def calc_Ub(dO2dt, Uc, PQ =1):
    """
    Calculate HCO3- upatke rate
    Physiol. Plant, 90, 1994, Badger eat 1994, equation (5)
    similar to Hopkinson et al. 2011 PNAS, [S26] which has unit of mol/s
    here is to calculate the rate in µM/s(or similar), Ub_PNAS = Ub*Ve
    Parameters
    ----------
    dO2dt : float or 1-D array
        O2 evolution rate, µM/s or similar unit.
        the proxy of CO2 fixation rate
    Uc : float or 1-D array
        CO2 uptake rate.

    Returns
    -------
    Ub, HCO3- upatke rate.

    """
    Ub = dO2dt/PQ -Uc#using PQ =1 in accordance with earlier work
    return Ub