Hodograph analysisHodograph analysisHodograph analysisHodograph analysis

James LaDueJames LaDue

FMI Severe Storms WorkshopFMI Severe Storms Workshop

June 2005June 2005

James LaDueJames LaDue

FMI Severe Storms WorkshopFMI Severe Storms Workshop

June 2005June 2005

OutlineOutlineOutlineOutline

• The hodographThe hodograph• ShearShear

– Hodograph lengthHodograph length– Bulk shearBulk shear– Shear curvatureShear curvature– Shear orientationShear orientation

• Storm relative flowStorm relative flow• VorticityVorticity• Storm Relative HelicityStorm Relative Helicity

HodographHodographHodographHodograph

• Storm type is critically Storm type is critically dependent on vertical dependent on vertical wind shear and storm-wind shear and storm-relative windsrelative winds

• Vertical wind shear Vertical wind shear difficult to analyze by difficult to analyze by visualizing wind barbsvisualizing wind barbs

• Best way to visualize Best way to visualize vertical wind structurevertical wind structure

HodographHodographHodographHodograph

XYZ 0000 UTC 6/15/2002My Favorite 0-10 km Hodograph

10 km9 km8 km7 km5 km4 km1 km2 km3 km6 kmSFCVRMVLMVmw Vobs

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HodographHodographHodographHodograph

• The hodograph line The hodograph line segments are the segments are the shearshear

XYZ 0000 UTC 6/15/2002My Favorite 0-10 km Hodograph

10 km9 km8 km7 km5 km4 km1 km2 km3 km6 kmSFCVRMVLMVmw Vobs

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HodographHodographHodographHodograph

• The hodograph line The hodograph line segments are the segments are the shearshear

XYZ 0000 UTC 6/15/2002My Favorite 0-10 km Hodograph

10 km9 km8 km7 km5 km4 km1 km2 km3 km6 kmSFCVRMVLMVmw Vobs

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ShearShearShearShear

• Layer Shear Layer Shear magnitudemagnitude

• The shear The shear magnitude is the magnitude is the length of each length of each hodograph line hodograph line segmentsegment

XYZ 0000 UTC 6/15/2002My Favorite 0-10 km Hodograph

10 km9 km8 km7 km5 km4 km1 km2 km3 km6 kmSFCVRMVLMVmw Vobs

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ShearShearShearShear

• Total 0 – 6 km Shear Total 0 – 6 km Shear magnitudemagnitude– Equals the length of Equals the length of

the hodograph linethe hodograph line

XYZ 0000 UTC 6/15/2002My Favorite 0-10 km Hodograph

10 km9 km8 km7 km5 km4 km1 km2 km3 km6 kmSFCVRMVLMVmw Vobs

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1 km

2 km 3 km

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6 km

51 km 2 3 4 6

ShearShearShearShear

• Complications in the Complications in the meaning of meaning of hodograph length hodograph length with complicated with complicated hodographshodographs– Large hodograph Large hodograph

length but difficult to length but difficult to assess storm type.assess storm type.

XYZ 0000 UTC 6/15/2002My Favorite 0-10 km Hodograph

10 km9 km8 km7 km5 km4 km1 km2 km3 km6 kmSFCVRMVLMVmw Vobs

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ShearShearShearShear

• Mean shearMean shear– A simpler method of A simpler method of

estimating shear estimating shear magnitudemagnitude

– Subtract the 6 km Subtract the 6 km wind from the mean wind from the mean of the lowest 500 mof the lowest 500 m

XYZ 0000 UTC 6/15/2002My Favorite 0-10 km Hodograph

10 km9 km8 km7 km5 km4 km1 km2 km3 km6 kmSFCVRMVLMVmw Vobs

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0 km

ShearShearShearShear

• Shear curvatureShear curvature– Has as much Has as much

impact on storm impact on storm behavior as shear behavior as shear magnitudemagnitude

ShearShearShearShear

• Shear orientationShear orientation– Does not affect Does not affect

supercell behaviorsupercell behavior– May be an May be an

indication of large indication of large scale synoptic scale synoptic conditionsconditions

– Profile A indicates Profile A indicates cold air advection cold air advection and subsidenceand subsidence

