<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def thickness_hydrostatic(pressure, temperature, **kwargs):
 r"""Calculate the thickness of a layer via the hypsometric equation. This thickness calculation uses the pressure and temperature profiles (and optionally mixing ratio) via the hypsometric equation with virtual temperature adjustment .. math:: Z_2 - Z_1 = -\frac{R_d}{g} \int_{p_1}^{p_2} T_v d\ln p, which is based off of Equation 3.24 in [Hobbs2006]_. This assumes a hydrostatic atmosphere. Layer bottom and depth specified in pressure. Parameters pressure : `pint.Quantity` Atmospheric pressure profile temperature : `pint.Quantity` Atmospheric temperature profile mixing : `pint.Quantity`, optional Profile of dimensionless mass mixing ratio. If none is given, virtual temperature is simply set to be the given temperature. molecular_weight_ratio : `pint.Quantity` or float, optional The ratio of the molecular weight of the constituent gas to that assumed for air. Defaults to the ratio for water vapor to dry air. (:math:`\epsilon\approx0.622`). bottom : `pint.Quantity`, optional The bottom of the layer in pressure. Defaults to the first observation. depth : `pint.Quantity`, optional The depth of the layer in hPa. Defaults to the full profile if bottom is not given, and 100 hPa if bottom is given. Returns ------- `pint.Quantity` The thickness of the layer in meters. See Also -------- thickness_hydrostatic_from_relative_humidity, pressure_to_height_std, virtual_temperature """

    mixing = kwargs.pop('mixing', None)
    molecular_weight_ratio = kwargs.pop('molecular_weight_ratio', mpconsts.epsilon)
    bottom = kwargs.pop('bottom', None)
    depth = kwargs.pop('depth', None)

    # Get the data for the layer, conditional upon bottom/depth being specified and mixing
    # ratio being given
    if bottom is None and depth is None:
        if mixing is None:
            layer_p, layer_virttemp = pressure, temperature
        else:
            layer_p = pressure
            layer_virttemp = virtual_temperature(temperature, mixing, molecular_weight_ratio)
    else:
        if mixing is None:
            layer_p, layer_virttemp = get_layer(pressure, temperature, bottom=bottom,
                                                depth=depth)
        else:
            layer_p, layer_temp, layer_w = get_layer(pressure, temperature, mixing,
                                                     bottom=bottom, depth=depth)
            layer_virttemp = virtual_temperature(layer_temp, layer_w, molecular_weight_ratio)

    # Take the integral (with unit handling) and return the result in meters
    return (- mpconsts.Rd / mpconsts.g * np.trapz(
        layer_virttemp.to('K'), x=np.log(layer_p / units.hPa)) * units.K).to('m')