def ss_nonlinear_hilltop_curvature(C_0 = 0.001, D = 0.01, rho_ratio =2):
    """This returns the elevations along a transect using the analytical solutions of the hillslope equations. 
    From Roering et al 2007

    Args:
        C_0 (float): Steady uplift/erosion in m/yr
        D (float): sediment transport coefficient in m^2/yr
        rho_ratio (float): ratio between rock and soil density
        
    Returns:
        Curvature of the ridgetop at steady state

    Author:
        Simon M Mudd
        
    Date:
        14/05/2020  
    """    

    # This comes from the Roering et al. 2007 solution
    curv_analytical = -rho_ratio*C_0/D
    return curv_analytical