# **Sensitivity of the PM model to wind speed: Sympy study**
# **Sensitivity of the PM model to wind speed: Sympy study**
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# Part I - Methodology
# Part I - Methodology
## <u> Motivation </u>
## <u> Motivation </u>
### Theoretical background
### Theoretical background
When assessing the models sensitivity to changes in atmospheric forcings in notebook simpler_model.ipynb, we found out that the potential evapo-transpiration models had a counter intuitive sensitivity to wind speed:
When assessing the models sensitivity to changes in atmospheric forcings in notebook simpler_model.ipynb, we found out that the potential evapo-transpiration models had a counter intuitive sensitivity to wind speed:
This otebook aims at investigating the mathematical structure of the Penman-Monteith model to investigate the variation behavior of the equation to wind speed.
This otebook aims at investigating the mathematical structure of the Penman-Monteith model to investigate the variation behavior of the equation to wind speed.
### Modelling experiements
### Modelling experiements
Sympy is used in this notebook in order to compute the derivative of the Penman-Monteith equation to wind speed and to study its sign
Sympy is used in this notebook in order to compute the derivative of the Penman-Monteith equation to wind speed and to study its sign
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%%%% Output: stream
theta_sat
theta_sat
theta_res
theta_res
alpha
alpha
n
n
m
m
S_mvg
S_mvg
theta
theta
h
h
S
S
theta_4
theta_4
theta_3
theta_3
theta_2
theta_2
theta_1
theta_1
L
L
Mw
Mw
Pv
Pv
Pvs
Pvs
R
R
T
T
c1
c1
T0
T0
Delta
Delta
E
E
G
G
H
H
Rn
Rn
LE
LE
gamma
gamma
alpha_PT
alpha_PT
c_p
c_p
w
w
kappa
kappa
z
z
u_star
u_star
VH
VH
d
d
z_om
z_om
z_oh
z_oh
r_a
r_a
g_a
g_a
r_s
r_s
g_s
g_s
c1_e
c1_e
c2_e
c2_e
e
e
T_min
T_min
T_max
T_max
RH_max
RH_max
RH_min
RH_min
e_a
e_a
e_s
e_s
iv_T
iv_T
T_kv
T_kv
P
P
rho_a
rho_a
VPD
VPD
%%%% Output: stream
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## Importing the performance assessment functions defined in the analysis_function.py file
## Importing the performance assessment functions defined in the analysis_function.py file