Calibration of potential evapotranspiration methods

M. Vremec, R.A. Collenteur University of Graz, 2021

In this notebook it is shown how to calibrate various (potential) evapotranspiration (PET) equations, using a linear regression relationship between daily potential evapotranspiration obtained with the FAO-56 equation and daily PET estimates obtained with the alternative methods. This notebook requires Scipy and SkLearn python packages to run.

import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import least_squares
from sklearn.metrics import mean_squared_error

import pyet as pyet

1. Load KNMI Data

data = pd.read_csv("data/example_3/etmgeg_260.txt", skiprows=46, delimiter=",", 
                   skipinitialspace=True, index_col="YYYYMMDD", parse_dates=True).loc["2018",:]
data.head()

	# STN	DDVEC	FHVEC	FG	FHX	FHXH	FHN	FHNH	FXX	FXXH	...	VVNH	VVX	VVXH	NG	UG	UX	UXH	UN	UNH	EV24
YYYYMMDD
2018-01-01	260	225	45	50	90	2	10	18	190.0	2.0	...	2.0	75.0	3.0	7.0	84	96	17	73	1	3
2018-01-02	260	216	39	45	80	24	20	1	140.0	24.0	...	19.0	75.0	8.0	7.0	88	96	3	80	8	2
2018-01-03	260	257	82	88	120	11	70	4	290.0	3.0	...	1.0	75.0	4.0	8.0	73	95	1	65	9	1
2018-01-04	260	238	51	56	90	20	30	14	180.0	20.0	...	14.0	80.0	21.0	8.0	82	97	14	67	21	2
2018-01-05	260	225	38	40	60	1	20	17	150.0	16.0	...	15.0	75.0	1.0	6.0	87	96	17	71	3	2

5 rows × 40 columns

2.Estimation of potential evapotranspiration

# define meteorological variables needed for PE estimation
meteo = pd.DataFrame({"tmean":data.TG/10, "tmax":data.TX/10, "tmin":data.TN/10, "rh":data.UG, "wind":data.FG/10, "rs":data.Q/100})
tmean, tmax, tmin, rh, wind, rs = [meteo[col] for col in meteo.columns]
pressure =  data.PG / 100 # to kPa
wind = data.FG/10  # to m/s
lat = 0.91  # [rad]
elevation = 4 

pet_fao56 = pyet.pm_fao56(tmean, wind, rs=rs, elevation=elevation, lat=lat, 
                         tmax=tmax, tmin=tmin, rh=rh)  # FAO-56 method
pet_romanenko = pyet.romanenko(tmean, rh)  # Romanenko method
pet_abtew = pyet.abtew(tmean, rs)  # Abtew method

The model performance of the Abtew and Romanenko method will be evaluated using the root mean square error (RMSE), as implemented in SkLearn’s mean_squared_error method.

pet_fao56.plot()
pet_romanenko.plot()
pet_abtew.plot()
plt.ylabel("PE [mm/day]")
print("RMSE(Romanenko) = {} mm/d".format(mean_squared_error(pet_fao56, pet_romanenko, squared=False)))
print("RMSE(Abtew) = {} mm/d".format(mean_squared_error(pet_fao56, pet_abtew, squared=False)))

/home/docs/checkouts/readthedocs.org/user_builds/pyet/envs/dev/lib/python3.11/site-packages/sklearn/metrics/_regression.py:483: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pyet/envs/dev/lib/python3.11/site-packages/sklearn/metrics/_regression.py:483: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

RMSE(Romanenko) = 0.6919512654413198 mm/d
RMSE(Abtew) = 0.7387078735036147 mm/d

3. Calibration of different PE equations

The least squares approach is applied to estimate the parameters in the PE equations, by minimizing the sum of the residuals between the simulated (Abtew and Romanenko) and observed (FAO-56) data. The minimization of the objective function is done using the Trust Region Reflective algorithm, as implemented in Scipy’s least squares method.

3.1 Romanenko method

# Define function for computing residuals
def cal_romanenko(k, obs):
    return pyet.romanenko(tmean, rh, k)-obs

# estimate k in the Romanenko method
x0 = 4.5  # initial estimate of parameter
res_1 = least_squares(cal_romanenko, x0, args=[pet_fao56])
res_1.x

array([3.87304623])

# Compute RMSE using the calibrated value of k
pet_romanenko_cal = pyet.romanenko(tmean, rh, k=res_1.x)
print("RMSE(Romanenko) = {} mm/d".format(mean_squared_error(pet_fao56, pet_romanenko_cal, squared=False)))

RMSE(Romanenko) = 0.5470690023375226 mm/d

/home/docs/checkouts/readthedocs.org/user_builds/pyet/envs/dev/lib/python3.11/site-packages/sklearn/metrics/_regression.py:483: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

RMSE (calibrated) = 0.546 < RMSE (uncalibrated) = 0.694

3.2 Abtew method

# Define function for computing residuals and initial estimate of parameters
def cal_abtew(k,obs):
    return pyet.abtew(tmean, rs, k)-obs
x0 = 0.53

# estimate k in the Romanenko method
res_2 = least_squares(cal_abtew, x0, args=[pet_fao56])
res_2.x

array([0.45748986])

pet_abtew_cali = pyet.abtew(tmean, rs, res_2.x)
print("RMSE(Abtew) = {} mm/d".format(mean_squared_error(pet_fao56, pet_abtew_cali, squared=False)))

RMSE(Abtew) = 0.6127899429733885 mm/d

/home/docs/checkouts/readthedocs.org/user_builds/pyet/envs/dev/lib/python3.11/site-packages/sklearn/metrics/_regression.py:483: FutureWarning: 'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.
  warnings.warn(

RMSE (calibrated) = 0.613 < RMSE (uncalibrated) = 0.741

pet_fao56.plot()
pet_romanenko_cal.plot()
pet_abtew_cali.plot()
plt.ylabel("PET [mm/d]");