We evaulate the impact of measurement error on three components of a forest planning model: initial inventory, first period harvest and silvicultural activities chosen. Calculated initial inventory was off by as much as 15%, and significantly different objective function values and activity schedule also resulted.

1. Error Propagation in Forest Planning Models Karl R. Walters and Sean J. Canavan

6. Normal (0,1) PDF x 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -5 -4 -3 -2 -1 0 1 2 3 4 5 f(x)

7. Normal (O,1) CDF x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 F(x) = P(X < x)

10. Normal (O,1) CDF x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 F(x) = P(X < x)

11. Fitted CDF Equation 0.00 0.20 0.40 0.60 0.80 1.00 -1.5 -1 -0.5 0 0.5 1 1.5 Error Size Cumulative Probability  Pr(  = 0)  Pr(  < 0)  Pr(  > 0) P(X = x ) = Pr(  < 0)*Negative Error CDF  < 0 Pr(  < 0) + Pr(  = 0)  = 0 Pr(  < 0) + Pr(  = 0) + Pr(  > 0)*Positive Error CDF  > 0

12. Fits of Error Type Probabilities 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0.5 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 Dbh (inches) Probability P(e > 0) P(e = 0) P(e < 0)

13. Empirical Dbh Error CDF Surface Cumulative Probability Dbh (inches) Error (inches) 0.25 0.50 0.75 1.00 0.0 20.0 30.0 40.0 -0.6 0.0 0.6 1.2 1.8 10.0

14. Fitted Dbh CDF Surface

21. Unconstrained 4,838,760 5,142,948 4,925,347 5,180,696 Total Harvest 33,076 32,206 33,355 28,352 HW saw logs 4,403 4,275 4,428 4,333 RC saw logs 18,073 16,731 47,399 16,736 WW oversize logs 591,469 613,119 615,886 606,089 WW saw logs 224,367 220,707 232,815 221,610 DF oversize logs 3,467,413 3,756,908 3,480,189 3,795,724 DF saw logs 499,959 499,000 511,276 507,851 DF export logs Dbh_Ht Err Ht_Err Dbh_Err Clean 50 Year Summary

23. Unconstrained 36,766 36,144 36,423 35,213 commercial thin 49 19 49 - precomm thin 537tpa 36 - 19 266 precomm thin 436tpa - - - - precomm thin 360tpa - - - - precomm thin 300tpa 18,142 18,142 18,142 17,039 slashing - - - - planted NF 680tpa 5,656 5,656 5,656 5,108 planted NF 550tpa 19,381 20,504 19,381 30,342 planted DF 550tpa 30,912 29,820 30,850 19,586 planted DF 450tpa 55,948 55,980 55,886 55,036 clearcut Dbh_Ht Err Ht_Err Dbh_Err Clean 50 Year Summary

27. Nondeclining Yield 3,498,616 3,624,749 3,561,097 3,654,132 Total Harvest 35,169 33,695 34,992 33,844 HW saw logs 5,815 5,767 6,181 6,099 RC saw logs 27,815 27,137 57,946 27,880 WW oversize logs 798,669 803,591 819,808 824,113 WW saw logs 351,540 316,824 352,489 322,816 DF oversize logs 1,636,676 1,764,109 1,631,819 1,761,552 DF saw logs 642,932 673,628 657,862 677,828 DF export logs Dbh_Ht Err Ht_Err Dbh_Err Clean 50 Year Summary

29. Nondeclining Yield 22,493 21,884 21,600 21,368 commercial thin 228 19 1941 - precomm thin 537tpa 537 - 367 266 precomm thin 436tpa 161 256 - 716 precomm thin 360tpa 74 56 105 56 precomm thin 300tpa 18,142 17,094 17,145 17,094 slashing - - - - planted NF 680tpa 5,019 5,019 5,019 5,019 planted NF 550tpa 18,704 21,878 16,636 20,809 planted DF 550tpa 21,085 17,931 23,117 18,978 planted DF 450tpa 44,808 44,828 44,772 44,806 clearcut Dbh_Ht Err Ht_Err Dbh_Err Clean 50 Year Summary

34. Thank you. Any questions?