Storm-relative flowStorm-relative flowStorm-relative flowStorm-relative flow

• An observer sees An observer sees the winds in this the winds in this hodograph marked hodograph marked by the red vectorsby the red vectors

• The storm sees the The storm sees the winds in this winds in this hodograph marked hodograph marked by the blue vectorsby the blue vectors

Cross-wise vorticityCross-wise vorticityCross-wise vorticityCross-wise vorticity

• Crosswise vorticityCrosswise vorticity– Vorticity vector is Vorticity vector is

perpendicular to perpendicular to velocity vectorvelocity vector

– Vertical ascent Vertical ascent leaves vorticity leaves vorticity outside the outside the updraft.updraft.

vorticity

velocityshear

Cross-wise vorticityCross-wise vorticityCross-wise vorticityCross-wise vorticity

• Example of storm Example of storm seeing cross-wise seeing cross-wise vorticityvorticity– Storm motion is on Storm motion is on

the hodographthe hodograph– Updraft not initially Updraft not initially

correlated with correlated with vertical velocityvertical velocity

60 km

Vr

= horizontal vorticity

Vr = storm-relative velocity

C = Storm motion

C

Streamwise vorticityStreamwise vorticityStreamwise vorticityStreamwise vorticity

– Vorticity vector is Vorticity vector is parallel to velocity parallel to velocity vectorvector

– Vertical ascent Vertical ascent causes vertical causes vertical vorticity to vorticity to correlate with correlate with vertical velocityvertical velocity

vorticity

velocity

Streamwise vorticityStreamwise vorticityStreamwise vorticityStreamwise vorticity

• Example of storm Example of storm seeing streamwise seeing streamwise vorticityvorticity– Storm motion is off Storm motion is off

the hodographthe hodograph– Updraft is Updraft is

immediately immediately correlated with correlated with vertical vorticityvertical vorticity

6

0 km

VrC

Storm-Relative HelicityStorm-Relative HelicityStorm-Relative HelicityStorm-Relative Helicity

• DefinitionDefinition– Dot product of Dot product of

velocity and velocity and horizontal vorticityhorizontal vorticity

– SRH = SRH = V V dZ dZ– Integrate over a Integrate over a

vertical layer vertical layer – 0-1 km, 0-3 km0-1 km, 0-3 km

6

0 km

Vr

C

Velocity can be ground-relative or storm-relative

Storm-Relative HelicityStorm-Relative HelicityStorm-Relative HelicityStorm-Relative Helicity

• SRHSRH– Is proportional to the Is proportional to the

area swept out area swept out between the between the hodograph and C hodograph and C between two levelsbetween two levels

– The 0 – 3 km SRH is The 0 – 3 km SRH is swept outswept out

6

0 km

Vr

C

3

Storm-Relative Helicity Storm-Relative Helicity applicationsapplications

Storm-Relative Helicity Storm-Relative Helicity applicationsapplications

– SRH SRH 0-3 km 0-3 km The 0 – 3 The 0 – 3

km SRH is a good km SRH is a good indicator of supercell indicator of supercell potentialpotential

– SRH SRH 0-1 km 0-1 km The 0 – 1 The 0 – 1

km SRH is a good km SRH is a good indicator of supercell indicator of supercell tornado potentialtornado potential

6

0 km

Vr

C

3

Storm Relative HelicityStorm Relative HelicityStorm Relative HelicityStorm Relative Helicity

• LimitationsLimitations– Using storm-relative Using storm-relative

velocity, SRH velocity, SRH depends on storm depends on storm motion motion

– Storm motion is Storm motion is difficult to forecastdifficult to forecast

60 km

Vr

C

SRH vs shear as a supercell SRH vs shear as a supercell forecasting toolforecasting tool

SRH vs shear as a supercell SRH vs shear as a supercell forecasting toolforecasting tool

• Shear can be used Shear can be used without knowing storm without knowing storm motionmotion

• Once storm motion is Once storm motion is known, use SRH to known, use SRH to estimate supercell estimate supercell strengthstrength

60 km

Vr

C

SummarySummarySummarySummary

• We showed the creation of a hodographWe showed the creation of a hodograph

• ShearShear

• Storm-relative flowStorm-relative flow

• Stream-wise vs. Cross-wise vorticityStream-wise vs. Cross-wise vorticity

• Storm Relative HelicityStorm Relative Helicity