ParametricWeatherModel is a repository for forecasting surface temperature based primarily on latitude, longitude, day of year and hour of day.
The weather modeling script is less than 200 lines of python plus argument parsing, output and error handling. There are no external dependencies.
If you like ParametricWeatherModel, give it a star, or fork it and contribute!
Surface temperature forecast for latitude 47.6928, longitude -122.3038, day of year 229:
| Temperature prediction | Radiative processes |
|---|---|
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Predict surface temperature at specified latitude, longitude, day of year, ground temperature and initial surface temperature:
# Using short options
python parametricscheme.py -la 47.6928 -lo -122.3038 -da 229 -gt 54 -st 72 -pr 0.2 -de F
# The same using long options
python parametricscheme.py --latitude 47.6928 --longitude -122.3038 --day_of_year 229 --ground_temp 54 --surface_temp 72 --percent_net_radiation 0.2 --degrees F
# To list all command line options
python parametricscheme.py -hRequires a recent version of python (either 2 or 3 should work).
The following should work on any unix-ish environment:
wget https://raw.githubusercontent.com/makeyourownmaker/ParametricWeatherModel/master/parametricscheme.py
python parametricscheme.py -hThis repository contains code for a simple parameterization scheme to forecast the air temperature at the surface at a point over the next hour. It is based on chapter 2 from the book Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models by David J. Stensrud.
According to wikipedia: A parameterization scheme "in a weather or climate model in the context of numerical weather prediction is a method of replacing processes that are too small-scale or complex to be physically represented in the model by a simplified process." The obvious risk with this approach is producing an over-determined model.
The python code models the following radiative processes:
- Incoming solar radiation
- Upwelling longwave radiation from the surface
- Downwelling longwave radiation from the atmosphere
- Ground heat flux (heat transfer from the ground surface into the deeper soil levels)
- Sensible heat flux (heat transfer per unit area from the ground to the atmosphere)
- Latent heat flux (rate of moisture transfer per unit area from the ground surface to the atmosphere)
There are two options for calculating the sensible heat flux:
- The default method uses percent of net radiation ( --percent_net_radiation )
- The experimental method uses resistance to heat flux ( --resistance )
To use the experimental method the percent of net radiation must be set to 0:
# Using short options
python parametricscheme.py -la 47.6928 -lo -122.3038 -da 229 -gt 54 -st 72 -pr 0 -rh 1000 -de F
# The same using long options
python parametricscheme.py --latitude 47.6928 --longitude -122.3038 --day_of_year 229 --ground_temp 54 --surface_temp 72 --percent_net_radiation 0 --resistance 1000 --degrees FEquation and page numbers in the python code refer to Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models by David J. Stensrud.
The local hour of the sun approximation is from: pveducation.org
Included parameters:
- Required:
| Name | Short | Long | Description | Default |
|---|---|---|---|---|
| Latitude | -la | --latitude | -90 to 90; plus for north, minus for south | N/A |
| Longitude | -lo | --longitude | -180 to 180; plus for east, minus for west | N/A |
| Day | -da | --day_of_year | Julian day of year; 1 to 365 | N/A |
| Surface temperature | -st | --surface_temp | Initial surface air temperature (F or C) | N/A |
| Ground temperature | -gt | --ground_temp | Ground reservoir temperature (F or C) | N/A |
| Percent net radiation | -pr | --percent_net_radiation | Percent net radiation (0 to 1) | N/A |
| Degrees | -de | --degrees | Temperatures in Celsius or Fahrenheit | N/A |
- Optional:
| Name | Short | Long | Description | Default |
|---|---|---|---|---|
| Hour | -ho | --hour | Initial hour of day; 0 to 24 | 12 |
| Minute | -mi | --minute | Initial minute of hour; 0 to 59 | 59 |
| Albedo | -al | --albedo | Albedo; 0 to 1 | 0.3 |
| Cloud fraction | -cf | --cloud_fraction | Cloud fraction; 0 to 1 | 0 |
| Solstice | -ds | --day_of_solstice | Day of solstice; 172 or 173 | 173 |
| UTC offset | -uo | --utc_offset | UTC offset in hours; -12 to 12 | 0 |
| Forecast minutes | -fm | --forecast_minutes | Forecast minutes ahead; 1 to 1440 (24 * 60) | 60 |
| Report period | -rp | --report_period | Report period in minutes (including write to CSV file); 1 to 60 | 60 |
| Transmissivity | -tr | --transmissivity | Atmospheric transmissivity; greater than 0 | 0.8 |
| Emissivity | -em | --emissivity | Surface emissivity; 0.9 to 0.99 | 0.95 |
| Bowen ratio | -br | --bowen_ratio | Bowen ratio; -10 to 10 | 0.9 |
| Precipitable water | -pw | --precip_water | Precipitable water in cm; greater than 0 | 1.0 |
| Resistance to heat flux | -rh | --resistance | EXPERIMENTAL Resistance to heat flux (m s^-1) | 0 |
| File name | -fn | --filename | File name for comma separated value output | N/A |
| Help | -h | --help | Show this help message and exit | N/A |
