An Objective Nowcasting Tool that Optimizes the … · An Objective Nowcasting Tool that Optimizes the Impact of Frequent Observations in Short-Range Forecasts ... - Moisture from

Paper 2.26

An Objective Nowcasting Tool that Optimizes the Impact of Frequent Observations in

Short-Range Forecasts

Ralph Petersen1, Robert M Aune2

1 Cooperative Institute for Meteorological Satellite Studies (CIMSS), University of Wisconsin – Madison, Madison, Wisconsin, [email protected]

2 NOAA/NESDIS/ORA, Advanced Satellite Products Team, Madison, Wisconsin, [email protected]

Any Nowcasting Model Should:

Be used to update/enhance other numerical guidance:Be FastBe run frequently

Not constrained by longer-range NWP ‘stability’ issues

Use all available data:“Draw closely” to data

Be useful in anticipating rapidly developing weather events:“Perishable” guidance products – rapid delivery

Run Locally? – Few resources beyond comms, users easily trainedFocus on the “pre-storm environment”

Increase Lead Time / POD and Reduce FAR

Goals: - Increase the length of time that forecasterscan make good use of dependable data (vs. NWP output) for their short range forecasts

- Provide objective tools to help them do this

Background: ALL Forecast Models have 2 Essential Computational Components

The Model Dynamics-- The Equations of Motion --

The Model Physics-- Physically forced Processes --

Many occur at small scales and must have their effectsapproximated

In traditional grid-point NWP models, all of these calculations are performed on a fixed grid

(proposed by Richardson in the early 1900s)

But - For Nowcasting - Have we forgotten the First Rule of Forecasting

Always remember to look out of the window

What do you see? - Clouds

What are they doing? - Moving past us as ‘entities’

But advective terms in ‘classical’ models have to ‘recreate’ the clouds as they move from grid point to grid point

This CAN be changed - especially for Nowcasting! - If we follow a simpler path -

What is the impact of (and limitations imposed by) converting the Simplest LaGrangian Form of Equations of Motion

[ Parcel Acceleration = Sum of Coriolis and Pressure Gradient Forces ]

Into Local Eulerian Wind Change forms, which include calculations of advection - which, for wind, involves advection of inertia -

( and adds non-linear, spatially dependent calculations – and errors ! )

- Source of CFL Stability Criteria -20 km model should uses a 30 sec time step and typically

delivers 1 hr forecast 45 minutes after last data input

{ Inertial Advection Terms }

Note largehour to hourWind Changes- at stationarygrid points >>

0 &1 hr 300 hPa Winds --------- 0-1 hr Wind Change

Let’s look at a case to SEE the impacts of wind terms

0 hr LaGrangian hourly Acceleration – 300hPa

Let’s first look at the spatial and temporal variability of theaccelerations that would be applied to moving parcels

0-1 hr Change

Parcel Accelerations driven by:

Large-scale, well-organized patterns

Maxima 2-3x field mean

Hourly changes ½ of field mean

NWP - 0 hr Inertial Advective hourly Accel. – 300hPa

Next let’s look at theSpatial and temporalImpact of the EulerianInertial Acceleration Terms

0-1 hr Change

Grid point wind changes driven by:

Smaller-scale, less-well-organized patterns, with large gradients

Maxima 4-5x field mean

Hourly changes > same field mean

0 hr LaGrangian & NWP hourly Acceleration-300hPa

Intrl Adv hourly Accel.

Compare the fields driving wind changes:

The Top represents the LaGrangian, “moving parcel” approach

The Bottom is the complication added by using Stationary Grid Points


Eulerian hourly Accel.

