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ForestERA Data Layer Detail - Quadratic Mean Diameter (in centimeters)

Note to data users: Please carefully review the metadata provided with each layer. We request that users consult with the ForestERA project in advance of using these data in publications and/or presentations to ensure that the strengths and limitations of the data are considered.

Description

Quadratic mean diameter (hereafter QMD) is a measure used by foresters as an index of the size of trees in a stand. This layer is provided in units of centimeters and has a resolution of 90m (0.8 ha or 2 acres).

Purpose

This data layer was created as part of the ForestERA project to support landscape-scale forest restoration planning efforts by a broad group of stakeholders including federal and state agencies, academic institutions, and non-governmental entities. These data are intended for regional analyses over spatial extents on the order of tens to hundreds of thousands of acres, and were not developed for use at finer spatial scales, although they may be useful for some applications at finer scales.

Development

This layer was created using the basal area and tree density layers created by the ForestERA team. To produce the QMD layer from those two layers, the following steps were used;

1: multiply basal area (BA) (m2 / ha) by 10,000 to get basal area (cm2 / ha)

2: divide the result by tree density (TD) to get mean basal area per tree

3: divide basal area per tree by pi (3.14157) to get the mean of the square of the radius of trees

4: take the square root to determine the mean radius of trees

5: multiply by two to get QMD of all trees

The resulting formula appears as follows:

QMD = 2 * ((BA * 10,000) / TD) / ?)-2

In the case of our data, the resultant map of QMD did not have any unrealistically high values. However, the user should note that certain combinations of tree density and basal area, particularly in spots where one or both of these layers have errors, could result in extremely high QMD values for a few pixels on their map. We recommend using a maximum QMD value that is representative of the maximum likely QMD in the user’s area and reducing any unusually high values to this maximum value.

Accuracy Assessment

An external accuracy assessment was performed on the QMD layer using linear regression and 567 points of ground data collected by our field crew at 63 locations scattered across the study area. At each of these locations, groups of 9 plots were placed in a 3x3 grid pattern with plots 30m apart, approximating coverage of a 3x3 area of 30m pixels. The locations for taking this external dataset were determined using a “restricted stratified random sampling” scheme carefully designed by the research group. According to this protocol, we divided total basal area and total tree density into four categories each based on the predictive maps. We then created a set of sampling categories based on overlap between the four categories in each layer. Although 16 combinations were possible, only 9 actually occurred over significant portions of the landscape. Within these nine categories we randomly located 80 sampling locations, with number of locations in a given category determined by the proportion of the landscape occupied by that category. A threshold value of 1 km was set as the minimum distance between two samples within a category based on analysis of spatial autocorrelation of forest structure. In total we were able to obtain complete georeferenced data at 63 locations, with a minimum of 5 samples per category. Thus, though the ground dataset is not huge, it was broadly representative of the range of forest structure across the study area.

Linear regression was used to determine the relationships between the QMD values obtained from the ground data and the QMD estimates based on the procedure above. As the two measures of QMD are expected to be equal we used the best-fit line of a regression with intercept constrained to zero. The use of this line results in a lower r² value than that obtained from using the overall best-fit line. However, analysis of the slope of the line with intercept constrained to zero allows for detection of bias in the predictive dataset. Under conditions of no bias, the slope of this line should be equal to one.

An external accuracy assessment of the QMD layer at 30m resolution gave very poor results (r² < 0.1). This is due, in part, to imperfect co-registration between the ground data and the pixels in the predictive layer. Nevertheless, we did not feel that this result was good enough to allow use of the layer at 30m resolution. As lowering the resolution of a predictive map often reduces the co-registration error significantly, we took the mean value for the 9 ground plots at each of the sites where we collected data, and the mean value for the associated 9 pixels in the predictive layer for analysis. We then compared QMD values from the 63 ground data collection sites with the values from associated 90m cells in the predictive model. The results of this regression analysis indicated that a significant relationship exists between the two measures (Fig. 1; r² = 0.259, P < 0.001). The slope of the line from this relationship is 1.09 indicating that the ETM derived QMD estimate is nearly unbiased with relation to the ground estimate. However, the relatively low r² value indicates that there is not a particularly strong relationship between the predicted QMD and the actual QMD, even though strong relationships existed between the predicted basal area and tree density layers and actual basal area and tree densities on the ground.

Sources of errors

The poor accuracy of this layer appears to be the result of covariance between the basal area and tree density layers. Areas with very high values for basal area tend to have high values for tree density while areas with very low values for basal area also tend to have low values for tree density. In addition, predicted tree densities that diverge from the actual value tend to result in values of QMD that have proportionally more divergence from the actual value. Thus, the result of the covariance between basal area and tree density is compression of the predicted range of values for QMD. Predicted values of QMD tend to fall between 15cm and 35cm instead of ranging from 0 to over 50cm. Areas with very low actual values of QMD tend to have somewhat higher predicted values for QMD, while areas with very high values of QMD tend to have somewhat lower predicted values for QMD. While areas with low actual QMD values tend to have low predicted QMD values (< 25cm) and areas with high actual QMD values tend to have higher predicted QMD values (> 25cm), the actual QMD value for any given area is not well predicted.

Recommendations: We are using this layer in a limited fashion to create crown base height and stand height layers for fire modeling. However, this layer has low accuracy and many assumptions must be taken into consideration when it is used. We do not recommend its use for most modeling purposes, especially predicting tree sizes across the landscape in anything other than very general terms. We recommend that this layer be used at a minimum resolution of 90m (0.8 ha or 2 acres) for purposes of analysis and display. However, ForestERA data layers were not designed for analyses at the level of individual pixels, and uncertainty in the data will generally decline over greater spatial extents. Therefore, we recommend using larger analysis units, with groupings of at least 50 cells (40 ha or 100 acres). Finally, we reiterate that ForestERA data layers were developed for the purpose of regional landscape-level planning, and we suggest that the analyses be applied over spatial extents of tens to hundreds of thousands of acres. We recognize, however, that this layer may be useful for analyses over smaller spatial extents depending on the type and purpose of those analyses.

References

Davis, L. S. and K. N. Johnson. 1987. Forest Management, 3rd Edition. McGraw-Hill Publishing Company, New York.

Page last updated February 23, 2005