, 1919) Coile (1936) Diller (1935) Schumacher and Meyer (1937)

4. Holdaway (1990) Peterson and Peterson (1994) Peterson and Heath (1990/91) Wensel and Turnblom (1998) Yeh and Wensel (1999) Stage et al. (1999) Lopez-Sereno et al. (2005)

5. Primary Objective Add weather or climate to a known growth model –Is it possible? –If so, is it desirable?

6. Definition of Climate and Weather Climate: Defined as a 30-year average Weather: In my work was defined in five- year increments

7. Wanted to use existing model –That is widely used –That provided a starting point –That followed a more mathematically ‘honest’ form than a log-linear model Chose ORGANON –Exponential function –Won’t let trees grow smaller –Used to determine WA’s DFC rules

8. ORGANON Function

9. ORGANON Variables ΔD = 5-year change in diameter SI = site index SBAL = basal area larger SBA = stand basal area D = diameter CR = crown ratio I data = the location of the stand within the forests a i = the coefficients estimated for X i ’s

10. Tree data Forest Inventory and Analysis Data –Five-year increment –Eastern Washington Between lat 45.849 o and 48.927 o and long 117.096 o and 121.941 o Both mixed and pure Douglas-fir stands 7 stands measured in 1993 and 1998 10 stands measured in 1994 and 1999 3 stand measured in 1995 and 2000 28 stands measured in 1996 and 2001

11. Stand Statistics

12. Tree Statistics

13. Douglas-fir Statistics

14. Weather and Climate From Climate Source, Inc. –Parameter-elevation Regressions on Independent Slopes Model (PRISM) –Creates data for NOAA –2km by 2km grid of monthly total precipitation and average temperature for whole of WA. January 1950 through December 2002 Used to create other variables used in modeling the effects of weather and climate

15. Table 4. Basic weather variable description. D denotes dormant season (November through April), G denotes growing season (May through October), W denotes total seasonal (dormant or growing) precipitation (mm), X denotes average seasonal temperature ( o C), T denotes temperature sums, and P denote precipitation sums. Variable name (units) CalculationMeanStd Dev5th Pctl Median95th Pctl TG ( o C x 10) 3701.5372.90305536754377 TD ( o C x 10) -194.7419.54-900-275.5511 PG (mm) 1185.6413.8968410901990 PD (mm) 2953.61850.16121824336963

16. Dataset Creation Located each of the 48 stands in the proper cell on the 2km by 2km weather grid. Generated the weather and climate variables needed. 1019 Douglas-fir. Of these, 994 were suitable for our project.

17. Bootstrapped datasets Created 1500 random samples of n = 994 –With replacement –Better estimate of the variance for the coefficients of the models generated. –Small sample size –Allowed for more robust estimates of the parameters Used these datasets for analysis.

18. Three studies Add weather over the measurement interval to the model and see if it improves the model. Add climate and weather and various deviations from the average and see if that improves the model Use the Parameter Prediction Method in conjunction with weather and climate to improve the model

19. First Study IMPROVING MODELED PREDICTIONS OF SHORT-TERM DOUGLAS-FIR DIAMETER GROWTH IN EASTERN WASHINGTON, U.S.A., BY INCORPORATING LOCAL WEATHER INFORMATION

20. Revised ORGANON model Did not have SI for 30% of the stands Did have Mean Annual Increment at Culmination (ft 3 /ac 2 /yr). This is a function of SI. Used this instead of SI. (See Van Clay 1994).

21. Base Model D represents tree dbh LGD denotes ln(D + 1), where ln denotes natural logarithm LGSI denotes ln(SI – 4.5) BALT denotes LGCR denotes a i s represent equation coefficients to be fit with least squares regression

22. Where LGMAIC denotes ln(MAIC), and all other variables are as before

23. Base Model Statistics R 2 = 0.30886 BIAS = 0.00412 |BIAS| = 0.27674 STD Resid = 0.36261 SSE = 11.10882

24. Models with weather added Added weather to base model:

25. Models with weather added Used above models with base model fixed Refit with all parameters allowed to vary

26. Models with Base fixed M2 M3 M4

27. Models fitted simultaneously M5 M6 M7

28. Model Comparison Table 5. Fit statistics of the models. ModelR squaredBIASABS (BIAS) St ResidSSE Base 0.30886 0.004120.276740.3626111.10882 M2 0.33200-0.0003590.272400.3568810.74019 M3 0.34137-0.00100430.268140.3542610.65519 M4 0.34249-0.0012590.268280.3540610.63063 M5 0.33246 0.009530.269910.3568610.51866 M6 0.34372 0.000470.266740.3534910.45043 M7 0.35432 0.003950.265500.3505510.29739

29. Discussion Used the base model to test against Found any added weather improved the prediction At worst 7% –Only one added variable –Literature says in arid regions dormant season precipitation is the driving variable in year-to-year ring growth

30. Discussion At best 15% –More complicated model –Harder to interpret why it works –Best fit statistics save bias

31. Conclusions from First Study We can improve a model by adding weather. We can make simple changes that have a significant impact. More complex models give a better fit. –The trade-off between better fit and more complex model may not be desirable.