Compare the fields forcing wind change

The Top represents the LaGrangian, “moving parcel” approach

The Bottom is the Net Accelerationapplies at

Stationary (Eulerian) Grid Points

Comparison of accelerationused in

LaGrangian vs.Eulerian Models





Terms cancel slightly, butEulerian Accerations are:Smaller-scale & less-organized(and therefore larger spatial gradients

and greater spatial/temporal variability)

Maxima 2-3 times greaterChange greatly over time



Terms cancel slightly, butEulerian Accelerations are:Smaller-scale & less-organized(and therefore larger spatial gradients

and greater spatial/temporal variability)

with maxima 2x greater



NWP – 2 hr Wind Error – 300hPa


Visually similar though not exactPattern alikeMagnitudes different

Also – a driver for CFL stability and higher order (costly?) advection schemes (e.g., semi-LaGrangian)

Are wind forecast errorcorrelated to the inertial

advection terms?

To capture advection adequately in a grid point model, you need to sample wave (feature) thoroughly

More than 10 Grid Points are needed to retain features well - - - BUT many features important for

nowcasting are << than current model grid spacing

Is a LaGrangian Model feasible for Nowcasting?

Yes – What is needed at a minimum are height gradients and winds –from obs or analysis

- Interpolate height gradients to parcel locations- Calculate parcel accelerations (Error growth is predictable!)- Move parcels forward in time

- Can include much metadata (properties, quality …)

- Adjust mass fields (minimal impact in 3 h fcst)- Re-grid all ‘projected observations’ for output graphics

Can it be done?Yes – Runs with 15 minute time steps (vs. 1 m for 20 km NWP)

What are the limitations?- Wind errors may grow as forecast length approached

½ inertial period (9 hours), but in a predictable mannor- Any new road has hidden potholes- Not within existing development programs

- Data can be inserted (and combined) directly without ‘analysis smoothing’

– Retains maxima and minima and extreme gradients

- Spatial resolution adjusts to available data density- GOES derived products can be projected forward at full

resolution – even as they move into ‘data void’ cloudy areas - Data can be tracked (and aged) through multiple time periods- Use all data at time observed – not binned- Use best aspects of all available data sets

e.g., Cloud Drift winds can be combined with surface obs cloud heights to create a ‘partly cloudy’ parcel with good height and good motione.g., Wind Profiler data can be projected forward and include accelerations

What are the benefits?- Quick and minimal resources needed

- Can be used ‘stand-alone’ or to ‘update’ other NWP guidanceDATA DRIVEN

- Data can be inserted (and combined) directly without ‘analysis smoothing’ – retain maxs and mins – Forecast Imagery?


- Can be used ‘stand-alone’ or to ‘update’ other NWP guidance

DATA DRIVEN

Some Candidate Data Uses

- Winds from Raob, Aircraft (80,000 daily), VAD, Profilers, CDW- Moisture from GOES, POES, AIRS?, AERI, GPS?

-For example, AERI T&Q profiles from OK can be combinedwith Profiler winds and then project data forward in time,monitoring change in downstream moisture flux convergence

-Also, GOES moisture (θE?) can be combined withAircraft/Profiler/VAD winds and projected forward to forecast “stability images”

- Data can be inserted (and combined) directly without ‘analysis smoothing’ – retain maxs and mins – Forecast Imagery?


- Can be used ‘stand-alone’ or to ‘update’ other NWP guidance

DATA DRIVEN

Coordinate Independent

- Initial tests done in pressure for convenience- Propose developing isentropic system

- May be able to reduce dependence on ‘deep’ hybrid surface domain in isentropic models

-Will combined LaGrangian Dynamics and Eulerian surface model-Forward Data Projection technique preserves data and accelerationsfor use in mesoscale data assimilation

Objective Nowcasting Development to date

What are we trying to accomplish?

Forecasters now use GOES imagery to monitor weather – and makeSubjective forecasts into the future

Increasing use of Derived Image Products

We are developing tools to allow forecasters to:- Project detailed satellite products into the near future – objectively- Preserve observed extreme gradients and max/min features- Retain earlier IR information in areas where clouds later grow- Provide rapid and timely updates to NWP guidance- Focus on weather events of greatest local need- Mix multiple data sources

Why are we proposing to use aLaGrangian Approach for

Objective Nowcasting?

