Based on your observations, infer the depositional environments, erosional history, and paleoclimates that have existed in the Little Badlands from the time of the deposition of the oldest stratigraphic unit to the deposition of the Quaternary colluvium.  You need to discuss evidence for changes in:
1.      Depositional environments
2.      Provenance (source) of the sediments
3.      Flow velocities
4.      Climate
Support your discussion with:
1.      Reference to previous studies
2.      The stratigraphy represented in your geological map, cross-section and composite stratigraphic section
3.      Rose diagrams of cross-bedding and pebble imbrication
4.      Pebble analyses
5.      Comparison with conceptual models of facies and flow diagrams
6.      Photographs of stratigraphic relationships, facies and sedimentary structures
Possible references to consult [main emphasis shown in parenthesis]
Berggren, W. A. and Prothero, D. P. 1992. Eocene-Oligocene climatic and biotic evolution: an overview. In: Prothero, D.P. and Berggren, W. A. (eds.), Eocene-Oligocene Climatic and Biotic Evolution, pp.1-28, Princeton University Press [Global view of mid-Tertiary climate change and evolution].
Clark, J., Beerbower, J.R., and Kietzke, K.K. 1967. Oligocene sedimentation, stratigraphy, paleoecology and paleoclimatology in the Big Badlands of South Dakota. Fieldiana: Geology Memoirs 5, pp 1-158 [White River Group].
Clechenko, E.R., Kelly, D.C., Harrington, G.J., and Stiles, C.A., 2007. Paleocene-Eocene boundary in the Williston Basin of North Dakota: Geological Society of America Bulletin, v. 119, no. 3/4, p.428-442. [Golden Valley Formation]
Denson, N. M., and Gill, J. R., 1956, Uranium-bearing lignite and its relation to volcanic tuffs in eastern Montana and North and South Dakota. U.S. Geological Survey Prof. Paper 300, p.413-418. (Stratigraphy, map [fig. 140]) [Chadron Formation]
Evanoff, E., Prothero, D.R., and Lander, R.H. Eocene-Oligocene climatic change in North America: the White River Formation near Douglas, east-central Wyoming. In: Prothero, D.P. and Berggren, W. A. (eds.), Eocene-Oligocene Climatic and Biotic Evolution, pp.116- 130, Princeton University Press [Mid-Tertiary Climate in the Great Plains].
Hickey, L. J. 1972. Stratigraphic summary of the Golden Valley Formation (Paleocene-Eocene) of western North Dakota. In: Ting, F.T.C., ed. Depositional environments of the lignite-bearing strata in western North Dakota, pp. 105-122. NDGS Misc. Ser. No. 50 [Summary of the Golden Valley Formation].
Hickey, L. 1977. Stratigraphy and paleobotany of the Golden Valley (Early Tertiary) of western North Dakota. Geol. Soc. Amer. Mem.150, 183 p. [Golden Valley Formation]
Hoganson, J.W., Murphy, E.C., and Forsman, N.F. 1998. Lithostratigraphy, paleontology, and biochronology of the Chadron, Brule, and Arikaree Formations in North Dakota. in D.O. Terry, Jr., H.E. LaGarry, and R.M. Hunt, Eds. Depositional Environments, Lithostratigraphy, and Biostratigraphy of the White River and Arikaree Groups (Late Eocene to Early Miocene, North America): Geological Society of America Special Paper 325, p. 185-196. [Chadron, Brule and Arikaree Formations; White River Group]
Murphy, E. C., 2009. The Golden Valley Formation. ND Dept of Mineral Resources GeoNews, v. 36, no. 2, p. 1-4. [Golden Valley Formation]
Murphy, E. C., Hoganson, J. W., and Forsman, N. F. 1993. The Chadron, Brule, and Arikaree Formations in North Dakota. NDGS Report of Investigation No. 96, 144 p. [Chadron, Brule and Arikaree Formations; White River Group]
Retallack, G. J., 1983. A paleopedological approach to the interpretation of terrestrial sedimentary rocks: the mid-Tertiary fossil soils of Badlands Nation Park, South Dakota. Geol. Soc. of America Bulletin, v.94, p.823-840. [Brule Formation]
Seeland, D. 1985. Oligocene paleogeography of the northern Great Plains and adjacent mountains. In: Flores, R.M. and Kaplan, S.S. eds. Cenozoic Paleogeography of the west-central United States, pp. 187-205. SEPM Rocky Mountain Section [White River Group].
Stone, W. J. 1972. Middle Cenozoic Stratigraphy of North dakota. In: Ting, F.T.C., ed. Depositional environments of the lignite-bearing strata in western North Dakota, pp. 123-132. NDGS Misc. Ser. No. 50. [White River Group in North Dakota].
Stone, W. J. 1973. Stratigraphy and sedimentary history of Middle Cenozoic (Oligocene and Miocene) deposits in North Dakota. Ph.D. Thesis, University of North Dakota, 216 p [White River].
Stucky, R. K. Mammalian faunas in North America of Bridgerian to early Arikareean "Ages" (Eocene and Oligocene). in: Prothero, D.P. and Berggren, W. A., Eds., Eocene-Oligocene Climatic and Biotic Evolution, pp. 464-493, Princeton University Press [White River Group].
Some questions you might try to answer from the features associated with the different formations that would be useful to include in your discussion:
Golden Valley Formation
Where would different facies have been deposited with respect to fluvial system models? What can you infer about the paleoenvironment from fossils, silicified peat, fossil wood in silicified sandstone channel quartzites', root casts in iron concretions, convolute bedding, flame stuctures?
What does the mineralogy of the Golden Valley sandstones tell you about source area?
What does the iron staining tell you about paleoclimate?
What is the direction of flow based on a rose diagram plot of cross beds? Does the direction also help to delineate a source area for the sediments?
Chalky Buttes Member
What do the facies tell you about depositional environments?
What can you infer about provenance from the different lithologies (type or types of terrain and proximity)? What can you determine about flow velocities from grain size? How do they compare to the flow velocities of the Golden Valley Fm.? What can you determine about direction of flow from pebble imbrication and from the orientation of channel deposits? What can you tell about the source area and proximity from the mineralogy of the Chalky Buttes Member?
South Heart Member
What can you infer about the South Heart Member sediments from their lithology and mineralogy (aragonite, barite, uranium-bearing minerals, silicified silty bentonite)? Why is the South Heart Member so mineral-rich?
Brule Formation
What can you infer about sedimentary environments from facies and fossils (tortoises, oreodonts and other mammals)? What significance is the caliche? What is the source of the carbonate?
Quaternary deposits
What is the origin of the various types of Quaternary deposits and their fossils (alluvium, colluvium, loess, bison)?