Skip to main content
SpringerLink
Log in

Application of Hierarchy Theory to Cross-Scale Hydrologic Modeling of Nutrient Loads

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

We describe a framework called Regional Hydrologic Modeling for Environmental Evaluation (RHyME2) for hydrologic modeling across scales. Rooted from hierarchy theory, RHyME2 acknowledges the rate-based hierarchical structure of hydrological systems. Operationally, hierarchical constraints are accounted for and explicitly described in models put together into RHyME2. We illustrate RHyME2with a two-module model to quantify annual nutrient loads in stream networks and watersheds at regional and subregional levels. High values of R2 (>0.95) and the Nash–Sutcliffe model efficiency coefficient (>0.85) and a systematic connection between the two modules show that the hierarchy theory-based RHyME2 framework can be used effectively for developing and connecting hydrologic models to analyze the dynamics of hydrologic systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. Bootstrap analysis involves resampling with replacement from among the original size-n dataset (e.g., the 81-point and 576-point datasets in steps (c) and (e)) to create samples with the same size n in all iterations (Davison and Hinkley 1997).

References

  • Alexander RB, Smith RA, Schwarz CA (2000) Effect of stream channel size on the delivery of nitrogen to the Gulf of Mexico. Nature 403:758–761

    Article  Google Scholar 

  • Alexander RB, Smith RA, Schwarz GE, Boyer EW, Nolan JV, Brakebill JW (2008) Differences in phosphorus and nitrogen delivery to the Gulf of Mexico from the Mississippi River Basin. Environ Sci Technol 42(3):822–830

    Article  Google Scholar 

  • Allen TFH, Starr TB (1982) Hierarchy: perspectives for ecological complexity. University of Chicago Press, Chicago

    Google Scholar 

  • Arnold JG, Williams JR, Nicks AD, Sammons NB (1990) SWRRB—A basin scale simulation model for soil and water resources management. Texas A&M University Press, College Station

    Google Scholar 

  • Aulenbach, BT, Buxton HT, Battaglin WA, Coupe RH (2007) Streamflow and nutrient fluxes of the Mississippi–Atchafalaya River Basin and sub–basins for the period of record through 2005, U.S. Geol. Surv. Open File Rep., 2007–1080

  • Basu NB et al (2010) Nutrient loads exported from managed catchments reveal emergent biogeochemical stationarity. Geophys Res Lett 37(L23404):1–5

    Google Scholar 

  • Beven K (1987) Towards a new paradigm in hydrology, Water for the Future: Hydrology in perspective (Proceedings of the Rome Symposium, April 1987). IAHS Publ. no.164

  • Beven K (2001) How far can we go in distributed hydrological modelling? Hydrol Earth Syst Sci 5(1):1–12

    Article  Google Scholar 

  • Beven K (2002) Towards an alternative blueprint for a physically based digitally simulated hydrologic response modeling system. Hydrol Process 16:189–206

    Article  Google Scholar 

  • Bicknell BR, Imhoff JC, Kittle JL Jr, Jobes TH, Donigian AS Jr (2001) Hydrological simulation program-Fortran, HSPF version 12 user’s manual. AQUA TERRA Consultants, Mountain View, 873p

    Google Scholar 

  • Blöschl G (2001) Scaling in hydrology. Hydrol Process 15:709–711

    Article  Google Scholar 

  • Caraco NF, Cole JJ, Likens GE, Lovett GM, Weathers KC (2003) Variation in NO3 export from flowing waters of vastly different sizes—Does one model fit all? Ecosystems 6:344–352

    Article  Google Scholar 

  • Daly C, Taylor G (1998) United States average monthly or annual precipitation, 1961–90. Spatial Climate Analysis Service at Oregon State University, Corvallis

    Google Scholar 

  • Davison AC, Hinkley D (1997) Bootstrap methods and their application. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge

    Google Scholar 

  • Gaddis EJB, Voinov A (2010) Spatially explicit modeling of land use specific Phosphorus transport pathways to improve TMDL load estimates and implementation planning. Water Resour Manag 24:1621–1644

    Article  Google Scholar 

  • García AM, Hoos AB, Terziotti S (2011) A regional modeling framework of phosphorus sources and transport in streams of the Southeastern United States. JAWRA J Am Water Resour Assoc. doi:10.1111/j.1752-1688.2010.00517.x

  • Gentine P, Troy TJ, Lintner BR, Findell KL (2012) Scaling in surface hydrology: progress and challenges. J Contemporary Water Res Education 147:28–40

    Article  Google Scholar 

  • Gibson CA, Meyer JL (2007) Nutrient uptake in a large urban river. J Am Water Resour Assoc 43(3):576–587

    Article  Google Scholar 

  • Goolsby DA, Battaglin WA (2001) Long-term changes in concentrations and flux of nitrogen in the Mississippi River basin, USA. Hydrol Process 15(7):1209–1226

    Article  Google Scholar 

  • Hoos AB, McMahon G (2009) Spatial analysis of instream nitrogen loads and factors controlling nitrogen delivery to streams in the southeastern United States using spatially referenced regression on watershed attributes (SPARROW) and regional classification frameworks. Hydrologic Processes. doi:10.1002/hyp.7323

  • Howarth et al (1996) Regional nitrogen budgets and riverine N and P fluxes for the drainages to the North Atlantic Ocean—natural and human influences. Biogeochemistry 35:75–139

    Article  Google Scholar 

  • MathWorks (2011), MatLab User Guide, Available at http://www.mathworks.com/help/techdoc/matlab_product_page.html

  • McMahon G, Alexander RB, Qian S (2003) Support of TMDL programs using spatially referenced regression models. ASCE J Water Resour Plann Manag 129:315–329

    Article  Google Scholar 

  • Moore RB, Johnston CM, Robinson KW, Deacon JR (2004) Estimation of total nitrogen and phosphorus in New England streams using spatially referenced regression models, U.S. Geological Survey Scientific Investigations Report 2004–5012, 50p

  • Mulholland PJ et al (2008) Stream denitrification across biomes and its response to anthropogenic nitrate loading. Nature 452:202–205

    Article  Google Scholar 

  • Mulholland PJ et al (2009) Nitrate removal in stream ecosystems measured by 15 N addition experiments: denitrification. Limnol Oceanogr 54(3):666–680

    Article  Google Scholar 

  • Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I — A discussion of principles. J Hydrol 10(3):282–290

    Article  Google Scholar 

  • O’Neill RV, DeAngelis DL, Waide JB, Allen TFH (1986) A hierarchical concept of ecosystems. Princeton University Press, Princeton

    Google Scholar 

  • Overton WS (1974) Decomposability: a unifying concept? In: Levin SA (ed) Ecosystem analysis and prediction. SIAM, Philadelphia, pp 297–298

    Google Scholar 

  • Perveen S, James LA (2010) Multiscale effects on spatial variability metrics in global water resources data. Water Resour Manag 24:1903–1924

    Article  Google Scholar 

  • Preston SD, Brakebill JW (1999) Application of spatially referenced regression modeling for the evaluation of total nitrogen loading in the Chesapeake Bay watershed. U.S. Geological Survey Water-Resources Investigations Report 99–4054, 12p

  • Ruddy BC, Lorenz DL, Mueller DK (2006) County-Level Estimates of Nutrient Inputs to the Land Surface of the Conterminous United States, 1982–2001. U.S. Geological Survey Scientific Investigations Report 2006–5012, 17 p

  • Schwarz GE, Hoos AB, Alexander RB, Smith RA (2006) The SPARROW surface water-quality model: Theory, application and user documentation, U.S. Geological Survey Techniques and Methods Report, Book 6, Chapter B3, 2006

  • Simon HA (1962) The architecture of complexity. Proc Am Philos Soc 106:467–482

    Google Scholar 

  • Simon HA (1969) The sciences of the artificial. MIT Press, Cambridge

    Google Scholar 

  • Simon HA (1973) The organization of complex systems. In: Pattee HH (ed) Hierarchy theory. Braziller, New York, pp 3–27

    Google Scholar 

  • Smith RA, Schwarz GE, Alexander RB (1997) Regional interpretation of water-quality monitoring data. Water Resour Res 33(12):2781–2798

    Article  Google Scholar 

  • Thampi SG, Raneesh KY, Surya TV (2010) Influence of scale on SWAT model calibration for streamflow in a river basin in the humid tropics. Water Resour Manag 24:4567–4578

    Article  Google Scholar 

  • USEPA and USGS (2006) National Hydrography Dataset Plus (NHDPlus). Available at http://www.horizon-systems.com/nhdplus/

  • Vogelmann JE et al (2001) Completion of the 1990’s national land cover data set for the conterminous United States. Photogramm Eng Remote Sens 67:650–662

    Google Scholar 

  • Xu CY, Singh VP (2004) Review on regional water resources assessment models under stationary and changing climate. Water Resour Manag 18:591–612

    Article  Google Scholar 

  • Yevjevic V (1991) Tendencies in hydrology research and its applications for 21st century. Water Resour Manag 5:1–23

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geography, University of Tennessee, 1000 Phillip Fulmer Way, Knoxville, TN, 37996-0925, USA

    Liem T. Tran & Carol Harden

  2. Oneida Total Integrated Enterprises (OTIE), Oak Ridge, TN, 37830, USA

    Robert V. O’Neill

  3. U.S. Environmental Protection Agency, Office of Research and Development, National Exposure Research Laboratory, Research Triangle Park, NC, 27711, USA

    Elizabeth R. Smith

  4. U.S. Environmental Protection Agency, Ecological Exposure Research Division, National Exposure Research Laboratory, Cincinnati, OH, 45268, USA

    Randall J. F. Bruins

Authors
  1. Liem T. Tran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert V. O’Neill
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elizabeth R. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Randall J. F. Bruins
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Carol Harden
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liem T. Tran.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tran, L.T., O’Neill, R.V., Smith, E.R. et al. Application of Hierarchy Theory to Cross-Scale Hydrologic Modeling of Nutrient Loads. Water Resour Manage 27, 1601–1617 (2013). https://doi.org/10.1007/s11269-013-0260-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11269-013-0260-0

Keywords

Search

Navigation