Background: Nowcasting Task Description

•A new objective nowcasting tool has been formulated which:

•Preserves and takes full advantage of both:

•Horizontal and vertical detail (discontinuities) inherent in future hyper-spectral satellite products and•Frequent information updates available from current and future geostationary instruments.

•The techniques is:

•Fast (a must due to the parishability of information regarding severe weather development),

•Preserves observed data to the fullest extent (e.g., retains data extremes) and

•Integrates GOES data with data other sources in a timely and faithful manner.

•Update conventional NWP guidance•Uses minimal computing resources, a necessity for forecast office application.

Perform analytical accuracy and performance tests

Tests showed marked reduction in advection amplitude and phase errors, especially for shortest wavelength features

Tests also showed efficiency – Allows 8-15 minute time steps

E ule r i a n Sine Wa ve Ampl i tude E r r or

A f t e r 1 W av e le ngth T r ans lat ion

y = 0 . 4958x-1 .3 2 8 5

0%

10%

20%

30%

40%

50%

60%

8 12 16 20 24 28 32 36 40

P t s i n W a v e

Std Dev Erro r

Power (Std Dev Erro r)

Euler ian Sine Wave Phase Er r orA f t e r 1 W av e le ngth T r ans lat ion

y = 39. 793x-1 .4 1 2 9

0

10

20

30

40

50

8 12 16 20 24 28 32 36 40

P t s i n W a v e

Std De v E r r or

P owe r (Std De v E r r or )

Eliminates non-linearInertial Advection terms

Sample of a LaGrangian Diagnostic Study of

The development of a Pre-Convective Environment

using 3-hourly Analyses of Radiosonde DataFrom SESAME

From Kocin et al., 1986.

At 1500 GMT on 305K -Southerly flow at ABI and SEP MAF flow is from South-South-West

Key: Pressure Wind

Mixing (kt)Ratio

Let’s see if a different approachcan better preserve

observed data variations

An example using real data

By 1800 GMT on 305K - Flow at ABI and SEP has increased and moistened MAF flow has increase and backed to South-WestBy 2100 GMT -Flow at ABI and SEP has increased and backed MAF has warmed and moved undergroun

Key: Pressure Wind

Mixing (kt)Ratio

Where did the air passing over. MAF, ABI and SEP Originate?Backward Trajectories were constructedFrom 1800 and 1500 GMT starting at MAF, ABI and SEP

Key: AGeo PressureWind

Saturation (kt)Deficit Speed

Used LaGrangian forms of Equations of Motion:

du / dt = f v - g MZ / Mx dv / dt = - f u - g MZ / My

This eliminated difficult non-linear inertial advection terms

Where did the air passing over. MAF, ABI and SEP Move To ? Forward Trajectories were constructedFrom 1800 and 2100 GMT starting at MAF, ABI and SEP

Key: AGeo PressureWind

Saturation (kt)Deficit Speed

Used LaGrangian forms of Equations of Motion:

du / dt = f v - g MZ / Mx dv / dt = - f u - g MZ / My

This eliminated difficult non-linear inertial advection terms

DIV=(-1294/1624)/7200 = -1.1x10-4 s-1

Clearly shows Development of Interplay between

Dry Line from West and Moist Gulf Flow from South

DIV=(-1294/1624)/7200 = -1.1x10-4 s-1

262o

255o

237o

218o

262o

268o

Angle of line connecting

MAF and ABI Trajectories

With the LaGrangian approach, DIVERGENCE at a point can be determined from the change of vorticityof sets of parcels moving over that point, using:

d/dt (ξ + f) = - (ξ + f) DIVergence or

DIV = - d/dt (ξ + f) / (ξ + f)

What other diagnostic toolsdoes a LaGrangian approach

facilitate?

