A multiple regression model to estimate the suspended sediment yield in Italian Apennine rivers by means of geomorphometric parameters


A new statistical prediction model, aimed to assess the mean annual suspended sediment yield (SY) in ungauged rivers of Italian Apennines, is here presented. A multiple linear regression equation was obtained by the stepwise technique investigating the relationships between a series of hydro-geomorphometric variables and sediment yield data from 41 river basins located along peninsular Italy and Sicily. The model variables were computed from hydrological data records and from vector river network lines and drainage divides derived from official maps and DEM. The analysis revealed a large variance in the observed sediment yield data. Nonetheless, an optimal result in terms of model significance and efficiency (r2adj = 0.91 at p < 0.05 significance level; Nash–Sutcliffe model efficiency NSE = 0.855; Willmott’s indexes of performance: d = 0.965; d1 = 0.862; dr = 0.862) was finally achieved. According to stepwise regression, the catchment relief and perimeter, together with the topological organization of stream network, the bedrock erodibility and the stream gradient, expressed by specific parameters, appeared as determinant features for SY prediction in the catchments here investigated. The developed model could be helpful to practitioners and scholars for rapid assessments of SY at any point of the river network in the geographic area here concerned. However, the same technique can be utilized wherever in the world since the statistical method itself allows to recognize the number and type of parameters to be used in a given geographic area, on the basis of their local significance.

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Data availability

All the basic data (ancillary data and cartographic sources) were downloaded from public web repositories cited in the paper.

Code availability

The SSPS® Statistics software package v.25 is commercially available; the QMorphoStream toolset consists of vector and raster tools available on the QGis open-source platform.


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The authors thank the European Soil Data Centre (ESDAC), European Commission Joint Research Centre, for making available the soil loss data.


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Author information




S.G. and F.P. conceived the study, contributed to writing and original draft preparation, and reviewed and edited the manuscript. S.G. performed the methodology, done the formal analysis and supervised the study. C.T. and M.G. contributed to resources. C.T. contributed to software.

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Correspondence to Sergio Grauso.

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List of geomorphometric parameters used for the present study. For a complete description, see references in brackets

  1. (1)

    Pm (km): basin perimeter

  2. (2)

    A (km2): basin area

  3. (3)

    Hmax (m): basin maximum elevation

  4. (4)

    Hmin (m): basin minimum elevation

  5. (5)

    Hmean (m): basin mean elevation

  6. (6)

    Hr (m): basin elevation range

  7. (7)

    Le (km): Euclidean distance between the outlet point and the farthest point on the watershed (Tebano et al. 2017)

  8. (8)

    Lnet (km): distance between the outlet point and the main river source point (Tebano et al. 2017)

  9. (9)

    θm (deg): mean slope steepness (computed in 20 × 20 m DEM by GIS tools)

  10. (10)

    SsO: stream slope weighted mean by hierarchic order (Grauso et al. 2018a)

  11. (11)

    SsN: stream slope weighted mean by frequency (Grauso et al. 2018a)

  12. (12)

    SSave: average stream slope (Grauso et al. 2018a)

  13. (13)

    SSup: mean up-valley stream slope (Grauso et al. 2018a)

  14. (14)

    ∆Ss: differential (down-valley/up-valley) stream channel slope (Grauso et al. 2018a)

  15. (15)

    Rbarit: arithmetic average of bifurcation ratios (Horton 1932, 1945; Strahler 1952a, b, 1957)

  16. (16)

    Rbdarit: arithmetic average of direct bifurcation ratios (Horton 1932, 1945; Strahler 1952a, b, 1957)

  17. (17)

    Rarit: arithmetic average of bifurcation indexes (Horton 1932, 1945; Strahler 1952a, b, 1957)

  18. (18)

    Rbpon: weighted average of bifurcation ratios (Horton 1932, 1945; Strahler 1952a, b, 1957)

  19. (19)

    Rbdpon: weighted average of direct bifurcation ratios (Horton 1932, 1945; Strahler 1952a, b, 1957)

  20. (20)

    Rpon: weighted average of bifurcation indexes (Horton 1932, 1945; Strahler 1952a, b, 1957)

  21. (21)

    Na: number of hierarchical (Avena et al. 1967)

  22. (22)

    Ia: index of hierarchical anomaly (Avena et al. 1967)

  23. (23)

    Da (km−2): density of hierarchical anomaly (Avena et al. 1967)

  24. (24)

    Ltot (km): total length of stream network

  25. (25)

    Fs (km−2): stream frequency (Horton 1932, 1945)

  26. (26)

    Dd (km−1): drainage density (Horton 1932, 1945)

  27. (27)

    MoDd: modified drainage density (Grauso et al. 2008)

  28. (28)

    Hf: Fournier’s orographic coefficient (Fournier 1960b)

  29. (29)

    Hy: hypsometric integral (Strahler 1952b)

  30. (30)

    Rc: circularity ratio (Strahler 1964)

  31. (31)

    Rh: relief ratio (Schumm 1956; Strahler 1952b)

  32. (32)

    Re: elongation ratio (Schumm 1956)

  33. (33)

    SCI: Simplified Connectivity Index (Grauso et al. 2018a)

  34. (34)

    SSP (Mg*ha*y−1): sediment supply potential (Grauso et al. 2018a)

  35. (35)

    Lem: index of bedrock erodibility (Grauso et al. 2018a)

  36. (36)

    Ptot (mm): average yearly total rainfall

  37. (37)

    Pdepth (mm): overland rainfall depth (depth of water layer with volume equal to the catchment rainfall amount in a time interval)

  38. (38)

    Qdepth (mm): overland flow (depth of water layer with volume equal to the water flown at the catchment outlet in a time interval)

  39. (39)

    Cr: run-off coefficient (Qdepth/Pdepth)

  40. (40)

    Ptot × σ (mm2): average yearly rainfall amount multiplied by its standard deviation

  41. (41)

    R (MJ*mm*ha−1*h−1*year−1): average yearly rainfall erosivity (Diodato 2004)

  42. (42)

    R × σ (MJ*mm*ha−1*h−1*year−1)2: average yearly rainfall erosivity multiplied by its standard deviation

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Grauso, S., Pasanisi, F., Tebano, C. et al. A multiple regression model to estimate the suspended sediment yield in Italian Apennine rivers by means of geomorphometric parameters. Model. Earth Syst. Environ. 7, 363–371 (2021). https://doi.org/10.1007/s40808-020-01077-1

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  • River sediment yield
  • Geomorphometric analysis
  • Linear regression
  • Apennines
  • Italy