Topic No. 1
Tropical Cyclone Movement
Tropical Cyclone Ensemble Forecast
Nanjing, China
9:00 – 12:00
2011.12.15 (Thr)
Munehiko Yamaguchi
Typhoon Research Department,
Meteorological Research Institute of the Japan Meteorological Agency
Basic concept of TC movement
The basic idea of TC movement is that the TC vortex is
“steered” by its surrounding flow
(Chan 2010, Global Perspectives on Tropical Cyclones).
Dynamically, steering is the advection of the relative vorticity (ζ)
of the TC by the surrounding horizontal flow (V)
Time evolution of the
relative vorticity of the TC
Advection of the relative
vorticity by the surrounding
horizontal flow
Steering flow
The advection effect causes the TC to move downstream along the
direction of V, which is referred to as the “steering flow”.
Although this concept of steering is very simple, it has been
used extensively to explain and predict TC movement with
relatively good success especially in short-tem forecasts.
(Chan 2010, Global Perspectives on Tropical Cyclones).
Let’s take a look at how much the steering concept is
valid to explain the TC movement in NWP models.
Case study to visualize the steering flow
Let’s have a look at the steering flow at the before-, during-, and
after-recurvature stages of Typhoon Sinlaku in 2008.
Observed Track of Typhoon Sinlaku (2008)
In order to visualize the steering flow, spatial low-pass filter
is applied to a total wind field to separate the TC circulation
and the surrounding, steering flow.
Total wind (streamfunction) field before recurvature
First of all, let’s see the Sinlaku’s movement in an NWP model.
Here the ECMWF’s NWP model is considered as an example.
Streamfunction field at 500 hPa at T+0
Typhoon Sinlaku
Total wind (streamfunction) field before recurvature
First of all, let’s see the Sinlaku’s movement in an NWP model.
Here the ECMWF’s NWP model is considered as an example.
Streamfunction field at 500 hPa at T+24 (forecasted field)
Sinlaku moves north in the model at this time
Typhoon Sinlaku
Separation of the total field
Total field
spatial low-pass filter
Steering flow
TC circulation
+
Layer image
Steering flow from the south to north can be seen. The direction of the steering
flow matches with that of the movement of Typhoon Sinlaku.
Typhoon Sinlaku
Total wind (streamfunction) field during recurvature
Let’s see the Sinlaku’s movement in an NWP model.
Here the ECMWF’s NWP model is considered as an example.
Streamfunction field at 500 hPa at T+0
Typhoon Sinlaku
Total wind (streamfunction) field during recurvature
Let’s see the Sinlaku’s movement in an NWP model.
Here the ECMWF’s NWP model is considered as an example.
Streamfunction field at 500 hPa at T+24 (forecasted field)
Sinlaku moves northeast in the model at this time
Typhoon Sinlaku
Separation of the total field
Total field
spatial low-pass filter
Steering flow
TC circulation
+
Layer image
Steering flow from the southwest to northeast can be seen. The direction of the
steering flow matches with that of the movement of Typhoon Sinlaku.
Typhoon Sinlaku
Total wind (streamfunction) field after recurvature
Let’s see the Sinlaku’s movement in an NWP model.
Here the ECMWF’s NWP model is considered as an example.
Streamfunction field at 500 hPa at T+0
Typhoon Sinlaku
Total wind (streamfunction) field after recurvature
Let’s see the Sinlaku’s movement in an NWP model.
Here the ECMWF’s NWP model is considered as an example.
Streamfunction field at 500 hPa at T+24 (forecasted field)
Sinlaku moves east-northeast in the model at this time
Typhoon Sinlaku
Separation of the total field
Total field
spatial low-pass filter
Steering flow
TC circulation
+
Layer image
Steering flow from the west-southwest to east-northeast can be seen. The direction
of the steering flow matches with that of the movement of Typhoon Sinlaku.
Typhoon Sinlaku
Practice
Let’s calculate the steering vector and compare it with
the TC motion vector in the model!!!
Sketch the steering vector on the distributed answer sheet
on which the TC motion vector is already plotted.
Use
to calculate the amplitude of the vector.
For the direction of the vector, visually determine it.
Note that the TC motion vector is calculated from the minimum sea level pressure
positions at T+0h and T+24h (forecasted field of ECMWF). Later, we will compare
the steering vector and the TC motion vector with the observed track.
Steering vector before recurvature
Streamfunction (ψ) field
Contour interval: 2 x 10^5
Unit: m^2/s
Steering flow
Central position of Typhoon Sinlaku
Steering vector before recurvature
Estimate
from the figure, calculate the amplitude
of the steering vector and plot it.
1m/s
2m/s
3m/s
4m/s
5m/s
6m/s
Note that the TC motion vector (arrow in green) is plotted based on the minimum
sea level pressure positions at T+0h and T+24h (forecasted field of ECMWF). Later,
we will compare the TC motion vector with the observed track.
Steering vector during recurvature
Streamfunction (ψ) field
Contour interval: 5 x 10^5
Unit: m^2/s
Steering flow
Central position of Typhoon Sinlaku
Steering vector during recurvature
Estimate
from the figure, calculate the amplitude
of the steering vector and plot it.