| Verbose | -v | --verbose | Print additional information | N/A |
- Mutually exclusive option group 1 parameters:
- Choose --cloud_temp_constant or --cloud_temp_adjust but not both
| Name | Short | Long | Description | Default |
|---|---|---|---|---|
| Cloud temperature constant | -ct | --cloud_temp_constant | Temperature of the base of the cloud constant | Surface temperature |
| Cloud temperature adjustment | -tc | --cloud_temp_adjust | EXPERIMENTAL Temperature of the base of the cloud adjustment | 0 |
- Mutually exclusive option group 2 parameters:
- Choose --atmos_temp_constant or --atmos_temp_adjust but not both
| Name | Short | Long | Description | Default |
|---|---|---|---|---|
| Atmospheric temperature constant | -at | --atmos_temp_constant | Air temperature at 40 hPa above the surface constant | Surface temperature |
| Atmospheric temperature adjustment | -ta | --atmos_temp_adjust | EXPERIMENTAL Air temperature at 40 hPa above the surface adjustment | 0 |
Note:
- The cloud fraction and cloud base temperature options are largely untested
- Both the atmospheric and cloud temperatures default to the surface temperature value unless otherwise specified
- Temperature range checks start at -150 F and end at 150 F (-100 C and 66 C)
- This wide range of input values may not be compatible with all the parameterization scheme assumptions
The atmospheric temperature adjustment calculation equals the surface temperature plus/minus the supplied argument Similarly for the cloud temperature adjustment. These two options are intended to provide a simple method to vary these temperatures over a 24 hour period as shown in the comparison section below. This simple approach is not suggested in the Parameterization Schemes book.
Constants used:
Note: Strictly speaking some of these values are not constants; meaning constant values have been used as simpliying approximations.
| Constant | Value | Unit | Simpliying approximation |
|---|---|---|---|
| Stefan-Boltzmann | 5.67 * 10**(-8) | W m^-2 K^-4 | No |
| Thermal conductivity of air | 2.5 * 10**(-2) | W m^-1 K^-1 s^-1 | No |
| Solar irradiance | 1368 | W m^-2 | No |
| Soil heat capacity | 1.4 * 10**5 | J m^-2 K^-1 | Yes |
| Thermal diffusivity of air | 11 | J m^-2 K^-1 s^-1 | Yes |
| Specific heat at constant pressure | 1004 | J K^-1 kg^-1 | No |
| Density of air at sea level and 15 degrees C | 1.225 | kg m^-3 | No |
Predictions from Luke Madaus Digging into a "simple" weather model can be used for comparison with my implementation.
Madaus does not provide source code and the explanation is terse. I suspect not all of the parameters involved nor necessary assumptions have been listed. Also, I may have used a different local hour of the sun approximation and atmospheric temperature ajustment. So, I would not expect identical results. The final T_S plot below shows reasonable agreement between the Madaus predictions and mine for surface temperature (RMSE is approximately 3.05). Madaus results are plotted in green. I am not a meteorologist, so I am not certain all the results are reasonable. Constant Q_Ld and Q_Lu are unrealistic.
The plots are in order from left to right and top to bottom:
| Variable | Description |
|---|---|
| Q_S | Solar radiation |
| Q_Ld | Downwelling radiation |
| Q_Lu | Upwelling radiation |
| N_R | Net radiation (Q_S + Q_Ld - Q_Lu) |
| Q_H | Sensible heat flux |
| Q_E | Latent heat flux |
| Q_G | Ground heat flux |
| d_T_s | Change in surface temperature |
| T_s | Surface temperature |
| Error | Difference between my predictions and Madaus |
| Radiation | Q_S (dotted) , Q_Ld, Q_Lu, N_R (dashed) |
| Surface flux | Q_H, Q_E, Q_G |
To recreate the results above start with the following command line parameters:
# Using short options
python parametricscheme.py -la 47.6928 -lo -122.3038 \
-da 229 -ho 13 \
-gt 54 -st 72 \
-uo -8 -pw 1.27 \
-al 0.1866694 \
-em 0.8110634 \
-tr 0.6351528 \
-pr 0.3305529 \
-at -46.5617064 \
-de F \
-fm 1440 \
-rp 60 \
-fn data/data.csv
# The same using long options
python parametricscheme.py --latitude 47.6928 --longitude -122.3038 \
--day_of_year 229 --hour 13 \
--ground_temp 54 --surface_temp 72 \
--utc_offset -8 --precip_water 1.27 \
--albedo 0.1866694 \
--emissivity 0.8110634 \
--transmissivity 0.6351528 \
--percent_net_radiation 0.3305529 \
--atmos_temp_constant -46.5617064 \
--degrees F \
--forecast_minutes 1440 \
--report_period 60 \
--filename data/data.csvThe --albedo, --emissivity, --transmissivity, --percent_net_radiation and --atmos_temp_constant arguments used above were produced from an optimisation process over the full 24 hour forecast period. The optimisation process minimised temperature difference with Madaus predictions (RMSE of approximately 3.05 but many other albedo etc values gave very similar RMSE). It is possible to get RMSE values of 2.05 using my experimental --atmos_temp_adjust option but using that option may mean the model is over-determined. A multi-objective optimisation process, considering also some of the radiative processes, may give more realistic results. I am not a meteorologist, so I am not certain this combination of values is reasonable.
