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ENDGame: A new dynamical corefor seamless atmospheric prediction

July 2014

Contents

1 Executive summary 2

2 Introduction 3

3 ENDGame description 7

4 Improvements to physics, resolution, data assimilation and satellite data usage 9

4.1 Improvements to the physical parametrizations . . . . . . . . . . . . . . . . . . . . . 9

4.2 Resolution upgrade to the deterministic global NWP model and data assimilation . . 9

4.3 Additional package of satellite changes . . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Performance benefits 12

5.1 Improved representation of extra-tropical and tropical storms . . . . . . . . . . . . . 12

5.2 Improved representation of tropical equatorial waves and the Madden–Julian Oscillation 17

5.3 Improvements to the model representation of gravity waves . . . . . . . . . . . . . . 19

5.4 Improved forecasts of aviation “jet level” winds . . . . . . . . . . . . . . . . . . . . . 19

6 Conclusions and future direction 23

Appendix A List of improvements to the model’s physics 24

© Crown Copyright 2014 1

1 Executive summary

At the Met Office we are continually developing our weather and climate models to improve

their accuracy and provide new capability. Usually these upgrades are the combination of

a number of small improvements made at short but regular intervals that contribute to the

development of the models. This year, however, we have made a major change by adopting

the new “ENDGame” dynamical core. This is the culmination of over 10 years work and is

an important step in our ongoing model development plans. In this report we describe the

motivation for ENDGame and the benefits that it brings.

Modern computer models of the atmosphere include many complex physical processes that each

have local influences and feed back into the general circulation. At the heart of these models,

however, is the solution of the dynamical equations of motion (Newton’s laws applied to a gas). For

this reason, the model component that solves these equations is called the “dynamical core”. The

dynamical core used in the Met Office Unified Model prior to July 2014 is known as “New Dynamics”

and was first introduced in 2002. The introduction of New Dynamics was a major step forward as

it solved an unprecedentedly accurate set of equations. This allowed us to pursue our seamless

modelling approach by using the same dynamical core for very high-resolution weather forecasts

as for centuries-long climate projections. To solve the New Dynamics equations both stably and

quickly, we needed to apply artificial damping, which removes detail from the forecasts. In addition,

its scalability (the increased speed achieved by using more computer processors) was approaching

its limit, which impeded our ability to run higher resolution models on our supercomputers.

To improve these aspects of the model, whilst maintaining the benefits of New Dynamics, our

Dynamics Research team and Professor John Thuburn from the University of Exeter developed

“ENDGame” (Even Newer Dynamics for General atmospheric modelling of the environment). This

development took nearly 10 years and in the past two years staff from across the Met Office

have tested and evaluated its impact and prepared our operational systems for its implementa-

tion. ENDGame is now being used for global weather and climate prediction work and we will move

our regional and seasonal prediction systems to use ENDGame over the next year.

In global models, ENDGame’s improved accuracy and reduced damping produces more de-

tail in individual synoptic features such as cyclones, fronts, troughs and jet stream winds.

In the tropics, a combination of ENDGame, increased resolution and improvements to the

model’s physics provides unprecedented improvements to our predictions of tropical cy-

clone intensity and position. ENDGame’s improved scalability has allowed us to increase

the resolution of our global weather forecasts which provides additional improvements to

forecast accuracy. It will also allow us to further increase the model’s resolution when our

supercomputing capability increases.


2 Introduction

At its simplest the Earth’s atmosphere can be considered to be a rotating body of gas subjected to

heating and cooling. The heating and cooling arises from the absorption, emission and subsequent

reabsorption of solar energy. In particular the heating and cooling varies in both time and space.

This variation causes changes in pressure which drive the winds. Newton’s second law of motion

together with the first law of thermodynamics and conservation of mass (the governing equations)

determine how the gas responds to the heating and cooling (see Tech Box 1). This simple picture is

complicated by the presence of the liquid and frozen phases of water and associated latent heats,

as well as surface emissions and chemical reactions.

Tech Box 1: Dynamical core (dry) equations

Newton’s second law of motion:

Dv

Dt+ 2Ω× v + cpθ∇Π− g = Sv

The first law of thermodynamics:Dθ

Dt= Sθ

Conservation of mass:Dρ

Dt+ ρ∇ · v = 0

Equation of state for a perfect gas:

Π(1−κ)/κ =R

p0θρ

v is the three-dimensional wind vector; Ω is the Earth’s rotation vector; cp is the specific heatcapacity of air at constant pressure; θ is potential temperature; Π is Exner pressure; g isthe gravitational acceleration; Sv represents the effects of the physical parametrizations onv; Sθ represents the effects of the physical parametrizations on θ; ρ is the density of dry air;κ = R/cp where R is the gas constant; and p0 is a reference pressure value. D/Dt indicatesthe rate of change following an air parcel.

In principle, the governing equations tell us everything about the motion of the gas, from planetary

scales down towards the molecular scale. In practice however, we have to solve the equations on

a computer. To do this we digitise the equations by averaging them over a relatively large box (a

grid box). The size of this box is called the resolution of the model. Similar to the definition of a

television screen, increasing the resolution of the model gives sharper more realistic features and

finer, smaller scale processes are resolved. It is the dynamical core of the Unified Model (UM)

that is responsible for solving Newton’s laws on these grid boxes. The dynamical core is therefore

responsible for the larger scale features (be that fronts and high pressure systems in a global model,

or for example sea breezes in a high resolution, limited area model). The effects of the “missing”

processes, those that are either diabatic or occur at scales that cannot be resolved by the grid boxes,


are provided by the physical parametrizations; these determine the details close to the resolution of

the model, such as convective clouds and details of the rainfall.

No matter how accurate a forecast is, its value is strongly dependent on the timeliness of its delivery

— the perfect forecast today for yesterday’s weather is of no use to anyone! To meet the demands

of our customers, the operational forecast system has to process a vast range and number of

observations to provide the starting point for the model and then go on to produce a forecast for the

entire globe for 7 days ahead, all within approximately 1 hour.

