Munehiko Yamaguchi Typhoon Research Department, Meteorological Research Institute of the Japan Meteorological Agency 9:00 – 12: (Thr) Topic No. 1 Tropical Cyclone Movement Tropical Cyclone Ensemble Forecast Nanjing, China

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. Let’s take a look at how much the steering concept is valid to explain the TC movement in NWP models. (Chan 2010, Global Perspectives on Tropical Cyclones).

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 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) Typhoon Sinlaku Sinlaku moves north in the model at this time

Separation of the total field Total field Steering flowTC circulation + spatial low-pass filter

Layer image Typhoon Sinlaku 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.

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) Typhoon Sinlaku Sinlaku moves northeast in the model at this time

Separation of the total field Total field Steering flowTC circulation + spatial low-pass filter

Layer image Typhoon Sinlaku 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.

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) Typhoon Sinlaku Sinlaku moves east-northeast in the model at this time

Separation of the total field Total field Steering flowTC circulation + spatial low-pass filter

Layer image Typhoon Sinlaku 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.

Practice 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. Let’s calculate the steering vector and compare it with the TC motion vector in the model!!! 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 Steering flow Central position of Typhoon Sinlaku Streamfunction (ψ) field Contour interval: 2 x 10^5 Unit: m^2/s Use 321 km for

1m/s 2m/s 3m/s 4m/s 5m/s 6m/s Steering vector before recurvature 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. Estimate from the figure, calculate the amplitude of the steering vector and plot it.

Steering vector during recurvature Steering flow Central position of Typhoon Sinlaku Streamfunction (ψ) field Contour interval: 5 x 10^5 Unit: m^2/s Use 266 km for

1m/s 2m/s 3m/s 4m/s 5m/s 6m/s Steering vector during recurvature Estimate from the figure, calculate the amplitude of the steering vector and plot it. 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 Steering flow Central position of Typhoon Sinlaku Streamfunction (ψ) field Contour interval: 5 x 10^5 Unit: m^2/s Use 281 km for

1m/s 2m/s 3m/s 4m/s 5m/s 6m/s Estimate from the figure, calculate the amplitude of the steering vector and plot it. 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

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.

Before recurvatureDuring recurvatureAfter recurvature Discussion However, there are some differences between the steering vector and the TC motion vector (in the model). Let’s discuss the reasons! We learned that the steering concept is largely valid.

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 Steering flowTC circulation + spatial low-pass filter Technically impossible

Reason 2 -Practical problem- Before recurvature The 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). 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 Background flows associated with synoptic features Total flow Steering vector TC circulation itself Axisymmetric circulation Asymmetric circulation Asymmetric propagation vector Total flow minus Background flow HL Spatial low-pass filter

Distinctive feature of azimuthal wavenumber 1 perturbation Only azimuthal wavenumber 1 perturbation can create (advection) flows over the maximum vortex area. HL H H LL HH H L L L Azimuthal wavenumber 1 perturbation Azimuthal wavenumber 2 perturbation Azimuthal wavenumber 3 perturbation Advection flow canceled

Beta effect Meridional gradient of the Coriolis parameter creates a wavenumber 1 asymmetry, which advent the TC vortex toward the northwest. 1200km Advection flow 2400km Beta gyres Contour: Stremfunction H L Fiorino and Elsberry (1989)

Initially symmetric TC-like vortex moves toward the northwest Move of TC movement by beta effect -Experiment using a nondivergent barotropic model-

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.

Before recurvatureDuring recurvatureAfter recurvature 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. Prediction error The difference of the TC motion vectors in green and blue is the prediction error of TC track prediction.

Discussion 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 best- estimate 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 causes the prediction error?

Move on to the next topic on the initial condition sensitivity of TC track prediction What we have learned so far is that the steering concept is largely valid. What we will learn from now is that the representation of the steering flow in NWP models is critical for accurate TC track predictions.