The first is based on a compilation of delta sedimentation rates:
Zhang, P., Molnar, P.& Downs, W. R. Increased sedimentation rates and grain sizes 2–4 Myr ago due to the influence of climate change on erosion rates. Nature 410, 891–897 (2001).
The second uses thermochronology, mostly Apatite Fission Track analyses:
Herman F, Seward D, Valla PG, Carter A, Kohn B,Willett SD, Ehlers TA. 2014. Worldwide acceleration of mountain erosion under a cooling climate. Nature 504: 423–426. DOI: 10.1038/nature12877
Both interpret the acceleration of erosion as a result of the changes in Earth's climate during that period: initiation of the glacial interglacial cycle in the northern hemisphere.
Due to the gaps in the geological outcrop record, and to our limited capacity of dating sediments, my bet is that it will take decades at least to have a reliable graph like the one you aim at.
Hope this helps.