Wet-bulb Temperature

Wet-bulb Temperature#

Wet-bulb temperature is a critical meteorological parameter that represents the lowest temperature to which air can be cooled by evaporation at constant pressure. It is widely used in weather forecasting, heat stress assessment, and climate studies. The easyclimate library provides multiple methods to compute wet-bulb temperature, including iterative approaches, empirical formulas, and approximations based on established research.

The example is structured into several sections, each performing a specific task, such as data initialization, mesh grid creation, wet-bulb temperature calculations using different methods, and plotting results for analysis. The following sections describe the intent of each part.

This part imports necessary Python libraries for data manipulation and visualization:

import easyclimate as ecl
import xarray as xr
import numpy as np
import matplotlib.pyplot as plt

This section creates synthetic datasets to represent atmospheric conditions:

temp_data: A 1D array of temperatures ranging from -20°C to 50°C.
relative_humidity_data: A 1D array of relative humidity values from 0% to 100%.
deltaT_data: A 1D array representing the temperature difference (\(T - T_d\)) from 0°C to 30°C.

These arrays serve as input for subsequent calculations, covering a wide range of conditions to test the wet-bulb temperature methods.

temp_data = xr.DataArray(
    np.linspace(-20, 50, 71),
    dims="temp",
    coords={'temp': np.linspace(-20, 50, 71)}
)
relative_humidity_data = xr.DataArray(
    np.linspace(0, 100, 101),
    dims="rh",
    coords={'rh': np.linspace(0, 100, 101)}
)

deltaT_data = xr.DataArray(
    np.linspace(0, 30, 31),
    dims="deltaT",
    coords={'deltaT': np.linspace(0, 30, 31)}
)

This section defines the generate_mesh function, which creates 2D mesh grids from two 1D xarray.DataArray inputs. The function:

Uses numpy.meshgrid to generate grid arrays.
Constructs xarray.DataArray objects for each grid, preserving coordinates and dimensions.
Returns two DataArray objects representing the meshed variables.

This function is used to create 2D grids for temperature, relative humidity, and dewpoint differences, enabling calculations over a range of conditions.

def generate_mesh(
    da1: xr.DataArray,
    da2: xr.DataArray,
):
    da1_grid, da2_grid = np.meshgrid(da1, da2)

    dim_1 = da2.dims[0]
    dim_2 = da1.dims[0]
    dim_1_array = da2[dim_1].data
    dim_2_array = da1[dim_2].data

    da1_dataarray = xr.DataArray(
        da1_grid,
        dims=(dim_1, dim_2),
        coords={dim_1: dim_1_array, dim_2: dim_2_array}
    )
    da1_dataarray.name = dim_2

    da2_dataarray = xr.DataArray(
        da2_grid,
        dims=(dim_1, dim_2),
        coords={dim_1: dim_1_array, dim_2: dim_2_array}
    )
    da2_dataarray.name = dim_1

    return da1_dataarray, da2_dataarray

This section applies the generate_mesh function to create 2D grids:

temp_mesh1, rh_mesh: Meshes of temperature and relative humidity.
temp_mesh2, deltaT_mesh: Meshes of temperature and temperature difference.
td_mesh: Dewpoint temperature calculated as temp_mesh2 - deltaT_mesh.

These grids are used as inputs for wet-bulb temperature calculations.

temp_mesh1, rh_mesh = generate_mesh(temp_data, relative_humidity_data)
temp_mesh2, deltaT_mesh = generate_mesh(temp_data, deltaT_data)
td_mesh = temp_mesh2 - deltaT_mesh

Stull (2011) Calculation#

Single Point#

This section tests the easyclimate.physics.calc_wet_bulb_temperature_stull2011 function for a single data point (T = 20°C, RH = 50%):

Computes wet-bulb temperature using Stull’s empirical formula.
Converts the result from Kelvin to Celsius for consistency.