DIV=(-1294/1624)/7200 = -1.1x10-4 s-1

262o

255o

237o

218o

262o

268o

Angle of line connecting

MAF and ABI Trajectories

10.9

12.4

16.7

17.2

Vorticityx 10-5 s -1

With the LaGrangian approach,

d/dt (ξ + f) = - (ξ + f) DIVergence or DIV = - d/dt (ξ + f) / (ξ + f)

(6/57)/3600=2.92x10-5+8x10-5=1.092x10-4(7/57)/3600=3.41x10-5+8x10-5=1.241x10-4

(18/57)/3600=8.77x10-5+8x10-5=1.677x10-4(19/57)/3600=9.26x10-5+8x10-5=1.726x10-4

Change in Vorticity at 1900 GMT yields1.04x10-4 CONVERGENCE

What other diagnostic toolsdoes a LaGrangian approach

facilitate?Vorticity Change >> Divergence

DIV=(-1294/1624)/7200 = -1.1x10-4 s-1

262o

255o

237o

218o

262o

268o

10.9

12.4

16.7

17.2

Vorticityx 10-5 s -1

With the LaGrangian approach,

d/dt (ξ + f) = - (ξ + f) DIVergence or DIV = - d/dt (ξ + f) / (ξ + f)

(6/57)/3600=2.92x10-5+8x10-5=1.092x10-4(7/57)/3600=3.41x10-5+8x10-5=1.241x10-4

(18/57)/3600=8.77x10-5+8x10-5=1.677x10-4(19/57)/3600=9.26x10-5+8x10-5=1.726x10-4

Change in Vorticity at 1900 GMT yields1.04x10-4 CONVERGENCE

This rapid localized development Low-level Convergence

was coincident with drying andGrowth of Divergence in the

Exit of the Jet Streak Aloft

Objective Nowcasting Model development

Analytical tests of advantage of LaGrangian techniques to different dynamical processes especially relevant to nowcasting have been built emphasizing the Jet Streak. The goals are two-fold:

1) To provide evidence of the advantage of the LaGrangian approach in a manner relevant to forecasters and

2) To provide a tools for teaching:

1) A more thorough understanding of the dynamical processes involved in mesoscale systems – especially those related to creating an environment conducive to severe storm development – and

2) How the result of these dynamics is shown in rapidly changing GOES satellite data

A Microsoft EXCEL version of the LaGrangian Parcel method has been developed to simulate the full dynamical evolution for air parcels moving:

From a situation of completely balanced, straight-line flow

• Into a sinusoidal geopotential field supporting an Idealized Jet Streak.

Options are available to:

• Change the strength and shear in the basic balanced flow and

• Modify the size, intensity and Jet Streak’s propagation rate

A Variety of output diagnostics are available.

Results can be viewed in either earth and flow relative domains – an important feature for following the evolution of mesoscale processes.

(Due to use of Excel - System is fully transportable)

Examples follow

User Interface – Straight line flow if no Jet Streak specified

Specifying a Jet Core strength alone is not sufficient alone

Note that the parcels confluence is offset downstream from pressure gradient (geostrophic wind) maxima

Specifying Jet Core propagation rate resolves the problem

The (observed) rule of thumb that Jet Streaks propagate at 50% of the speed of the basic flow

works very well for parcels in center of Jet StreakNote: Parcels to North and South of Jet Streak axis

accelerate at different rates – sooner (an non-symetically) to the north and later to the south – new insights

Adding shear to the basic flow makes the Jet Streak shape more realistic

Diagnosed vorticity showsconsistent + and – areas,

But not divided into four symmetrical quadrants as classic models suggest

Divergence/Convergence is also not divided into four symetrical quadrants.Divergence on the cyclonic side is offset slight ahead and left of the Geostrophic max and extends well ahead of the core on the nticyclonic

side. Divergence fields are dominated by cross-stream flow components.Convergence in anticyclonic exit region aloft corresponds with “dry Slots’ in WV imagery,

with strong Divergence/Convergence

transition ahead

Increase in strength of Jet Streak Core is limited

As strength of pressure gradient in Jet Streak increases, Parcels exiting the jet streak nearly collide.