This is a significant challenge and to achieve it the equations used in almost all dynamical cores are

only approximations to the full equations. An important and distinguishing aspect of the evolution

of UM dynamical cores has been the gradual removal of these approximations. This has led to us

using ever more accurate equations but perhaps more importantly it means that the same dynam-

ical core can be used across a wide range of scales, from the large planetary scales of 1000s of

kilometres down to small scale weather events at a kilometre or even less. This approach has been

fundamental to the Met Office seamless modelling strategy.

A significant step in delivering that strategy was the development of the current dynamical core

of the UM, known as New Dynamics (Davies et al.1). It became operational in 2002 and was the

first operational model to solve the virtually unapproximated equations — the deep-atmosphere,

nonhydrostatic equations (see Tech Box 2). To do so whilst respecting the strict time constraints

for delivery of the forecasts was a remarkable feat. This was achieved by implementing state-of-

the-art numerical methods but applied innovatively well beyond their usual scope. These numerical

methods are referred to as “semi-implicit semi-Lagrangian” (see Tech Box 3).

New Dynamics has served us well over more than a decade: not only have we continued to im-

prove the skill of our large scale forecasts at the rate of 1 day lead time per decade (so for example

today’s 3 day forecast is as accurate as the 2 day forecast was 10 years ago) but we have seen

the introduction of a very high resolution (1 12 km) model over the UK which provides unprecedented

levels of detail to our forecasters. Our seasonal forecast (GloSea) demonstrates skill in predicting

large-scale circulation patterns in the tropics (e.g. associated with the El Nino Southern Oscilla-

tion) and extra-tropics (North Atlantic Oscillation — Scaife et al.2) and our climate predictions have

demonstrated high levels of skill compared to other coupled models across a range of metrics (e.g.

Martin et al.3). However, to achieve what it did, with the knowledge and understanding available

at the time of its design, certain aspects of the numerical schemes used in New Dynamics are un-

stable (which means that the computer program sometimes fails to successfully complete). This1T Davies et al. “A new dynamical core for the Met Office’s global and regional modelling of the atmosphere”. In: Quarterly

Journal of the Royal Meteorological Society 131 (2005), pp. 1759–1782.2A. A. Scaife et al. “Skillful long-range prediction of European and North American winters”. In: Geophysical Research

Letters 41 (2014), pp. 2514–2519.3G M Martin et al. “Analysis and Reduction of Systematic Errors through a Seamless Approach to Modeling Weather and

Climate”. In: Journal of Climate 23 (2010), pp. 5933–5957.


Tech Box 2: Approximate vs unapproximated equations

Hydrostatic vs nonhydrostatic: the hydrostatic approximation assumes that the pressureat any location is determined by the weight of air above that point. It therefore ignores theeffects of the acceleration of vertical motion. This is a very accurate assumption for resolvedscales greater than 10 km but becomes increasingly less accurate at smaller scales. BothNew Dynamics and ENDGame are nonhydrostatic models and so do not suffer from beinglimited to large scale applications.

Shallow vs deep: the shallow approximation exploits the fact that the depth of the tropo-sphere (the region of the atmosphere primarily responsible for our weather) is much shal-lower than the radius of the Earth. This means that locally the curvature of the Earth canbe neglected. This is a very accurate approximation which only becomes questionable if weare interested in detailed processes much higher up in the atmosphere, for example spaceweather. However, associated with the shallow approximation is a simplification of the Cori-olis effect — the important influence that Earth’s rotation has on our weather and climate.This is a much less accurate approximation, increasingly so towards the equator, particularlyfor deep tropical vertical motion. Removing this assumption was the primary motivation forremoving the shallow approximation from the UM and making it a deep model. Both NewDynamics and ENDGame are deep-atmosphere models.

effect was partly mitigated by the addition of artificial damping and diffusion (which smooths out

the solution compared to reality) but the model still suffers from occasional failures, which require

additional computational or human resource to resolve. To address these issues, a programme of

research, known as ENDGame (Even Newer Dynamics for General atmospheric modelling of the

environment), was instigated soon after New Dynamics became operational. More than a decade

later that work is now coming to fruition as ENDGame replaces New Dynamics in our global model

configurations of the UM.

This report describes the ENDGame dynamical core and its benefits for performance on both

weather and climate prediction timescales. On 15 th July 2014 ENDGame became operational

in our global (deterministic4 and ensemble5) Numerical Weather Prediction (NWP) systems follow-

ing completion of operational trialling. Also included in the global deterministic model upgrade and

briefly described in this report are:

• An increase in the horizontal resolution from 25 km (labelled N512) to 17 km (N768).

• Important revisions to the physical parametrizations.

• Improvements to the resolution used in our data assimilation process to define the initial state.

• Improved use of satellite data in this data assimilation.4A single forecast run with the highest resolution affordable from our best estimate of the initial state of the atmosphere.5Multiple runs (25-50) of a model (usually at lower resolutions) from slightly perturbed initial conditions and with small

perturbations to the model’s physical formulation. Ensembles are designed to capture the inherent uncertainty in the mea-surement of the initial atmospheric state and in our knowledge of the model physics to provide a probabilistic estimate of therisk of severe weather.


Tech Box 3: Semi-implicit semi-Lagrangian

Crucial to making good forecasts is the accurate transport of the properties of a parcel ofair by the wind. Many methods for achieving this can be impractically expensive on a globallatitude-longitude grid. However the semi-Lagrangian (SL) method is both accurate andpractical on such grids. It works by tracing back where a parcel of air has come from andevaluating its properties at that point by interpolation. The downside to this method thoughis that it does not exactly conserve the quantity being transported.

The remaining terms of the equations (those not associated with transport) are responsiblefor the various wave-like motions of the atmosphere: planetary waves, gravity waves andsound waves. Each of these modes is more or less important for the evolution of theatmosphere but each needs to be handled stably by the numerical scheme. For examplesound waves play a negligibly small direct role in determining the weather yet they are thefastest propagating waves and therefore could dramatically increase the time it takes forthe model to run. This problem is overcome by applying the semi-implicit (SI) scheme tothese terms. This involves averaging each term over the time step. The various waves arethen stable but only those that vary slowly enough (which are those waves of interest andimportance) are handled accurately.

