Equations For Predicting Diameter, Height, Crown Width, and Leaf Area Of San Joaquin Valley Street Trees

Paula J. Peper; E. Gregory McPherson; Sylvia M. Mori

doi:10.48044/jauf.2001.034

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Figure 1.
Actual measurements (asterisks), predicted responses (solid line), and confidence intervals (dotted lines) for zelkova growing in Modesto, California. Equation (2), E(leaf area_i) = a*(e^b*dbh_i – 1) where E = expected value and a and b are parameters to be estimated, was used to model leaf area for 12 species. Equation (1), E(y_i) = a*[log(x_i + 1)]^b was used to predict all other dimensions.

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Table 1.

The range of years included in sample for each species along with the minimum and maximum ages are shown.

Common name	Min. age	Max. age	No. of years
Silver maple	5	67	62
Camphor tree	6	73	67
European ash	2	48	46
Ginkgo	8	35	27
Goldenrain tree	3	37	34
Crape myrtle	5	48	43
Sweetgum	15	39	24
Southern magnolia	8	49	41
Chinese pistache	4	36	32
London plane	4	89	85
Bradford pear	8	48	40
Zelkova	3	33	30

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Table 2.

Sample size, estimated regression coefficients, and mean standard error (MSE) values for predicting dbh from age, or tree height, crown diameter, or crown height from dbh, along with adjusted coefficients of determination for the modeling data set. Height, crown diameter, crown height, or dbh can be predicted by , where = the tree parameter to be estimated, EXP-the inverse of the natural logarithm, and x_i = age or dbh.

Species	Common name	n	Dbh vs. Age				Height vs. dbh				Crown diameter vs. dbh				Crown height vs. dbh
Species	Common name	n	Â	b	MSE	R²	Â	b	MSE	R²	Â	b	MSE	R²	Â	b	MSE	R²
Acer saccharinum	Silver maple	28	−0.365	3.502	0.21332	0.79	0.406	1.778	0.03789	0.90	−0.205	1.995	0.03091	0.93	−0.109	2.023	0.05484	0.88
Cinnamomum camphora	Camphor tree	30	0.385	2.723	0.11999	0.76	−0.165	1.959	0.05145	0.79	−1.150	2.615	0.02691	0.93	−1.207	2.513	0.08081	0.80
Fraxinus excelsior ‘Hessei’	European ash	27	0.995	2.072	0.15637	0.74	0.972	1.031	0.02168	0.79	−0.960	2.483	0.01828	0.96	0.725	0.991	0.05596	0.57
Ginkgo biloba	Ginkgo	31	−2.717	5.015	0.10769	0.83	0.534	1.465	0.03802	0.82	−0.471	1.989	0.03490	0.90	0.174	1.542	0.07857	0.71
Koelreutaria paniculata	Goldenrain tree	28	0.340	2.559	0.05686	0.94	0.461	1.454	0.02356	0.92	−0.232	1.873	0.02793	0.94	−0.262	1.719	0.10639	0.78
Lagerstroemia indica	Crapemyrtle	25	−0.160	2.249	0.15280	0.64	0.560	1.080	0.02942	0.72	−0.236	1.679	0.04358	0.81	−0.573	1.805	0.06868	0.76
Liquidambar styraciflua	Sweetgum	30	−0.720	3.509	0.07674	0.51	0.092	1.973	0.03924	0.55	−1.256	2.606	0.03890	0.68	−0.234	2.074	0.06311	0.45
Magnolia grandiflora	Southern magnolia	28	−0.010	2.609	0.09677	0.45	−0.553	2.280	0.03663	0.69	−0.609	2.095	0.03918	0.64	−1.402	2.733	0.06863	0.63
Pistacia chinensis	Chinese pistache	28	1.008	1.997	0.08051	0.71	0.033	1.898	0.03921	0.72	−0.237	2.081	0.02925	0.81	−0.541	2.078	0.10162	0.54
Platanus × acerifolia	London plane	27	1.941	1.441	0.10575	0.66	−0.090	2.066	0.04352	0.72	−0.569	2.286	0.03315	0.81	−0.569	2.245	0.04604	0.74
Pyrus catteryana ‘Bradford’	Bradford pear	29	1.396	1.719	0.12057	0.40	0.429	1.525	0.00488	0.90	−0.782	2.383	0.02399	0.81	−0.258	1.843	0.02628	0.69
Zelkova serrata	Zelkova	30	0.921	2.294	0.06311	0.85	0.222	1.676	0.02015	0.86	−0.438	2.259	0.02014	0.92	−0.784	2.218	0.03537	0.86

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Table 3.

The coefficient and mean standard error values (MSE) for predicting tree leaf area from dbh using Equation (2) for the modeling data set. Leaf area can be predicted by: , where LA = estimated leaf area and EXP = the inverse of the natural logarithm.

Common name	n	Leaf area vs. dbh
Common name	n	A	b	MSE	R²
Silver maple	27	5.465	0.017	0.14538	0.93
Camphor	28	3.482	0.046	0.21453	0.87
European ash	27	3.198	0.056	0.26392	0.88
Ginkgo	30	3.410	0.053	0.30207	0.86
Goldenrain tree	28	3.139	0.054	0.37021	0.87
Crape myrtle	25	2.634	0.073	0.55388	0.64
Sweetgum	30	4.547	0.034	0.22762	0.68
Southern magnolia	27	4.264	0.029	0.22067	0.66
Chinese pistache	24	3.421	0.065	0.13464	0.89
London plane	27	5.198	0.021	0.23508	0.74
Bradford pear	29	5.115	0.021	0.16544	0.71
Zelkova	30	4.033	0.045	.012706	0.91

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Table 4.

Predicted sizes for 12 species at 15 and 30 years after planting are shown sorted by fastest growth (dbh) in first 15 years after planting.

Common name	Dbh (cm)		Height (m)		Crown diameter (m)		Leaf area (m²)
Common name	15	30	15	30	15	30	15	30
London plane	38.11	48.17	13.97	15.51	11.48	12.89	262.22	353.87
Zelkova	37.89	53.38	11.36	12.85	12.64	14.91	297.44	589.15
Bradford pear	31.30	40.90	10.47	11.48	9.27	10.70	174.29	240.18
Silver maple	27.47	58.12	13.11	18.62	9.22	13.67	151.03	427.56
Chinese pistache	27.15	38.12	10.70	12.41	10.17	11.96	179.18	358.48
Camphor tree	26.60	46.05	9.12	12.21	7.38	10.90	86.67	264.01
European ash	24.19	39.12	9.18	10.27	7.54	9.89	93.92	220.47
Sweetgum	23.77	45.77	11.89	15.94	6.60	9.71	152.27	387.07
Goldenrain tree	21.87	37.15	8.77	10.50	7.17	9.04	72.43	175.21
Southern magnolia	18.98	30.19	7.55	9.80	5.80	7.38	65.83	113.87
Ginkgo	12.94	38.77	7.92	11.74	4.98	8.50	45.15	235.29
Crapemyrtle	10.44	16.24	4.79	5.50	3.77	4.68	23.41	41.76