In the paper, we present a method for space-efficient representation of geometric tree models, which are provided as skeletons with radii attached to individual branch segments. The proposed approach uses a new differential 3D chain code to encode orientation changes of consecutive branch segments, which allows optimizing chain code generation for increased compressibility while maintaining control over the model reconstruction error. The presented method is the first to encode the complete branching geometry including the branch radii and provides level-of-detail construction directly from the chain code. It is demonstrated that by using interpolative encoding of the resulting tree descriptors and radii sequences, the storage requirements for geometric description of a mixed all-aged forest can be reduced to less than 15 percent of its raw size while preserving the structural fidelity of tree models.