It is the use of this combination of schemes, the SISL approach, that allows both New Dy-namics and ENDGame to achieve the stringent efficiency requirements for operational use.

Finally, the ENDGame dynamical core will also be rolled out in our (1 12 km) UK NWP system and

global seasonal forecast (GloSea) in early 2015 and is already being used as the basis for the

atmospheric component of the next generation Earth-System climate prediction model (UKESM1)

being developed by the Met Office in collaboration with UK academia.


3 ENDGame description

ENDGame solves the same virtually unapproximated equations as New Dynamics and in essence

uses the same numerical approach. However, a number of significant changes to these numerical

schemes has been implemented that improves its behaviour and performance.

The most significant of these changes is the introduction of an iterative approach to solving the

set of equations. Essentially ENDGame uses something similar to the New Dynamics solution as

only a first estimate to its solution. From this (already very accurate) first estimate it then creates

successively better solutions, building on the knowledge of each earlier estimate (see Tech Box 4).

Tech Box 4: Iterative approach to the model time step

New Dynamics: This schematic illustrateshow the UM structures the tasks requiredwithin a single model time step, where thesolid lines denote the approach used in NewDynamics. “Slow” physical processes (suchas radiation, cloud and precipitation) areapplied to the solution from the previous timestep, whilst “fast” processes (such as sub-gridturbulence and convection) are applied aftertransport from the SISL scheme. Finally,we solve for the atmospheric pressure. InNew Dynamics, this solution for the pressurecontributes to a large proportion of the totalcomputational cost.

ENDGame: The dashed arrows denote theparts of the time step that are iterated inENDGame. The iterative approach to the “in-ner loop” allows a simpler, more scalable solu-tion for pressure. Iterations of the “outer loop”provide improved estimations for the end oftime step quantities to be used within the SISLscheme, improving the numerical accuracy ofthe final solution. Currently, we apply 2 itera-tions in each of these loops.

It might be imagined that this would significantly increase the cost of ENDGame compared with

New Dynamics and this was indeed a major concern during its development. However, there are

two factors that mitigate that cost. The first is that the iterative nature of the scheme permits us to

simplify certain aspects of each iteration whilst ending up solving the full equations without simplifi-

cation. This reduces the cost of each iterative step considerably, but when run on a small number

of processors ENDGame is still more expensive than New Dynamics. This is where the second

mitigating factor comes in: ENDGame is significantly more scalable than New Dynamics (Fig. 1).

This means that if the number of processors on which the model is run is doubled then the time it


ENDGameNew Dynamics

Number of Power 7 nodes

Strongscalingfactor

20018016014012010080604020

5

4.5

4

3.5

3

2.5

2

1.5

1

Figure 1: Strong scaling plot for ENDGame and New Dynamics forecasts at N768 resolution on the IBMPower 7 supercomputer. This shows the number of times faster the forecasts run on a given number of nodescompared to a baseline forecast on 24 nodes. 1 IBM node contains 32 processors.

takes ENDGame to complete is closer to half the original time than New Dynamics. On the number

of processors used for a typical production forecast ENDGame runs in a similar or shorter time

than New Dynamics. Indeed this increase in scalability is essential to us being able to increase the

mid-latitude resolution of the global model from 25 km to 17 km and still produce the forecast within

1 hour; New Dynamics could not achieve that because of its much poorer scalability.

The cause of the improved scalability of ENDGame is two-fold. The first is the simplifications of each

iteration alluded to above; each iteration is more straightforwardly scalable than the full scheme used

in New Dynamics. A more significant cause is that whilst both ENDGame and New Dynamics solve

the equations on a latitude-longitude grid with an associated clustering of meridians near each pole,

ENDGame radically changes how different variables are stored near to the pole. This removes the

need to solve a complex equation at the polar point. This directly improves scalability by reducing

communication between processors at the pole, but also indirectly improves it by providing a more

numerically stable solution, which requires more communication-intensive filtering near the poles.

In terms of its impact on the quality of the model forecast, the main benefit of ENDGame comes from

the improved numerical accuracy discussed above. This provides the technical benefit of making

the model more computationally robust (which allows it to run without program failures) but with

minimal artificial damping and no artificial diffusion (less smoothing of the solution). The impacts of

this will be demonstrated later in this report.


4 Improvements to physics, resolution, data assimilation and

satellite data usage

4.1 Improvements to the physical parametrizations

During the final stages of ENDGame’s development, we continued to pull through improvements

to the physical parametrization schemes, which in global models we have implemented alongside

ENDGame itself. A list of the most significant of these changes is included in Appendix A. In

presenting the impacts of ENDGame in Sec. 5, we highlight where the impact is largely due to

ENDGame alone (e.g. improvements to extra-tropical features and circulation) and where it is

due to a combination of ENDGame and physics changes (primarily in the tropics, where the im-

provements to the model’s convection scheme contribute to further increased variability). These

upgrades to the model’s physics schemes also provide significant improvements to other areas of

model performance, particularly the accuracy of forecasting “surface weather” parameters, which

are not discussed in detail here.

4.2 Resolution upgrade to the deterministic global NWP model and data as-

similation

At the same time as implementing the ENDGame dynamical core and improved physics, the hor-

izontal resolution of the global deterministic NWP model has been increased (Table 1) from N512

(corresponding to a grid spacing of approximately 25 km in the mid-latitudes6) to N768 (≈ 17 km

in the mid-latitudes). The model time step has been reduced accordingly, from 10 to 7.5 minutes.

The increase in horizontal resolution allows for more detail in surface features such as orography

(Fig. 2) and in the free atmosphere allows for more small-scale features (waves etc.) to be resolved,

improving the transfer of energy, heat and momentum between scales and improving forecasts.

Finally, alongside the upgrade to N768 in the model, we have increased the resolution of the data

assimilation component (4D-Var 7) used to provide the initial conditions for the model forecasts.

