improver.psychrometric_calculations.hail_size module

module to calculate hail_size

class HailSize(model_id_attr=None)

Bases: BasePlugin

Plugin to calculate the diameter of the hail stones from input cubes cloud condensation level (ccl) temperature, cloud condensation level pressure, temperature on pressure levels, the height of the wet bulb freezing level above sea level and orography.

From these, the values for three other cubes are calculated:

• Temperature of the environment at 268.15K (-5 Celsius) and the pressure level where this occurs.

• Temperature after a saturated ascent from ccl pressure to the pressure of the environment at 268.15K (-5 Celsius).

• Temperature after a dry adiabatic descent from the pressure of the environment at 268.15K (-5 Celsius) to the ccl pressure.

From these, two indexes are calculated as:

• Temperature after a dry adiabatic descent - the temperature of the atmosphere at 268.15K

• Temperature after a saturated ascent - the temperature of the atmosphere at 268.15K

These indexes can then be used to extract values of hail size depending on the wet bulb freezing altitude. The wet bulb freezing altitude is calculated by subtracting the orography from the wet bulb freezing altitude above sea level.

If the wet bulb freezing altitude is between 3350m and 4400m then the indexes are used to extract an initial hail value from the first table. A second table is then accessed to reduce the hail size. The second table is stored as a dictionary, with the key being the wet bulb freezing altitude and each column in the associated arrays referring to the previously calculated hail diameter being less than a pre-defined value. An updated hail_size is then extracted and stored.

If the wet_bulb_freezing_altitude is greater than 4400m then the hail size is set to 0 and if the wet bulb_freezing_altitude is less than 3350m then the originally calculated hail size is not altered.

Both tables are taken from Hand and Cappelluti (2011) which are a tabular versions of the graphs from Fawbush and Miller(1953)

References

• Hand, W., and G. Cappelluti. 2011. “A global hail climatology using the UK Met Office convection diagnosis procedure (CDP) and model analyses.” Meteorological Applications 18: 446-458. doi:https://doi.org/10.1002/met.236

• Fawbush, E.J., and R.C. Miller. 1953. “A method for forecasting hailstone size at the earth’s surface.” Bulletin of the American Meteorological Society 34: 235-244. doi: https://doi.org/10.1175/1520-0477-34.6.235

__init__(model_id_attr=None)

Sets up Class :type model_id_attr: Optional[str] :param model_id_attr: Name of model ID attribute to be copied from source cubes to output cube

_abc_impl = <_abc_data object>

check_cubes(ccl_temperature, ccl_pressure, temperature_on_pressure, wet_bulb_zero_asl, orography)

Checks the size and units of input cubes and enforces the standard coord order

Parameters:

• ccl_temperature (Cube) – Cube of cloud condensation level temperature

• ccl_pressure (Cube) – Cube of cloud condensation level pressure

• temperature_on_pressure (Cube) – Cube of environment temperature on pressure levels

• wet_bulb_zero_asl (Cube) – Cube of the height of the wet bulb freezing level above sea level

• orography (Cube) – Cube of the orography height.

Return type:

None

static dry_adiabatic_descent_to_ccl(ccl_pressure, temperature_at_268, pressure_at_268)

Calculates the temperature due to a dry adiabatic descent from the pressure of the environment at 268.15K to the cloud condensation level pressure.

Parameters:

• ccl_pressure (Cube) – Cube of cloud condensation level pressure

• temperature_at_268 (Cube) – Cube of the temperature of the environment at 268.15K

• pressure_at_268 (Cube) – Cube of the pressure of the environment at 268.15K

Return type:

ndarray

Returns:

Cube of temperature after the dry adiabatic descent

get_hail_size(vertical, horizontal, wet_bulb_zero)

Uses the lookup_table and the vertical and horizontal indexes calculated to extract and store values from the lookup nomogram.

The hail size will be set to 0 if

1. there are masked data points,

2. vertical or horizontal values are negative,

3. the wet bulb freezing altitude is greater that 4400m.

If the wet bulb freezing altitude is greater that 3300m then the hail_size is reduced.

Parameters:

• vertical (ndarray) – An n dimensional array containing the values used to calculate the vertical indexes

• horizontal (ndarray) – An n dimensional array containing the values used to calculate the horizontal indexes

• wet_bulb_zero (ndarray) – An n dimensional array containing the height of the wet bulb freezing level

Return type:

ndarray

Returns:

an n dimension array of values for the diameter of hail (mm)

hail_size_data(temperature_at_268, pressure_at_268, ccl_pressure, ccl_temperature, humidity_mixing_ratio_at_ccl, wet_bulb_zero)

Gets temperature of environment at 268.15K, temperature after a dry adiabatic descent from the pressure of air at 268.15K to ccl pressure and the temperature after a saturated ascent from ccl pressure to the pressure of air at 268.15K. From these values it calculates vertical and horizontal indices. It also masks data where the ccl_temperature is below 268.15K.

