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

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• Old assumptions no longer valid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

Literature

• Douglass (1909, 1919)

• Coile (1936)

• Diller (1935)

• Schumacher and Meyer (1937)

• 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)

Primary Objective

• Add weather or climate to a known growth model– Is it possible?– If so, is it desirable?

Definition of Climate and Weather

• Climate: Defined as a 30-year average

• Weather: In my work was defined in five-year increments

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

ORGANON Function

7

0i i

aa X

D e

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• ai = the coefficients estimated for Xi’s

Tree data

• Forest Inventory and Analysis Data– Five-year increment– Eastern Washington

• Between lat 45.849o and 48.927o and long 117.096o and 121.941o

• 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

Stand Statistics

Table 1.

Variable § N Mean Std Dev Minimum Lower Quartile

Median Upper Quartile

Maximum

BA (ft2/ac) 48 96.89 60.52 3.98 56.83 87.69 123.11 310.92 SI

(ft. @ 50 yr) 48 92.81 23.43 54.00 76.50 89.50 109.00 155.00

MAIC (ft3/ac/yr)

48 67.36 31.01 25.89 46.97 59.41 82.47 176.97

TPA (no/ac) 48 120.19 89.01 7.18 56.75 90.65 161.87 426.11

QMD (in) 48 12.68 5.18 1.79 9.82 12.20 15.80 31.68

Volume (ft3/ac) 48 2570.88 2947.89 14.55 907.77 1600.61 3135.71 14684.44

Tree Statistics

Table 2.

Variable §

N Mean Std Dev

Minimum Lower Quartile

Median Upper Quartile

Maximum

D (in) 2231 0.54 0.44 -0.20 0.20 0.50 0.80 2.50 D (in) 2231 14.20 8.08 5.00 7.70 13.30 17.90 57.10

CR 2231 5.28 2.20 1.00 3.00 5.00 7.00 9.00 H (ft) 2231 75.30 30.84 12.00 51.00 74.00 93.00 199.00

Douglas-fir Statistics

Table 3.

Variable §

N Mean Std Dev Minimum Lower Quartile

Median Upper Quartile

Maximum

D (in) 994 0.66 0.44 -0.20 0.30 0.60 1.00 2.50 D (in) 994 15.23 8.78 5.00 8.10 14.00 18.70 57.10

CR 994 5.69 2.14 1.00 4.00 6.00 7.00 9.00 H (ft) 994 80.09 32.12 25.00 54.00 80.00 96.00 199.00

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

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 (oC), T denotes temperature sums, and P denote precipitation sums.

5

G1

10 X t

t

5

D1

10 X t

t

5

G1

Wt

t

5

D1

Wt

t

Variable name (units)

Calculation Mean Std Dev 5th Pctl

Median 95th Pctl

TG (oC x 10)3701.5 372.90 3055 3675 4377

TD (oC x 10)-194.7 419.54 -900 -275.5 511

PG (mm)1185.6 413.89 684 1090 1990

PD (mm)2953.6 1850.16 1218 2433 6963

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.

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.

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

First Study

IMPROVING MODELED PREDICTIONS

OF SHORT-TERM DOUGLAS-FIR DIAMETER GROWTH

IN EASTERN WASHINGTON, U.S.A.,

BY INCORPORATING LOCAL WEATHER INFORMATION

Revised ORGANON model

• Did not have SI for 30% of the stands

• Did have Mean Annual Increment at Culmination (ft3/ac2/yr). This is a function of SI. Used this instead of SI. (See Van Clay 1994).

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 • ai s represent equation coefficients to be fit with

least squares regression

250 1 2 3 4 6( )a a LGD a D a LGSI a LGCR a BALT a BAD e

ln 5

BAL

D

0.2ln

1.2

CR

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

250 1 2 3 4( )a a LGD a D a LGMAIC a LGCR a BAD e

Base Model Statistics

• R2 = 0.30886

• BIAS = 0.00412

• |BIAS| = 0.27674

• STD Resid = 0.36261

• SSE = 11.10882

Models with weather added

• Added weather to base model:

41 2 3( + + + ) WA

bTG b TD b PG b PDD D e

6 7 8[ PG/(PG+PD) + TD/(TG - TD)]WA

b b bD D e

Models with weather added

• Used above models with base model fixed

• Refit with all parameters allowed to vary

+6 7( PD/1000) WA

b bD D e

+ +6 7 8{ PG/(PG+PD) TD/(TG-TD)}WA

b b bD D e

6 7 8 9{ PG/(PG+PD) +b TD/(TG-TD) PG/(PG+PD)*TD/(TG-TD)}WAD D

b b be

Models with Base fixed

M2

M3

M4

Models fitted simultaneouslyM5

20 1 2 3 4 5 6 7( TD +c PD) c c LGD c D c LGMAIC c LGCR c BA c

D e

M62

0 1 2 3 4 5 6 7( [PG/(PG+PD)] +c [TD/(TG-TD)]) c c LGD c D c LGMAIC c LGCR c BA cD e

M72

0 1 2 3 4 5

6 7 8

( )

{ PG/(PG+PD) +c TD/(TG-TD) PG/(PG+PD)*TD/(TG-TD)}

c c LGD c D c LGMAIC c LGCR c BAD e

c ce

Model Comparison

Table 5. Fit statistics of the models.