The resolution used in 4D-Var will go from N216 (≈ 60 km in the mid-latitudes) to N320 (≈ 40 km).

This increase in resolution helps to produce a more accurate initial analysis. The vertical resolu-

tion of the global NWP configuration remains unchanged with 70 levels in total, approximately 50

in the troposphere (the lowest 10-18 km of the atmosphere), approximately 20 in the stratosphere-6See Table 1 for a description of the resolution notation.7Four dimensional data assimilation (4D-Var) is the technique used to provide an optimal and balanced initial state of the

atmosphere from which to run the global forecasts. The 4D-Var process produces an initial state by using a huge range ofremote sensing and in-situ observations of the atmosphere (land and ocean) combined in a statistically optimal way with a”first guess” of the atmospheric state from a previous model run. It is four dimensional as it uses information across the 3spatial dimensions (latitude, longitude, height) and also a 6 hr “window” in time. The outcome is an analysis that is our bestestimate of the current state of the atmosphere.


mesosphere (regions immediately above the troposphere) and a model lid at 85 km (where the

pressure is ≈ 0.1 hPa). Research is underway to assess the benefits of increasing vertical resolu-

tion as part of a future model upgrade on our next supercomputer in 2016-17.

Horizontal resolution (N number) N512 (New Dynamics) N768 (ENDGame)Grid points (EW×NS) 1024×769 1536×1152Physical resolution (NS) 26.1 km 17.4 kmPhysical resolution (EW @ 50° N/S) 25.1 km 16.7 kmPhysical resolution (EW @ equator) 39.1 km 26.1 km

Table 1: Details of the resolution upgrade to the N768 ENDGame grid. The N number refers to the maximumnumber of 2 grid-point waves that can be represented in the east-west direction.

4.3 Additional package of satellite changes

The assimilation of observations to provide an accurate initial state is also a key component in

producing accurate weather forecasts. The final component of the changes made to the global

deterministic NWP system on 15 th July 2014 is the improved use of satellite (remote sensing)

observations. These include:

• Reduced thinning of IASI data, leading to a doubling of the data ingested.

• Reduced thinning of ATOVS data, leading to a 30% increase in the data ingested.

• Reduced thinning of scatterometer data, leading to a 50% increase in the data ingested.

• Improved assimilation of GPS Radio Occultation data, allowing for tangent point drift.

• Introduction of Meteosat-7 MVIRI clear sky radiances over the Indian Ocean.

• Changes to the snow analysis to make use of both the model’s snow depth and amount.

In tests, this package has been shown to provide a modest improvement to the global forecasts.


Figure 2: The orography fields and schematic of the grid resolutions for the UM at N96, N144, N216, N320,N512, and N768. The grid overlay on each model is shown at 8 times the actual grid box size for clarity, but therelative increase between each resolution is accurate. Note the increased detail in the orography as we moveto higher resolution, for example over the Alps, East African highlands, Iran, Pakistan and Afghanistan. TheN144 resolution was used for operational forecasting in the early 1990’s, N216 from 1998-2005, N320 from2005-2010 in and N512 from 2010 to present. N96 was the resolution used for HadGEM2 climate simulationssubmitted to IPCC-AR5


5 Performance benefits

In previous sections we described how the improvements in stability and scalability have improved

the efficiency of our global predictions. Here, we describe how the improved numerical accuracy and

reduced damping in ENDGame improve the quality of our global predictions and also highlight the

additional benefits arising from the improved physical parametrizations and increased resolution.

5.1 Improved representation of extra-tropical and tropical storms

One of the clearest benefits from ENDGame is an increase in atmospheric variability. This is man-

ifest in improved details and intensity of large-scale storms in both weather forecasts and climate

predictions, which arises from the use of less artificial damping in the ENDGame formulation. A sim-

ple measure of the atmospheric variability (or “storminess”) is provided by the globally integrated

eddy kinetic energy 8 (KE — Fig. 3). This forms one component of the important energy stores

in the atmosphere originally described by Lorenz,9 the others being the zonal kinetic energy (KZ)

and the zonal and eddy available potential energy (AZ and AE) which measure how much energy

is available in the atmosphere for conversion into motions such as storms and winds (Fig. 3(a)).

As forecasts run forward in time they tend to lose KE due to the damping processes in the model

(a) (b)

Figure 3: (a) Globally integrated Lorenz energy cycle showing zonal and eddy available potential energystores (AZ, AE) and zonal and eddy kinetic energy stores (KZ, KE). The arrows connecting the energy storesshow the various energy conversion terms (CA,CZ,CE,CK), while the arrows on the left are the generationof available potential energy through diabatic heating (GZ,GE) and on the right the removal of kinetic energythrough frictional dissipation (DZ,DE), (b) Globally integrated eddy kinetic energy (KE) for various resolutionfrom a set of 12 3-day forecasts initialised from ECMWF analyses. KE for the independent ECMWF analysis(green), New dynamics (red), and ENDGame (blue) are shown.

required to control numerical noise. This means that storms and associated winds are not as in-

tense as they are in the real atmosphere. For New Dynamics the 3-day forecast KE is less than8A typical eddy described here is a large-scale atmospheric tropical or extra-tropical cyclone covering 1000s of kilometres.9E.N. Lorenz. “Available potential energy and maintenance of the general circulation”. In: Tellus 7 (1955), p. 157.


the ECMWF analysis10 (by around 8%) with a larger reduction at lower resolution (compare red and

green lines in Fig. 3(b)). The ENDGame 3-day forecasts (blue line in Fig. 3(b)) are a significant im-

provement with much higher levels of KE at all resolutions and a closer match to the analysis value.

We can also see the benefits of increasing the resolution of the global model (i.e. decreasing the

size of the grid boxes to provide more detail). Moving from 130 km (N96) resolution to 17 km (N768)

gives much more accurate values of atmospheric variability (KE — Fig. 3(b)). Averaged across a

number of forecasts the 60 km resolution ENDGame forecasts have higher levels of KE than even

the equivalent 17 km forecasts using New Dynamics. This 60 km resolution is already operational

in our seasonal forecasts (GloSea) and will be the typical resolution for our climate predictions for

the next IPCC assessment report (AR6). This ability to maintain higher and more accurate levels of

KE throughout the forecast range is a significant benefit from ENDGame and improves our ability to

provide accurate risk based predictions of extreme weather events in our global deterministic and

ensemble systems.

Extra-tropical cyclones

To investigate the impact of ENDGame on storms in the extra-tropics we have applied the method

of Froude11 to track storms in our global UM predictions. Figure 4 shows the track and intensity

(a) Distance errors NH

0 20 40 60 80 100 120Forecast range (hrs)

0

2

4

6

8

Dis

tance to a

naly

sis

(deg)

N96 New DynamicsN216 New DynamicsN320 New DynamicsN96 ENDGameN216 ENDGameN320 ENDGame

(b) Distance errors SH


0

2

4

6

8

Dis

tance to a

naly

sis

(deg)

(c) Intensity difference NH


-0.6

-0.4

-0.2

0.0

0.2

Inte

nsity d

iffe

rence (

10

-5s

-1) (d) Intensity difference SH


-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Inte

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iffe

rence (

10

-5s

-1)

Figure 4: Track error in degrees (top) and intensity drift measured in 850hPa vorticity (bottom) in all extra-tropical cyclones identified in the northern hemisphere (left) and southern hemisphere (right) from a set of 200forecasts initialised from ECMWF analyses and run at 3 different resolutions (N96, N216 and N320) and forthe two different dynamical cores: ENDGame (dashed lines) and New Dynamics (solid lines).

10An analysis is a best estimate of the initial state of the atmosphere at any time and is a combination of all availableobservations and an initial estimate of the model state from a previous forecast. The analysis is also used as the startingpoint for our forecasts.

11L. S. R. Froude. “TIGGE: Comparison of the Prediction of Northern Hemisphere Extratropical Cyclones by DifferentEnsemble Prediction Systems”. In: Weather and Forecasting 25 (2010), pp. 819–836.


errors in extra-tropical cyclones as a function of forecast range from a set of 200 forecasts initialised

from ECMWF analyses. The different colours show results from simulations at different resolutions,

whilst the different line styles distinguish New Dynamics and ENDGame simulations. The spin-

down of extra-tropical cyclone intensity in the ENDGame configuration is significantly less than

that from New Dynamics and as with the global eddy kinetic energy, the impact of the change in

dynamical core can be as large as the impact of a change in horizontal resolution. For example, the

N216 (60 km) ENDGame cyclones are on average deeper than their N320 (40 km) New Dynamics

counterparts.

We also see improvements in the representation of extra-tropical cyclones at climate timescales

(Fig. 5). In particular, the underestimate of cyclone intensity in the Pacific and Atlantic stormtracks

in boreal winter (DJF) seen with New Dynamics is significantly reduced with ENDGame.

(a) New Dynamics NH DJF

-2 -1.2 -0.4 0.4 1.2 2

4

4

4

5

5

6

6

(b) ENDGame NH DJF

-2 -1.2 -0.4 0.4 1.2 2

4

4

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5

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6

(c) New Dynamics SH JJA

-2 -1.2 -0.4 0.4 1.2 2

4

4

5

5

6

(d) ENDGame SH JJA

-2 -1.2 -0.4 0.4 1.2 2

4

4

5

5

6

Figure 5: Bias (Model − ERA-Interim re-analysis) in cyclone intensity (units 10−5 s−1) derived from cyclonetracking in N216 atmosphere-only climate simulations. New Dynamics and ENDGame results for the northernhemisphere are shown in (a) and (b) respectively with the equivalent plots for the southern hemisphere in (c)and (d). The local winter results are shown for each hemisphere.

Tropical cyclones

In the tropics, cyclonic systems (hurricanes and typhoons) tend to be more intense than their

mid-latitude counterparts and difficult to resolve at global model resolutions. The change to the

ENDGame dynamical core combined with the increased horizontal resolution and upgrades to the

model’s convection scheme significantly improves our ability to model these features.


As an example of this we show N768 ENDGame and N512 New Dynamics forecasts of tropical

cyclone Amanda, a category 5 tropical cyclone that formed in the east Pacific during the latter part

of May 2014 and was the first hurricane of the season (Fig. 6). The N768 ENDGame 36 hour

forecasts provide a deeper tropical cyclone with more intense winds and precipitation near the

tropical cyclone’s core, in closer agreement with the observed storm which can be clearly seen to

have a well defined ”eye” in the NASA visible satellite imagery (Fig. 6(a)). A further example of

(a)

(b) (c)

Figure 6: Tropical Cyclone Amanda (a) NASA Aqua satellite view of Amanda (the first namedstorm of the 2014 hurricane season) in the Americas southwest of Manzanillo, Mexico, on May 25(http://earthobservatory.nasa.gov/IOTD/view.php?id=83778) (b) mean sea level pressure (contours), 10mwinds (arrows) and precipitation (colours) for the operational N512 New Dynamics 36 hour forecast initialisedat 00:00GMT on 26 May 2014, (c) the equivalent N768 ENDGAME+revised physics forecast.

the changes in intensity forecasts throughout the lifetime of a tropical cyclone is provided by Fig. 7,

which shows successive forecasts for the central pressure of Typhoon Bolaven (a severe typhoon

from the 2012 season) throughout its lifetime compared to the official estimates of its “observed”

pressure. The New Dynamics forecasts do not approach anything like the observed intensity for

Bolaven, apart from late on in its lifetime, when the cyclone was filling rapidly. The ENDGame

forecasts have much deeper central pressures, which in the deepening phase of the cyclone’s

lifetime are much closer to the observations. Secondly, we see that the pressures at the beginning

of each subsequent ENDGame forecast are not much deeper than in New Dynamics. This shows

that the 4D-Var analysis is not able to capture the intensities sustainable by the model and observed

in the true system. It is possible that this is due to limitations in the resolution or variability within

4D-Var, or due to the processing or methods of assimilation for the available observations. One

potential way to improve this in the near future may be to assimilate estimated cyclone positions


Figure 7: Official estimates of the “observed” central pressure for Typhoon Bolaven in August 2012, comparedto successive forecasts in the N512 New Dynamics control and N768 ENDGame trial. The analysed pressurefor each forecast is marked as a dot at the beginning of its trace.

and central pressures from official tropical cyclone warning centres. Another interesting feature

highlighted in Fig. 7 is that both the ENDGame and New Dynamics forecasts continue to deepen

the cyclone until very close to landfall, whilst in reality the cyclone loses intensity several days prior

to this. It is likely that this is due to some missing or poorly modelled physics, such as coupling

to the sea surface temperature or some other boundary layer process. Although this leads to the

ENDGame forecast depth of the cyclone being deeper than the observations, the rates of both

intensification and decay are more realistic in this model than in the New Dynamics counterpart.