Parameters:

• temperature_at_268 (Cube) – Cube of the temperature of the environment at 268.15K

• pressure_at_268 (Cube) – Cube of the pressure of the environment at 268.15K

• ccl_pressure (Cube) – Cube of cloud condensation level pressure

• ccl_temperature (Cube) – Cube of cloud condensation level pressure

• humidity_mixing_ratio_at_ccl (array) – Array of humidity mixing ratio at the pressure of the environment at the CCL

• wet_bulb_zero (Cube) – Cube of the height of the wet-bulb freezing level

Return type:

ndarray

Returns:

An n dimensional array of diameter of hail stones (m)

static make_hail_cube(hail_size, ccl_temperature, ccl_pressure, attributes)

Puts the hail data into a cube with appropriate metadata

Parameters:

• hail_size (ndarray) – An n dimensional array of the diameter of hail stones (m)

• ccl_temperature (Cube) – Cube of cloud condensation level pressure

• ccl_pressure (Cube) – Cube of cloud condensation level pressure

• attributes (dict) – Dictionary of attributes for the new cube

Return type:

Cube

Returns:

A cube of the diameter of hail stones (m)

static nomogram_values()

Sets-up an array of a table containing possible diameter of hail stones(mm). It is a transposed version of the table in Hand and Cappelluti (2011).

The axes of the table are as follows: :rtype: ndarray

• Horizontal axis is calculated from two values: the temperature after a dry adiabatic descent from the pressure of atmosphere at 268.15K to the cloud condensation level pressure and the temperature of the atmosphere at 268.15K. Each column represents a value calculated as the temperature after the dry adiabatic descent minus the temperature of the atmosphere at 268.15K rounded to the nearest 0.5K.

• The vertical axis is also calculated from two values: the temperature after a saturated ascent from the ccl pressure to the pressure of environment at 268.15K and the temperature of the atmosphere at 268.25K. Each row is represented by a value calculated as the temperature after the saturated ascent minus the temperature of the atmosphere at 268.15K rounded to the nearest 5K.

process(ccl_temperature, ccl_pressure, temperature_on_pressure, wet_bulb_zero_height_asl, orography)

Main entry point of this class

Parameters:

• ccl_temperature (Cube) – Cube of the cloud condensation level temperature

• ccl_pressure (Cube) – Cube of the cloud condensation level pressure.

• temperature_on_pressure (Cube) – Cube of temperature on pressure levels

• wet_bulb_zero_height_asl (Cube) – Cube of the height of the wet-bulb freezing level above sea level

• orography (Cube) – Cube of the orography height.

Return type:

Cube

Returns:

Cube of hail diameter (m)

static temperature_after_saturated_ascent_from_ccl(ccl_temperature, ccl_pressure, pressure_at_268, humidity_mixing_ratio_at_ccl)

Calculates the temperature after a saturated ascent from the cloud condensation level to the pressure of the atmosphere at 268.15K

Parameters:

• ccl_temperature (Cube) – Cube of cloud condensation level temperature

• ccl_pressure (Cube) – Cube of cloud condensation level pressure

• pressure_at_268 (Cube) – Cube of the pressure of the environment at 268.15K

• humidity_mixing_ratio_at_ccl (array) – Array of humidity mixing ratio at the pressure of the environment at the CCL

Return type:

ndarray

Returns:

Cube of temperature after the saturated ascent

updated_hail_size(hail_size, wet_bulb_height)

Uses the updated_nomogram values dictionary to access an updated hail size based on the original predicted hail size and a wet bulb freezing height.

Parameters:

• hail_size (array) – Integers of hail diameter value taken from the original nomogram

• wet_bulb_height (array) – Floats of the height of the wet bulb freezing level

Return type:

array

Returns:

An updated value for the hail diameter (mm)

static updated_nomogram()

Sets up a dictionary of updated hail diameter values (mm).

The dictionary keys are the height of the wet bulb freezing level (m) where, when accessing at some height value, it should be rounded to the nearest lower value (e.g. 3549m should access 3350m key).

Each key has an associated list in which each element is a new hail diameter based on the original hail size that was calculated from nomogram_values table. Specifically each column associated hail size (mm) is [<5,<10,<20,<25,<50,<75,<100,<125]. The largest possible value where the equality still holds should be used.

If the wet bulb freezing height is less than 3350m then the original hail size is used. If the wet bulb freezing height is greater than 4400m then all hail sizes are set to 0.

Return type:

Tuple[List, List, array]