Model R squared BIAS ABS (BIAS)

St Resid SSE

Base 0.30886 0.00412 0.27674 0.36261 11.10882

M2 0.33200 -0.000359 0.27240 0.35688 10.74019

M3 0.34137 -0.0010043 0.26814 0.35426 10.65519

M4 0.34249 -0.001259 0.26828 0.35406 10.63063

M5 0.33246 0.00953 0.26991 0.35686 10.51866

M6 0.34372 0.00047 0.26674 0.35349 10.45043

M7 0.35432 0.00395 0.26550 0.35055 10.29739

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

Discussion

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

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.

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.

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

Models developed2

50 1 2 3 4( )LGMAIa a LGD a D a a LGCR a BAD e

1 2 3 45 5 5 5D wa X X X XD TD PD TG PG

1 2 3 430 30 30 30D wa X X X XD TD PD TG PG

1 2 3 4D wa F F F FD ZTD ZPD ZTG ZPG

1 2 3 4D wa M M M MD ZTD ZPD ZTG ZPG

1 2 3 430 30 30 30D

M M M Mwa X X X XD TD PD TG PG

(1)

(2)

(3)

(4)

(5)

(6)

Results

Table 6. Parameter estimates for Models 2-6 and their standard errors.

1 2 3 4Model

Mean (Std Err) Mean (Std Err) Mean (Std Err) 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)

40.0089929(0.0003086)

-0.112175(0.0009094)

0.0692842(0.0004889)

0.0179885(0.0006876)

50.0411442(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)

Table 7. Fit statistics pertaining to Models 1-6.

ModelSSE Mean

ResidualResidual Std |Residual| r2 %

Biased

1 11.1088 0.00412 0.36261 0.27674 0.30886 0.62%

2 10.574 -0.0052 0.3525 0.26834  0.34657 - 0.78%

3 10.6608 -0.0064 0.35541 0.27304  0.33569 -0.96%

4 10.6446 0.00063 0.35735 0.27288  0.32867 0.10%

5 10.4891 -0.018 0.35478 0.27220  0.33819 -2.71%

6 10.6692 -0.0067 0.35558 0.27325  0.3351 -1.02%

Table 8. Ranks of each model, 1 through 6, by fit statistics.

Model

SSE Mean Residual

Residual Std

|Residual

|

r2 % Biased Sum of Ranks

1 6 2 6 6 6 3 29

2 2 3 1 1 1 2 10

3 4 4 3 4 3 4 22

4 3 1 5 3 5 1 18

5 1 6 2 2 2 6 19

6 5 5 4 5 4 5 28

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.

Third Study

CAN THE PARAMETER PREDICTION METHOD

IMPROVE DIAMETER PREDICTION WHEN USED

TO INCORPORATE WEATHER AND CLIMATE IN

AN EXISTING MODEL?

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.

Models Developed

(1)

3 5

25 5 5 50 1 2 4 6

85 5

7 9

ln ln ln ln100 100 100 100

ln ln100 100

b bX X X X

bX X

PD PD PD PGb b b LGD b D b LGMIAC

PD PGb LGCR b BA

wa eD

(2) 5 5 5 53 5 8

270 1 2 4 6 9

ln ln ln ln

100 100 100 100( )X X X X

b b bPD PD PD PD

wa

b b b LGD b D b LGMIAC b LGCR b BA

eD

Compared these to Best Models in Studies One and Two

(3)

20 1 2 3 4 5

6 75 5 5 5 5 5

8 5 5 5 5 5 5

( )

{ PG /(PG +PD ) +c TD /(TG -TD )

PG /(PG +PD )*TD /(TG -TD )}X X X X X X

X X X X X X

c c LGD c D c LGMAIC c LGCR c BAD e

c

ce

(4) 1 2 3 45 5 5 5D wa X X X XD d TD d PD d TG d PG

ResultsTable 9. Fit statistics for Eq. 1-4.

ModelSSE Mean

ResidualResidual

Std|Residual| r2 % Biased

Base 11.1088 0.00412 0.36261 0.27674 0.30886 0.62%

1 10.5332 0.00890 0.36135 0.27382 0.31623 1.34%

2 10.3243 0.00652 0.35415 0.26874 0.34198 0.98%

3 10.2974 0.00395 0.35055 0.26550 0.35432 0.81%

4 10.5740 -0.00520 0.3525 0.26834  0.34657 -0.78%

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.

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.

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

Limitations

• Only a small sample

• Only one dataset

• Only one species

• Limited geographic region

• Limited climatic variation

• Only a five-year interval

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.

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

Questions?