Averaged over many cases the tropical cyclone forecasts in N768 ENDGame show deeper inten-

sities compared to their N512 New Dynamics counterparts (Table 2). We have produced these

statistics by tracking individual storms in trial12 periods and comparing their position and other fea-

tures with those reported by official tropical cyclone warning centres. This shows a significant

increase in the average intensity of tropical cyclones, with the N768 ENDGame forecasts producing

an average central pressure more than 10 hPa deeper than the N512 New Dynamics forecasts, with

the average maximum windspeed being more than 13 kt faster and the average maximum vorticity

(measure of the“spin”) being higher by more than 150%. Whilst some of these improvements come

from the increase in resolution, a significant proportion comes from the change in both the dynam-

ical core and the physics (contrast column 1 and 2 in Table 2), with the most notable contribution

from the physics upgrades being from the increase in the deep convective entrainment rate.

Finally, Table 2 shows that the upgrade leads not only to significant improvements in tropical cyclone

intensity, but also to similar improvements in the forecast tracks of the cyclones. A breakdown of

track error by forecast ranges (not shown) shows only a small percentage decrease in track error in

the first 24 hours, increasing to a 7–10% reduction on days 2–4, with the track error at day 6 being12A trial is a test period, usually a month or two in duration, where we produce analyses and forecasts from an experimental

version of the model and from the current operational model. These forecasts sample the same weather regimes and allowa direct comparison of the predictive skill of the experimental and operational models (e.g. see Fig. 12).


ENDGame/Physics Impact ENDGame/Physics/Resol. Impactat N512 resolution N768 vs N512

Ave. central press. err. reduction 3.0 hPa 3.6 hPaCentral pressure reduction 7.1 hPa 11.1 hPaWindspeed error reduction 6.7 kt 9.0 ktMax. windspeed increase 8.9 kt 13.4 kt850 hPa vorticity increase 79% 155%Track error reduction 7.3% 8.6%Track skill score increase 3.8% 4.5%

Table 2: Collated tropical cyclone verification statistics across several months of trials. The first column showsthe impact of ENDGame and revised physics changes compared to New Dynamics at N512 resolution. Thesecond column is the additional impact from increasing resolution to N768 in ENDGame forecasts. Windspeedis shown here in knots ( kt).

reduced by over 15%. The average reduction of track error across all forecast ranges is as large as

8.6%, which is the biggest single improvement in tropical cyclone track errors in over 20 years.

These improvements in tropical cyclones are also found in our longer timescale climate predictions.

Analysis of the seasonal hindcasts using tropical cyclone tracking reveals the upgraded system to

have more storms in the Atlantic and more re-curving storms in both the Atlantic and Pacific basins

(both beneficial). However, the number of storms in the hindcasts are excessive in the West Pacific

(Fig 8).

Figure 8: Track density for tropical cyclones in the current GloSea (New Dynamics) and ENDGame hindcasts(left), and in ERA-Interim and observed (right).

5.2 Improved representation of tropical equatorial waves and the Madden–

Julian Oscillation

In addition to tropical cyclones, an important component of “tropical weather” are the tropical equa-

torial waves such as the Kelvin wave and Mixed Rossby Gravity wave (Matsuno13). These wave

motions are an integral part of the tropical atmosphere, are important for organising convective

rainfall in the tropics on timescales of days to weeks and play a role in transporting energy from13Taroh Matsuno. “Quasi-geostrophic motions in the equatorial area”. In: J. Meteor. Soc. Japan 44 (1966), pp. 25–43.


one part of the tropics to another (Kiladis et al.14). The observed wave number-frequency spectrum

(a) (b) (c)

Figure 9: Wave number-frequency power spectrum at 15N-15S (following Kiladis et al.15) for (a) GPCP ob-served precipitation (Adler et al.16), (b) New Dynamics precipitation (c) ENDGame and revised physics precip-itation. The theoretical dispersion curves for these equatorial models are also shown as lines.

for tropical precipitation,based on the GPCP climatology (Adler et al.17), shows significant spectral

peaks associated with the eastward travelling Kelvin waves and with the westward travelling Equato-

rial Rossby waves (ER), with a smaller spectral signature from the Inertia Gravity waves (Fig. 9(a)).

The New Dynamics simulations have very weak amplitudes for all of the equatorial waves, whereas

simulations using the ENDGame dynamical core + upgraded physics show a significant increase in

Kelvin wave activity and a more modest increase in Equatorial Rossby waves.