The default cloud fraction (0) and Bowen ratio (0.9) have been used.
The -fn and --filename options specify a file to output the following variables to:
| Variable | Description |
|---|---|
| Day | Day |
| Hour | Hour |
| Minute | Minute |
| Q_S | Solar radiation |
| Q_Ld | Downwelling radiation |
| Q_Lu | Upwelling radiation |
| Q_H | Sensible heat flux |
| Q_E | Latent heat flux |
| Q_G | Ground heat flux |
| d_T_s | Change in surface temperature |
| T_s | Surface temperature |
These variables are separated by tabs.
The variables are written to file at the end of the calculations. Optionally intermediate values during the calculations can be written using the -rp or --report_period option. This option specifies appending to the file in regular minute intervals.
# Using short options
python parametricscheme.py -la 47.6928 -lo -122.3038 \
-da 229 -ho 13 \
-gt 54 -st 72 \
-uo -8 -pw 1.27 \
-al 0.1147677 \
-em 0.7314196 \
-tr 0.7736024 \
-pr 0.3595031 \
-ta 54.0513927 \
-de F \
-fm 1440 \
-rp 60 \
-fn data/data.csv
# The same using long options
python parametricscheme.py --latitude 47.6928 --longitude -122.3038 \
--day_of_year 229 --hour 13 \
--ground_temp 54 --surface_temp 72 \
--utc_offset -8 --precip_water 1.27 \
--albedo 0.1147677 \
--emissivity 0.7314196 \
--transmissivity 0.7736024 \
--percent_net_radiation 0.3595031 \
--atmos_temp_adjust 54.0513927 \
--degrees F \
--forecast_minutes 1440 \
--report_period 60 \
--filename data/data.csvMake intermediate forecasts in data.csv file every 60 mins for 24 hours (1440 = 24 * 60 mins).
The notebooks directory contains the plot_temperature_and_fluxes.ipynb notebook which will plot the data.csv file. In addition to Jupyter it requires the following packages to run locally:
Alternatively, check notebook(s) remotely:
- A host of atmospheric factors are ignored: refraction, humidity, pressure, wind, rain, snow, pollution etc
- A host of geographic factors are ignored: elevation, slope of terrain, soil type, soil moisture, vegetation etc
- Hardcoded parameters in the script:
- Soil heat capacity will vary with soil type etc
- Thermal diffusivity of air is affected by temperature, pressure etc
- Thermal conductivity of air is affected by temperature, pressure etc
- Solar constant may be influenced by sunspot activity
- Table A7 in lecture 10 of AS547 from Chris Bretherton gives thermal conductivity, thermal diffusivity and specific heat values for various surfaces
- The elliptical orbital ratio is an approximation
- Assumes temperature at 40 hPa above the ground surface equals surface temperature which it certainly does not
- Assumes temperature at the base of the cloud equals surface temperature which it certainly does not
- Temperature range checks start at -150 F and end at 150 F (-100 C and 66 C)
- This wide range of input values may not be compatible with all the parameterization scheme assumptions
- Will not work over water, snow ...
The repository is slowly maturing. It contains some limitations, hardcoded parameters and possibly errors. Please file an issue if you find a problem.
-
Rename script and repository to ParameterizationScheme
-
Perform more sanity checks:
- Sensible heat flux increases during morning reaching a maximum in the afternoon before decreasing to zero after sunset on cloudless summer days
- Surface energy budget should balance - Equation 2.102 Page 55
- Sensible heat flux (Q_H), latent heat flux (Q_E) and ground heat flux (Q_G) should be positive with high solar radiation (Q_S)
- Find recent local weather examples for comparison
- Find examples from the literature for comparison
- Compare current Euler integration with simple Runge-Kutta method
-
Expand documentation:
- Justify values used in command line argument range checks
-
Add unit tests:
- Setup GitHub Actions or similar testing environment
- Find range of test cases where surface temperature and all parameters are known
- Examples from the literature for each of the heat fluxes
- Preferably observations
- Examples from the literature for each of the heat fluxes
- What is an acceptable prediction interval?
-
Explore sensitivity analysis:
- It would be interesting (but possibly overkill) to look at how uncertainty in the inputs affects the model predictions
Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.
-
Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models by David J. Stensrud
-
The ESCOMP repositories particularly the Community Land Model included in CTSM which has detailed radiative flux and heat flux calculations
-
Table 10.1 in lecture 10 of AS547 from Chris Bretherton gives albedo and emissivity values for a range of natural surfaces
-
Radiation balance is discussed by Constance Brown on the G109 course
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My related weather repositories: