SIMPLIFICATION OF ATMOSPHERIC MODELS
FOR REAL-TIME WIND FORECAST
Qing-Guo Wang, Zhen Ye and Lihong Idris Lim
Department of Electrical and Computer Engineering, National University of Singapore
10 Kent Ridge Crescent, 119260, Singapore
Keywords:
Real-time wind forecast, Partial differential equations, MM5, Kalman filter.
Abstract:
In wind energy industry, it is well known that real-time wind forecast can improve the performance of wind
turbines if the prediction information is well used to compensate the uncertainty of the wind. Unfortunately,
neither model nor method is available to give a real-time forecast of wind so far. This paper proposed a
real-time wind forecast model by simplifying existing weather forecast model, MM5. Details on model sim-
plification, forecast error correction as well as other issues like boundary conditions and simulations are also
discussed.
1 INTRODUCTION
Owing to increasing concern over the global environ-
ment, there is much interest throughout the world in
renewable energy, of which one of the most promis-
ing is wind power due to its mature technology, low
cost and less environmental impact. Unlike the nor-
mal electrical power generation using generated wa-
ter steam with certain temperature and pressure, wind
power utilizes natural but uncertain wind. The wind
uncertainty is the root cause for most of the issues in
wind power systems, such as nonlinearity, coupling,
interaction, and so on. Therefore, it would be much
helpful to improve the performance of wind turbines
if we could predict the wind and take actions in ad-
vance. It would be better if the prediction is real-time
since wind is varying all the time.
A natural thought for wind prediction is to make
use of weather forecasting models, which has been
developed since 1970s and now achieves good pre-
diction for wind, temperature, pressure, moisture, and
other weather conditions. Actually in wind power
prediction, weather forecasting model has already
been applied, see (Landberg, 1999; Joensen et al.,
1999; Kazuhito et al., 2006) and references there in,
but none of them can give real-time predictions. To
the best of our knowledge, not much work has been
done yet so far in the real-time wind forecast for wind
turbines. This is because:
1. Weather forecasting model is developed for a
long-term and large scale forecast, which is not
suitable for wind prediction in wind energy indus-
try where only a short-term and small scale fore-
cast is only required;
2. Due to model complexity, the highest temporal
resolution of current weather forecasting model is
hourly, which is hardly used for real-time predic-
tion.
3. Weather forecasting model lacks of the scheme of
correcting prediction error, which is much needed
in wind prediction for wind energy industry, espe-
cially for real-time forecast.
This paper aims to find a suitable forecasting
model for real-time wind prediction. Based on the
Fifth-Generation NCAR/Penn State Mesoscale model
(MM5) for weather forecast, all possible methods of
simplification are discussed to achieve the real-time
forecast. Ideas of Kalman filter used to correct the
forecast error are also addressed as well as issues on
boundary conditions and simulations.
2 MM5 FORECASTING MODEL
MM5 forecasting model is the latest in a series de-
veloped from a mesoscale model used by Anthes at
Penn State in the early 1970s that was later docu-
mented by (Anthes and Warner, 1978). Since that
time, it has undergone many changes designed to
168
Wang Q., Ye Z. and Idris Lim L. (2009).
SIMPLIFICATION OF ATMOSPHERIC MODELS FOR REAL-TIME WIND FORECAST.
In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Signal Processing, Systems Modeling and
Control, pages 168-171
DOI: 10.5220/0002248001680171
Copyright
c
 SciTePress

broaden its applications, including (i) a multiple-nest
capability; (ii) nonhydrostatic dynamics; (iii) a four-
dimensional data assimilation (Newtonian nudging)
capability; (iv) increased number of physics options;
and (v) portability to a wider range of computer plat-
forms.
In terms of terrain following coordinates (x,y,σ),
the partial differential equations for the nonhydro-
static model’s basic variables excluding moisture are:
Pressure
∂p
′
∂t
− ρ
0
gw+ γp∇· V= V· ∇p
′
+
γp
T

˙
Q
c
p
+
T
0
θ
0
D
θ

,
(1)
Momentum (x-component)
∂u
∂t
+
m
ρ

∂p
′
∂x
−
σ
p
∗
∂p
∗
∂x
∂p
′
∂σ

= −V· ∇u
+v

f + u
∂m
∂y
− v
∂m
∂x

− ewcosα −
uw
r
+ D
u
, (2)
Momentum (y-component)
∂v
∂t
+
m
ρ

∂p
′
∂y
−
σ
p
∗
∂p
∗
∂y
∂p
′
∂σ

= −V· ∇v
−u

f + u
∂m
∂y
− v
∂m
∂x

+ ewsinα−
vw
r
+ D
v
, (3)
Momentum (z-component)
∂w
∂t
+
ρ
0
ρ
g
p
∗
∂p
′
∂σ
+
g
γ
p
′
p
= −V· ∇w+ g
p
0
p
T
′
T
0
−
gR
d
c
p
p
′
p
+ e(ucosα− vsinα) +
u
2
+ v
2
r
+ D
w
, (4)
Thermodynamics
∂T
∂t
= −V· ∇T +
1
ρc
p

∂p
′
∂t
+ V· ∇p
′
− ρ
0
gw

+
˙
Q
c
p
+
T
0
θ
0
D
θ
, (5)
where p, ρ, T are pressure (Pa), density (kg· m
−3
),
and temperature (K), respectively. The subscript “0”
represents the reference-state. u, v, w are component
of wind velocity (m· s
−1
) in eastward, northward, and
vertical direction, respectively. Q is diabatic heating
rate per unit mass (J· kg
−1
· s
−1
). c
p
is specific heat at
constant pressure for dry air. γ = c
p
/(c
p
− R) is ratio
of heat capacities. R = 287J· kg
−1
· K
−1
is ideal gas
constant. θ is potential temperature (K). D
A
is diffu-
sion and PBL tendency for variable A. m is map-scale
factor. p
′
= p− p
0
is perturbation pressure (Pa). p
∗
=
p
s
− p
t
, p
s
and p
t
are surface and top pressures respec-
tively of the reference state. σ = (p
0
− p
t
)/(p
s
− p
t
)
is nondimensional vertical coordinate of model. f is
Coriolis parameter, e = 2Ωcosλ, α = φ− φ
c
, Ω is an-
gular velocity of the earth, λ is latitude, φ is longitude,
and φ
c
is central longitude. r is the radius of the earth.
V· ∇A ≡ mu
∂A
∂x
+ mv
∂A
∂y
+
˙
σ
∂A
∂σ
, (6)
˙
σ = −
ρ
0
g
p
∗
w−
mσ
p
∗
∂p
∗
∂x
u−
mσ
p
∗
∂p
∗
∂y
v, (7)
∇· V = m
2
∂
∂x

u
m

−
mσ
p
∗
∂p
∗
∂x
∂u
∂σ
+ m
2
∂
∂y

v
m

−
mσ
p
∗
∂p
∗
∂y
∂v
∂σ
−
ρ
0
g
p
∗
∂w
∂σ
. (8)
The derivations of above model equations (1)-(5)
are based on the gas law and first law of thermody-
namics. More details can be found in (Grell et al.,
1995; Dudhia et al., 2005). Obviously, MM5 is a
5-dimensional model of partial differential equations
with structure of coupled variables, which causes its
solving time consuming. Currently, the forecast of
MM5 can only achieve hourly updation. To imple-
ment real-time forecast of wind, simplifications have
to be made.
3 SIMPLIFICATION TO MM5
FOR WIND FORECAST
Comparing with weather forecast, wind forecast for
wind turbines has its own uniqueness.
1. The rotor blade length of wind turbine is usually
less than 150m, so the pressure change along the
vertical direction for wind turbine is not too much.
2. The rotation of wind turbine is not driven by the
vertical pressure on the blade, but by the horizon-
tal velocity difference on its top and bottom sur-
faces. Pressure or vertical velocity has less contri-
bution.
3. Temperature may not be a necessary option in
real-time forecast as the rotation of wind turbine
is not sensitive to temperature change.
Thus, the MM5 model of equations (1)-(5) can be
simplified in the following way:
For real-time forecast, the time interval of two
continuous predictions should be very small, say one
minute. In such a short period, temperature changes
can be neglected. Therefore, ∂T/∂t = 0, V· ∇T = 0
and (5) becomes
˙
Q
c
p
+
T
0
θ
0
D
θ
= −
1
ρc
p