32. Second Study USING LOCAL SHORT-TERM WEATHER AND LONG-TERM CLIMATE INFORMATION TO IMPROVE PERIODIC DIAMETER GROWTH PREDICTION FOR DOUGLAS-FIR GROWING IN PURE AND MIXED STANDS IN EASTERN WASHINGTON, U.S.A.

33. Added weather, climate, and deviations from base model See handout for calculation of variables used. Attached these variables to the fixed base model presented above. –Solved for best fit of added variables –Compared fit statistics

34. Models developed (1) (2) (3) (4) (5) (6)

35. Results Table 6. Parameter estimates for Models 2-6 and their standard errors. Model Mean (Std Err) 2 -0.000033295 (0.00000129) 0.000266644 (0.00000501) -0.000256282 (0.00000457) 0.000173920 (0.00000125) 3 -0.000192813 (0.00000395) 0.000234076 (0.00000135) -0.000065027 (0.00000173) -0.000348663 (0.00000717) 4 0.0089929 (0.0003086) -0.112175 (0.0009094) 0.0692842 (0.0004889) 0.0179885 (0.0006876) 5 0.0411442 (0.0002172) 0.0178382 (0.0003289) 0.0041056 (0.0000909) -0.0857754 (0.0004335) 6 -0.000178292 (0.00000419) -0.000313852 (0.00000742) 0.000228476 (0.00000142) -0.000074115 (0.00000173)

36. Table 7. Fit statistics pertaining to Models 1-6. Model SSEMean Residual Residual Std|Residual|r2r2 % Biased 111.1088 0.004120.362610.276740.30886 0.62% 210.574-0.00520.35250.26834 0.34657- 0.78% 310.6608-0.00640.355410.27304 0.33569 -0.96% 410.6446 0.000630.357350.27288 0.32867 0.10% 510.4891-0.0180.354780.27220 0.33819 -2.71% 610.6692-0.00670.355580.27325 0.3351 -1.02%

37. Table 8. Ranks of each model, 1 through 6, by fit statistics. Model SSEMean Residual Residual Std |Residua l| r2% BiasedSum of Ranks 162666329 223111210 344343422 431535118 516222619 655454528

38. Conclusions from Second Study Weather works better than climate at predicting diameter change. Deviations work too, but not quite as well. Climate improves the model, but not as well as weather or deviations from weather.

39. Third Study CAN THE PARAMETER PREDICTION METHOD IMPROVE DIAMETER PREDICTION WHEN USED TO INCORPORATE WEATHER AND CLIMATE IN AN EXISTING MODEL?

40. Parameter Prediction Method Three-step method –Fit base model plot by plot –Examine relationship between weather and climate variables and the coefficients of the base model fits to each plot. –Use these relationships in a new equation that incorporates the exogenous information into the base model, simultaneously fitting all first and second step parameters.

41. Models Developed (1) (2)

42. Compared these to Best Models in Studies One and Two (3) (4)

43. Results Table 9. Fit statistics for Eq. 1-4. Model SSEMean Residual Residual Std |Residual|r2r2 % Biased Base11.10880.004120.362610.276740.308860.62% 110.53320.008900.361350.273820.316231.34% 210.32430.006520.354150.268740.341980.98% 310.29740.003950.350550.265500.354320.81% 410.5740-0.005200.35250.26834 0.34657-0.78%

44. Conclusions from Third Study PPM does work to improve prediction change in diameter over a five-year increment in Douglas-fir. PPM does not a provide a significant improvement in model fit over other methods. May not be worth the extra effort it takes to use three steps, where one seems to do as well.

45. Contributions of the Study Prediction of Five-year diameter increment of Douglas-fir in Eastern Washington can be improved by incorporating Precipitation and Temperature. Site-specific weather is most helpful The model used climate in the initial modeling, rather than as an adjustment post hoc.

46. Contributions of the Study Model should correct to conditions without the need for recalibration Easily replicated: climate data is available and inexpensive Easily transportable to other locations Could help predict the impacts of weather cycles

47. Limitations Only a small sample Only one dataset Only one species Limited geographic region Limited climatic variation Only a five-year interval

48. General Conclusions Different ways of using weather produce similar results, which gives us confidence that the results are valid. It is possible to use weather to improve diameter increment models. Climate was not useful in this case.

49. Future Research Larger geographic area More variation in type of weather experienced –In this study it was generally drier and cooler than average. More species Expand to include height growth Expand to use with mortality models

50. Questions?