1m/s
2m/s
3m/s
4m/s
5m/s
6m/s
Note that the TC motion vector (arrow in green) is plotted based on the minimum
sea level pressure positions at T+0h and T+24h (forecasted field of ECMWF). Later,
we will compare the TC motion vector with the observed track.
Steering vector after recurvature
Streamfunction (ψ) field
Contour interval: 5 x 10^5
Unit: m^2/s
Steering flow
Central position of Typhoon Sinlaku
Steering vector after recurvature
Estimate
from the figure, calculate the amplitude
of the steering vector and plot it.
1m/s
2m/s
3m/s
4m/s
5m/s
6m/s
Note that the TC motion vector (arrow in green) is plotted based on the minimum
sea level pressure positions at T+0h and T+24h (forecasted field of ECMWF). Later,
we will compare the TC motion vector with the observed track.
Let’s check the answers.
Steering vector before recurvature
1m/s
2m/s
3m/s
4m/s
5m/s
6m/s
Steering vector during recurvature
1m/s
2m/s
3m/s
4m/s
5m/s
6m/s
Steering vector after recurvature
1m/s
2m/s
3m/s
4m/s
5m/s
6m/s
Let’s discuss reasons of the
difference between the steering
vector and the TC motion vector.
Discussion
We learned that the steering concept is largely valid.
However, there are some differences between the steering
vector and the TC motion vector (in the model). Let’s
discuss the reasons!
Before recurvature
During recurvature
After recurvature
Reason 1 -Practical problem-
It is technically impossible to exactly separate the steering
flow and the TC circulation from the total wind field.
Total field
spatial low-pass filter
Steering flow
TC circulation
+
Reason 2 -Practical problemThe TC motion vector (arrow in green) is computed assuming the
motion vector is constant over the first 24 hours while the steering
vector is an instantaneous vector at T+0h.
Before recurvature
TC motion vector (arrow in green) is
calculated based on the minimum sea level
pressure positions at T+0h and T+24h
(forecasted field of ECMWF).
Before recurvature
TC motion vector (arrow in green) is
calculated based on the minimum sea level
pressure positions at T+0h and T+6h
(forecasted field of ECMWF).
Reason 3 –Scientific issue-
The TC is not steered by the “steering flow” at single level
layer (500 hPa in this presentation).
Concept of deep layer mean
Mass weighted deep-layer mean wind in several layers
such as 850 hPa, 500 hPa, 250 hPa is widely used as the
steering flow (e.g. George and Gray 1976).
However, there are still controversial arguments among researchers about
(1) the depth of the “deep-layer”,
(2) the width of the radial band to average the winds, and
(3) the dependency of the depth on the TC intensity.
Reason 4 –Scientific issue-
The asymmetric component of the TC circulation also
advects the TC vortex.
Asymmetric forcing
-External forcing
1)
Vertical wind shear
2)
PV anomaly in the mid- and upper-troposphere
3)
Surface inhomogeneities including the effect of geography
-Internal forcing
Dynamical forcing
1) Beta effect
Thermodynamic forcing
2) Convection
Decomposition of flows in the vicinity of TCs
Total flow
TC circulation
itself
Total flow minus
Background flow
Background flows associated
with synoptic features
Axisymmetric
circulation
Asymmetric
circulation
Steering
vector
Asymmetric
propagation
vector
L
H
Distinctive feature of azimuthal wavenumber 1 perturbation
Only azimuthal wavenumber 1 perturbation can create
(advection) flows over the maximum vortex area.
Azimuthal wavenumber
1 perturbation
Azimuthal wavenumber
2 perturbation
H
L
H
L
Azimuthal wavenumber
3 perturbation
L
H
L
H
H
L
H
L
Advection flow canceled
Beta effect
Meridional gradient of the Coriolis parameter creates a wavenumber
1 asymmetry, which advent the TC vortex toward the northwest.
Beta gyres
Contour: Stremfunction
1200km
Advection flow
Fiorino and Elsberry (1989)
2400km
Move of TC movement by beta effect
-Experiment using a nondivergent barotropic model-
Initially symmetric TC-like vortex moves
toward the northwest
Let’s see the difference between the TC
motion vector in the model and the actual TC
motion vector based on the best track data.
Prediction error
TC motion vector in the model (arrow in green) is calculated based on the minimum sea
level pressure positions at T+0h and T+24h (forecasted field of ECMWF) while the actual
TC motion vector (arrow in blue) is based on the best track positions at T+0h and T+24h.
Before recurvature
During recurvature
After recurvature
The difference of the TC motion vectors in green and blue is
the prediction
error of TC track prediction.
Discussion
What causes the prediction error?
1) Analysis errors:
Analysis errors in initial conditions for NWP evolve
into large forecast errors. Note that NWP models
affect the accuracy of the initial conditions because they
are created by blending observations and the bestestimate of the atmosphere, which is a short-range, say
six-hour, forecast by NWP models.
2) Model errors:
Our NWP models are not perfect (discretization,
computational errors, approximations in the physics
schemes, etc.)
3) Others:
There might be some physics that we have not known yet
What we have learned so far is that
the steering concept is largely valid.
Move on to the next topic on
the initial condition sensitivity of TC
track prediction
What we will learn from now is that
the representation of the steering flow in NWP models is
critical for accurate TC track predictions.