LaGrangian approach has allowed parcels to transition frombalanced flow and 111 km intervals to turbulent flow and spacing of a few kms – using 15 minute time steps. Can’t be done that efficiently with Eulerian approaches

As Jet Streak Speed and basic flow Shear increase, Vorticity, Vorticity Tendency and Divergence increase in left exit region

Parcels to left of Jet Streak Core accelerate first more slowly and then more quickly than parcels farther north. This causes parcel Vorticity to first increase and then decrease,which, in a LaGrangian framework, has a direct effect on increasing first Convergence

and then, within only a few hours, Divergence

South parcel lagsothers

South parcel hascaught up

Small additions to Jet Streak Speed and basic flow Shear result in very rapid Changes of Vorticity, Vorticity Tendency and Divergence in left exit region,

25% increase in Jet Streakmore than doubles magnitudeof changes to parcel Convergence/Divergenceand shortens interval between

Further Increase in strength of Jet Streak

leads to development of Dynamic Instability

(negative absolute vorticity)and results in extreme

Convergence/Divergencecouplets and

instantaneous overturning (Clear Air Turbulance)

Daily Testing of the initial prototype LaGrangian nowcasting model updating system has begun at CIMSS to provide short-range satellite image nowcasts

The LaGrangian Nowcasting model is being upgraded using 10 km RUC grids as backgrounds.

This change will allow:

Better compatibility with full resolution GOES DPIs

Higher resolution initial winds

Integration of other data sources.

Results are being produced in “DPI lookalike Formats”

Visualization tools must be incorporated to allow forecasts to see the predicted DPIs in formats identical to the current observational products.

Daily results will be posted on a web page.

Incorporating of other data sources

Aircraft, Wind Profiler and cloud tracked wind data will be integrated to provide observed wind as well as moisture data updates.

Offline test of the LaGrangian approach using observed Wind Profiler data[and in the near future AERI data (used to emulate GOES-R) and current GOES data]have begun using data from the May 1999 Oklahoma City tornado case.

The sample shown below illustrates how parcels (initialized at any location and any level) can be projected forward in time to identify:

• Air Parcel Source Regions• Projected paths• Future development of Divergence/Convergence• Multiple level combinations• Development of Convective Instabilities• CAPE / CINH

Using the trajectory procedure in both a Forward (forecast) and Backward (diagnosis) mode.

-Wind Profiler data taken at 2100UTC (shortly prior to the first severe thunderstorm development) are both traced backward (to trace the origins of the air parcels) and forward (to project their future paths and indicate potential divergence) for 3 hours.

Note:1- the increase in convergence between 2100 and 0000 UTC and 2- the increased cyclonic curvature during the period of storm development, an area which 3 hours earlier had shown divergence.

These results are consistent with diagnostic calculation of divergence and moisture flux divergence made using the Wind Profile and AERI data.

Incorporating of other data sources

Although the Wind Profilers are land based, they provide an excellent source of wind data to be used in conjunction with GOES Water Vapor information in order to monitor Moisture Flux Convergence.

- AERI data over this area will be used to emulate GOES-R retrievals and compared with results from the current GOES systems in additional tests.

One advantage of the ‘off-line, stations based’ system used in these tests is that it is very simple and PC based – thereby easily transferred to WFO use – and can be run in ‘true real time’ and refreshed whenever new data arrive, without waiting for 45-60 minute after each hour to view the most timely NWP base guidance currently available (the RUC).

Summary - A LaGrangian Nowcasting Model Can:

Be used to update/enhance other numerical guidance:Be FastBe run frequently

Not constrained by longer-range NWP ‘stability’ issues

Use all available data:“Draw closely” to data (retain maxima, minima and extreme gradients)

Be useful in anticipating rapidly developing weather events:“Perishable” guidance products – rapid delivery

Run Locally? – Few resources beyond comms, users easily trainedFocus on the “pre-storm environment”

Increase Lead Time / POD and Reduce FAR

Goals: - Increase the length of time that forecasterscan make good use of dependable data (vs. NWP output) for their short range forecasts

- Provide objective tools to help them do this

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An Objective Nowcasting Tool that Optimizes the … · An Objective Nowcasting Tool that Optimizes the Impact of Frequent Observations in Short-Range Forecasts ... - Moisture from