The other prominent feature in the observed GPCP wavenumber-frequency power spectrum is the

large amplitude signal at low wavenumbers (1-4) and lower frequencies (30-90 days). This is the

Madden–Julian Oscillation (MJO — Madden and Julian18) which is a key mode of intra-seasonal

precipitation and circulation variability in the tropics. This typically has a suppressed and enhanced

tropical precipitation dipole signal which propagates from the western Indian Ocean to Central Pa-

cific with a timescale of 30-90 days. Again New Dynamics has a weak signal and the ENDGame and

upgraded physics simulation has a stronger amplitude for the MJO but is still too weak compared

to observations and spans too small a wavenumber range. Independent tests of ENDGame and

the physics upgrades show the MJO improvements come mainly from the physics, particularly the

increase to the entrainment parameter in the convection scheme (Klingaman and Woolnough19),

whilst for the Kelvin waves ENDGame has the biggest impact.14G N Kiladis et al. “Convectively coupled equatorial waves”. In: Rev. Geophys (2009).17Robert F Adler et al. “The Version-2 Global Precipitation Climatology Project (GPCP) Monthly Precipitation Analysis

(1979–Present)”. In: http://dx.doi.org/10.1175/1525-7541(2003)004<1147:TVGPCP>2.0.CO;2 (2007), pp. 1–21.18Roland A Madden and Paul R Julian. “Detection of a 40–50 Day Oscillation in the Zonal Wind in the Tropical Pacific”. In:

http://dx.doi.org/10.1175/1520-0469(1971)028<0702:DOADOI>2.0.CO;2 (1971).19N. Klingaman and S. Woolnough. “Using a case-study approach to improve the Madden–Julian oscillation in the Hadley

Centre model”. In: Q. J. R. Metereol. Soc. (in press).


5.3 Improvements to the model representation of gravity waves

The use of reduced damping in ENDGame has a marked effect on the model’s ability to explic-

itly represent internal gravity-wave motion. ENDGame global forecasts contain resolved gravity

waves with much larger amplitude than those in equivalent New Dynamics simulations. Compa-

rable wave amplitudes can be achieved with New Dynamics, but numerical stability issues mean

that this requires very small time steps (Shutts and Vosper20), which are not practical in NWP or

climate simulations. Tests have shown that even at relatively coarse NWP resolutions (e.g. N320)

ENDGame global forecasts explicitly represent gravity wave motion in the stratosphere and their

presence clearly adds to the realism of the model and contributes to its improved variability. Oro-

graphic gravity waves (mountain waves) are seen above the major mountain ranges in the model.

At N768 resolution ENDGame is able to explicitly represent the large amplitude mountain waves

which break and produce clear air turbulence (CAT) above some of the broader mountain ranges.

Forecast tests for known cases of aircraft encounters with mountain-wave CAT over Greenland

have shown that the model’s representation of the waves near the tropopause is now sufficiently

good that the location and timing of CAT can be accurately diagnosed from the model flow fields

directly, suggesting that aviation CAT forecasts could be substantially improved in the near future.

An example of such a forecast is shown in Fig. 10.

Finally, it is also worth noting that in high-resolution (1 12 km) limited area configurations of the model

(UKV), the gravity-wave improvements are manifested in the existence of trapped lee waves. Tests

suggest that long trains of lee waves, with horizontal wavelengths as short as 15 km, are well

represented in ENDGame versions of UKV, which are completely absent in the equivalent New

Dynamics simulations (see Fig. 11). The downdraughts and turbulent gusts associated with lee

waves represent a hazard to light aircraft, and can also generate dangerous gusts downwind of

hills, causing tree and property damage and over-turning of high-sided vehicles. The improvements

to this aspect of the model will allow better forecasts of hazardous conditions to the public and to

aviation communities.

5.4 Improved forecasts of aviation “jet level” winds

The accurate prediction of the upper atmospheric “jet stream” winds is particularly important for the

aviation industry, which relies on accurate forecasts of the position and strength of the jet streams

for planning intercontinental flights. A consistent improvement seen in all tests of ENDGame is a

reduction of the slow bias in tropospheric windspeeds, which is a long-standing feature of the global

model. Figure 12 shows verification for 6 day forecasts of northern hemisphere and tropical wind

profiles against radiosonde observations from a Nov/Dec 2012 trial. The mean error at this forecast20G. J. Shutts and S. B. Vosper. “Stratospheric gravity waves revealed in NWP model forecasts”. In: Quart. J. Roy.

Meteorol. Soc. 137 (2011), pp. 303–317.


Figure 10: ENDGame global forecast of mountain wave breaking over Greenland. The flow is easterly (rightto left) across Greenland and the vertically propagating wave motion is evident in undulations of the poten-tial temperature surface (solid contours, units K). The red shading denotes regions of high turbulent kineticenergy associated with wave breaking. The case shown (25 th May 2010) was studied by Sharman, Doyle,and Shapiro21 and is a well documented case of an aircraft encounter with mountain wave turbulence along atransatlantic route across Greenland. The global ENDGame forecast provides a good prediction of the locationand timing of the turbulence.

(a) (b) (c)

Figure 11: Lee waves over the UK. Panel (a) shows visible satellite imagery. The lee wave motion is evident inthe banded cloud patterns, particularly across the hills and mountains of Wales and northern England. Panel(b) shows the UKV forecast using New Dynamics. Very little wave motion is present in the simulation. Incontrast, panel (c) shows the equivalent ENDGame UKV forecast. The model produces realistic lee wavecloud patterns which correspond well with the satellite image.


range is improved by about 50%. As with some of the cyclone results above, this bias is much less

sensitive to the change in resolution than to the change in dynamical core. Resolution does improve

the root mean square (RMS) error in northern hemisphere by around 1% at jet levels (250hPa).

In the tropics we see that the ENDGame and upgraded physics make the RMS errors worse at

this level and the enhanced resolution degrades this further. In this region, we have seen that

ENDGame and the upgraded physics and resolution leads the model to have too much variability

compared to the model’s analysis. Work is ongoing to improve this through future upgrades to the

model’s convection scheme.

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Figure 12: Verification of day 6 northern hemisphere (left hand 4 panels) and tropical (right hand 4 panels)wind profiles vs radiosonde observations from a Nov/Dec 2012 trial. Three experiments are shown: the N512New Dynamics control (red line), the N512 ENDGame and upgraded physics (blue line), and the enhancedresolution N768 ENDGame and upgraded physics (green line). In each figure, the top-left panel shows thebias, the top-right panel shows the difference in bias from the New Dynamics control (i.e. the red line). Thebottom-left panel shows the RMS error and the bottom-right shows the difference in this from the control.