Grid#

This section applies easyclimate.physics.calc_wet_bulb_temperature_stull2011 to the 2D grid (temp_mesh1, rh_mesh):

Calculates wet-bulb temperature across the grid using Stull’s formula.
Converts the output from Kelvin to Celsius.
Stores the result in wet_bulb_stull2011.

This enables comparison with the iterative method.

wet_bulb_stull2011 = ecl.physics.calc_wet_bulb_temperature_stull2011(
    temp_mesh1, rh_mesh, "degC", "%"
)
wet_bulb_stull2011 = ecl.utility.transfer_data_temperature_units(wet_bulb_stull2011, "K", "degC")

Comparison (Iteration vs. Stull)#

This section visualizes the results of the iterative and Stull methods:

Creates a contour plot of wet_bulb_iteration with levels from -20°C to 50°C. Overlays contours of wet_bulb_stull2011 in black for comparison. Computes and plots the difference (wet_bulb_stull2011 - wet_bulb_iteration) to highlight discrepancies.

The plots help assess the agreement between the two methods across different conditions.

fig, ax = plt.subplots(figsize = (6, 6))

wet_bulb_iteration.plot.contourf(
    levels = np.arange(-20, 50, 5),
    cbar_kwargs = {'location': 'bottom', 'aspect': 60}
)

cf = wet_bulb_stull2011.plot.contour(levels = np.arange(-20, 50, 5), colors='k')
plt.clabel(cf, inline = True, fontsize = 10)

<a list of 14 text.Text objects>

diff = (wet_bulb_stull2011 - wet_bulb_iteration)
diff.plot.contourf(
    levels = np.linspace(-1, 1, 21),
    cbar_kwargs = {'location': 'bottom', 'aspect': 60, 'label': 'diff'}
)

<matplotlib.contour.QuadContourSet object at 0x7f10da9ea080>

Sadeghi (2013) Calculation#

Grid#

This section computes wet-bulb temperature using easyclimate.physics.calc_wet_bulb_temperature_sadeghi2013 at three elevations (0 m, 2000 m, 5000 m):

Uses temp_mesh1 and rh_mesh as inputs, with height specified as an xarray.DataArray.
Outputs results in °C for each elevation.

Comparison (0 m vs. 5000 m)#

This section visualizes the Sadeghi results:

Creates a contour plot of wet_bulb_sadeghi2013_0m.
Overlays contours of wet_bulb_sadeghi2013_5000m in black.
Plots the difference (wet_bulb_sadeghi2013_0m - wet_bulb_sadeghi2013_5000m) to show elevation effects.

These plots illustrate how elevation influences wet-bulb temperature.

wet_bulb_sadeghi2013_0m.plot.contourf(levels = 21)
wet_bulb_sadeghi2013_5000m.plot.contour(levels = 21, colors='k')

<matplotlib.contour.QuadContourSet object at 0x7f10dd7bf1c0>

diff = wet_bulb_sadeghi2013_0m - wet_bulb_sadeghi2013_5000m
diff.plot.contourf(
    levels = np.linspace(-6, 6, 21)
)

<matplotlib.contour.QuadContourSet object at 0x7f10db0d0700>

Conclusion#

The example demonstrates the application of multiple wet-bulb temperature calculation methods provided by the easyclimate library. By generating synthetic data, creating 2D grids, and applying iterative, empirical, and approximation-based methods, the script enables a comprehensive comparison of results. Visualizations highlight differences between methods and the influence of parameters like elevation, aiding in the evaluation of their accuracy and applicability in meteorological analysis.

Total running time of the script: (0 minutes 7.982 seconds)

Wet-bulb Temperature

Contents

Wet-bulb Temperature#

Iterative Calculation#

Stull (2011) Calculation#

Single Point#

Grid#

Comparison (Iteration vs. Stull)#

Sadeghi (2013) Calculation#

Grid#

Comparison (0 m vs. 5000 m)#

Davies-Jones (2008) Calculation#

Grid#

Plot Davies-Jones Results#

Conclusion#