∂p
′
∂t
+ V· ∇p
′
− ρ
0
gw

. (9)
SIMPLIFICATION OF ATMOSPHERIC MODELS FOR REAL-TIME WIND FORECAST
169

Substituting (9) into (1) yields
∂p
′
∂t
− ρ
0
gw+ p∇ · V = V· ∇p
′
, (10)
since p/(ρTc
p
) = 1− γ
−1
according to gas law. Thus,
(1) is simplified to be (10) and model dimension is
reduced as (5) is missing.
As pressure changes along the vertical direction
of wind turbine is not too much, ∂p
′
/∂z ≈ 0. By the
coordinate transformation (x,y,z) → (x,y,σ),

∂
∂x

z
→

∂
∂x

σ
−

∂z
∂x

σ
∂
∂z
, (11)
where dz = −dp
0
/(ρ
0
g) = −(p
∗
dσ + σdp
∗
)/(ρ
0
g),
so

∂
∂x

z
→

∂
∂x

σ
−
σ
p
∗
∂p
∗
∂x
∂
∂σ
. (12)
Thus,

∂p
′
∂x

z
→

∂p
′
∂x

σ
−
σ
p
∗
∂p
∗
∂x
∂p
′
∂σ
= 0, (13)

∂p
′
∂y

z
→

∂p
′
∂y

σ
−
σ
p
∗
∂p
∗
∂y
∂p
′
∂σ
= 0, (14)
and (2) and (3) can be simplified as
∂u
∂t
= −V· ∇u+ v

f + u
∂m
∂y
− v
∂m
∂x

−ewcosα−
uw
r
+ D
u
, (15)
∂v
∂t
= −V· ∇v− u

f + u
∂m
∂y
− v
∂m
∂x

+ewsinα −
vw
r
+ D
v
. (16)
If ignoring the effect of vertical velocity w on horizon-
tal momentum, (15) and (16) can be further simplified
as
∂u
∂t
= −V· ∇u+ v

f + u
∂m
∂y
− v
∂m
∂x

+ D
u
, (17)
∂v
∂t
= −V· ∇v− u

f + u
∂m
∂y
− v
∂m
∂x

+ D
v
. (18)
By the above approximation, MM5 model is sim-
plified as (10), (17) and 18) with less dimensions and
variables, which is suitable for the real-time predic-
tion.
4 BOUNDARY CONDITIONS
Both MM5 and simplified model are composed of
partial differential equations where only numerical
solutions are available. Thus, boundary conditions
have to be set in addition to initial values prior to
running a simulation. Here in our real-time wind
forecast, wind velocity, temperature and pressure are
specified as boundaries.
The boundary values can come from real-time ob-
servations of the wind. In this case, some weather sta-
tions have to be set up at the outer place of the wind
power plant for measurement. The distance from one
station to one wind turbine is a trade-off between pre-
diction accuracy and computation burden. The nearer
the station is to the wind turbine, the more accu-
rate the wind prediction, but the less time for solv-
ing the equations. Alternatively, the boundary values
can come from another model’s forecast (in real-time
forecasts).
The shape of the boundary can be determined
freely, depending on the convenience of computation.
Rectangle and circle are two types broadly used. The
area surroundedby the boundary is then grided evenly
and every grid point gives a wind prediction after
solving the model numerically. Normally, the wind
turbine should be one grid point inside the boundary.
But due to its unevenly distribution, this is usually not
the case. Therefore, linear interpolation has to be ap-
plied to give the final wind prediction.
5 ERROR CORRECTION
To improve the forecast accuracy, some “feedback”
strategy should be introduced for error correction by
comparing the estimated and true values. This can
be done by Kalman filter. Thus, the loss of accu-
racy caused by the model simplification can be made
up, but computation increases inevitably. Therefore,
trade-off should be made between model simplifica-
tion and Kalman filter design.
6 SIMULATIONS
To verify whether the proposed model can give real-
time forecast of wind, a simulation has to be con-
ducted. Two ways are available to this end. One is
to use the code of MM5 model, which is available at
the web site of National Center for Atmospheric Re-
search (NCAR) for free download. The other one is to
apply the Matlab Toolbox of partial differential equa-
tion to the proposed model. This part of work is still
under study and will supplemented in the final version
if possible.
ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics
170

7 CONCLUSIONS
This paper proposed a real-time wind forecast model
for wind energy industry by simplifying the existing
MM5 model of weather forecast. Details of the sim-
plification method is given as well as other issues on
model implementation. To our best knowledge, no
similar model is available for wind forecast in wind
energy industry so far.
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