A significant advantage of the reduced windspeed bias and improved jet locations is that it has

allowed us to remove the operational scaling of pressure level winds. Previously, winds between

700 and 70 hPa were scaled by factors of up to 4% (depending on the pressure level). This was

designed to improve flight time forecasts for aviation customers, but is also known to increase the

RMS error in these winds. Figure 13 shows predicted flight time errors as a function of the scaling

factor applied for forecast ranges between 24 and 30 hours. This and similar results from other

forecast ranges show that even with New Dynamics, there would have been a small improvement in

both flight time and RMS errors by reducing the maximum scaling to 2%. The N768 ENDGame and

upgraded physics configuration, however, shows even less need for wind scaling to be applied than


Figure 13: Flight time errors from both N512 New Dynamics (Control) and N768 ENDGame (Trial) as afunction of the amount of wind scaling applied for forecast ranges between 24 and 30 hours.

the New Dynamics control and at some forecast ranges even a 1% scaling is seen to be detrimental.

Moreover, the N768 ENDGame and upgraded physics forecasts with no scaling applied have lower

flight time errors than the N512 New Dynamics forecasts with any value of wind scaling. The

removal of this scaling, therefore, both improves the quality of the forecast products and makes

them consistent with the raw forecast model data.


6 Conclusions and future direction

The evidence collected in this report demonstrates that for global models, the adoption of the

ENDGame dynamical core provides a significant improvement to our current prediction capability.

It improves the variability of the model, particularly in the mid-latitudes, which leads to the improved

intensity and tracks of individual storm systems and other synoptic features and the reduction of

slow speed biases in tropospheric winds. In the tropics we see improvements to several modes of

variability, particularly the representation of tropical cyclones. This improved variability also leads

to the model supporting a wider envelope of potential solutions, which increases the spread of our

ensemble prediction systems with potential improvement to our ability to provide risk based predic-

tions of extreme weather. ENDGame’s improved stability and scalability allows us to upgrade the

deterministic global model resolution, reduces the overheads in maintaining operational and pro-

duction systems and will allow us to continue to improve the resolution of the global model as our

computers are upgraded over the course of the next decade.

In the coming year, we will implement ENDGame in the production global modelling systems still

using New Dynamics, namely our monthly-seasonal and decadal prediction systems. We will also

implement ENDGame in our limited-area weather and climate prediction models, where we expect

to see improvements to the representation of more local features such as lee wave clouds that

form downstream of hills and mountains in stably stratified conditions. After this, we can retire New

Dynamics from the model’s code base and revert to supporting a single dynamical core for use in

seamless prediction across all resolutions and timescales.

In a sense ENDGame finishes the work that New Dynamics started, but the development of our

dynamical cores doesn’t end here. Research has already started on the next-generation dynamical

core (named GungHo22) which we expect to replace ENDGame in about 10 years. Being developed

in collaboration between Met Office scientists, academics from across the UK and computational

scientists from the Hartree Centre, GungHo will be part of a completely new model that will deliver

the step change in scalability required to continue to exploit future generations of computers. This

will ensure that, together with our collaborators, we can continue to improve our weather and climate

services into the next decade and beyond.

22GungHo is an anglicised pronunciation of ”gong he”, where the Chinese characters ”gong” and ”he” are translatableindividually as ”work” and ”together”, so this name reflects both the ambitious and the collaborative nature of the project.


Appendix A List of improvements to the model’s physics

The lists below highlights the most significant improvements in the global NWP model’s physical

parametrizations that have been implemented alongside the upgrade to the ENDGame dynamical

core. Improvements marked † are physics options or schemes already being used in climate re-

search configurations of the model, such that applying these changes in NWP brings us closer to

using identical parametrizations across all global modelling systems.

Radiation

• Improved absorption of longwave radiation by CO2 and O3 which improves heating and cooling

in the stratosphere†.

• An increase in the frequency of calls to the radiation scheme (reducing the radiation time step

to 1 hour) which improves the accuracy of the calculations.

• In NWP and seasonal forecast systems, an improved use of climatological aerosol fields for

cloud condensation nuclei.

• An adjustment to the fraction of shortwave radiation reflected (albedo) over sea ice.

• Solar constant adjusted to the latest estimated value of 1361 Wm−2.

Boundary layer scheme

• Reduced turbulent mixing for stably stratified boundary layers. This has a better physical basis

than previous mixing formulations†.

• Revised stability functions for unstable boundary layers, which again have a better physical

basis†.

• Revised diagnosis of shear-dominated boundary layers, which improves the representation of

cloud in polar cold-air outbreak situations.

Large-scale cloud scheme

• An improved method to represent cloud erosion and a better definition for mixed-phase cloud.

• Improvements to the representation of ice cloud through a new cirrus term and use of the

model winds in the shear term in the treatment of falling ice cloud fraction.

• A smoother phase change for cloud condensate detrained from convective plumes.


Large-scale precipitation scheme

• Implementation of improved size distribution of water droplets for drizzle to better match ob-

servations.

• Improved microphysics substepping to perform multiple calculations over each column in a

single model time step.

• In NWP and seasonal forecast systems, an improvement to the use of climatological aerosol

fields in the microphysics schemes consistent with that made in the radiation scheme.

Convection scheme

• An increase of the entrainment rate for deep convection with related modifications to the de-

trainment rate.

• Smoothed adaptive detrainment of cloud liquid water, ice and tracers.

• An update to the code base with improvements to the robustness of the scheme.

Gravity wave and flow-blocking drag

• Introduction of a new orographic drag scheme, which has a better physical basis.

Land surface

• The numerical schemes used in the JULES land-surface model have been improved, to pro-

vide better accuracy.

• Use of the ”TOPMODEL” hydrology to better diagnose surface and subsurface runoff†.

• Changes to the surface thermal and momentum roughness lengths which improve the surface

energy budgets and drag.

• Improvements in the way the surface emissivity is calculated for different surface types, in-

cluding non-unity values for the sea surface and sea ice.


Paper authored by:

David Walters

Nigel Wood

Simon Vosper

Sean Milton

with contributions from:

Clare Bysouth

Paul Earnshaw

Julian Heming

Marion Mittermaier

Claudio Sanchez

Malcolm Roberts

Warren Tennant


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