investigation of systematic errors by relaxation experiments

Q. J . R . Meteorol. SOC. (1990), 116, pp. 57S594 551.509.333:551.509.5:551.558.21

Investigation of systematic errors by relaxation experiments

By E. KLINKER European Centre for Medium Range Weather Forecasts, Reading

(Received 13 February 1989; revised 2 November 1989)

SUMMARY The systematic errors of the ECMWF forecast model have been investigated by relaxing forecasts towards

analyses in selected regions. This method proved to be a useful tool to study the initial error growth in a certain region and the subsequent error propagation.

The forecast fields in the tropics were relaxed towards the analysis by adding a contribution proportional to the current forecast error to the tendencies of temperature and momentum. From the comparison of control forecasts with tropically relaxed forecasts it was possible to separate large errors generated in the extra-tropics from comparatively small errors penetrating from the tropics into the extra-tropics.

Relaxation in the major mountain regions showed different results for the Rocky Mountains and the Himalayas. The errors originating from the Rocky Mountains are substantial contributors to errors of both transient eddies and stationary eddies. The baroclinic waves in the Atlantic storm track are weakened and the stationary eddies develop a wave-train-like error pattern which is typical for many operational forecasts in the winter season.

The errors in the Pacific are much less dependent on errors from the mountainous region. The error structure of the transient and stationary eddies, as revealed from experiments in which the Asian mountains are excluded or included from the relaxation, shows little similarity to operational forecast errors.

1. INTRODUCTION

Although diagnostic investigations of the ECMWF model forecasts (Arpe and Klinker 1986; Heckley 1985) have led to a comprehensive documentation of systematic errors, little is known for certain about their sources. Errors of the mean zonal flow for instance have often been compared with errors in the divergence of the eddy momentum flux, as there exists a good correlation between the two. Errors in one quantity can be described by errors of another quantity. However, the source of these errors and their location are often obscured.

The aim of this investigation is to identify the regions which contribute most to systematic errors in the extra-tropical flow. Large errors of the ECMWF operational forecasts occur in the exit regions of the two major jets over the Pacific and over the Atlantic (Arpe and Klinker 1986). Error diagnostics for the tropical forecasts (Heckley 1985) as well as barotropic model experiments (Simmons et al. 1983) suggest a close connection between errors in the tropics and the mid-latitudes. The sensitivity of model errors to mountain forcing (Wallace et al. 1983) points to additional error sources in extra-tropical latitudes. To estimate the downstream importance of error sources we use an experimental approach. We compare forecast experiments where error production in certain regions is suppressed by relaxation towards analyses with control experiments without relaxation. The relaxation is carried out by adding terms to the forecast equations which relax the forecast towards the analysis in selected regions where we expect that errors originating there have a large downstream effect. This type of error analysis is only possible after the event, as the relaxation towards analysis is done for the verifying time of the forecast.

In the examination of the model results we will discuss two aspects of the systematic errors:

(if time mean errors over periods of five and ten days, and (ii) transient wave errors as defined by departures from the 10-day time mean.

573

574 E. KLINKER

Forecast errors of transient waves have been investigated by Klinker and Capaldo (1986). Using a large ensemble of analyses and forecasts for 1980/81 and 1981/82 they showed a marked weakening of the baroclinic wave activity over North America and the Atlantic by day 3 of the forecast. Similar calculations for the following winter seasons up to the 1986/87 winter season confirm the earlier results that in the American-Atlantic sector the dominant forecast errors produce a weakening of the baroclinic waves at middle latitudes.

For our experiments we have investigated errors of the transient waves in a slightly different way. We have calculated the spectrum for the total forecast length of 10 days (model output values twice daily) and excluded the long period ( T > 3.3 days) variance. We use this technique in two ways, first by calculating error variance of vorticity to document error tracks, and second by calculating the variance and variance errors of the meridional wind to investigate the behaviour of the baroclinic waves.

In section 2 we explain the relaxation method. The residual error which is left after global relaxation is discussed in section 3. The following sections deal with error propagation from selected regions, propagation from the tropics in section 4, from continental regions in section 5, and from the Rocky Mountains and the Himalayas in sections 6 and 7 respectively. A summary is added in section 8.

2. METHOD

Relaxation of forecasts towards analyses is a technique which has already been used by Haseler (1982) to show the effect of tropical forecast errors on errors in the extra- tropical flow. Whereas Haseler replaced the tropical forecast fields by analysis fields, we have instead added a contribution proportional to the current forecast error to the tendencies of temperature and momentum. The relaxation of the wind field above the model’s boundary layer provides sufficient indirect relaxation of the surface pressure via the divergence terms in the surface-pressure equation. The tendency equation for the mass and wind fields V(u, u , T ) becomes d V / d t = . . . + A( qA - q), with A-’ = 8 h, where is the analysed variable and A is the relaxation coefficient which determines the magnitude of the remaining forecast error after relaxation. A relaxation coefficient of A-* = 8 h has been chosen from experimental results as a compromise between larger values which lead to a weak adjustment of the forecast fields and smaller values which can cause numerical instability. To achieve a continuous relaxation during the forecast we have interpolated the analysed fields of mass and wind from the 6-hourly values (archived in model level format) to half-hourly values matching the time-step of the model. The economical T42 (triangular truncation) version of the ECMWF spectral model has been used as resolutions beyond T42 have little effect on the character of time mean errors (Cubasch and Wiin-Nielsen 1986). The characteristics of the ECMWF operational model valid for January 1984 can be found in Arpe and Klinker (1986). The mountains were represented by an envelope orography, whereas gravity-wave drag was not included in the parametrization of momentum dissipation.

For the experimental investigation of the systematic errors we have selected four initial days of the winter season 1983/84. These days are spread over the season to avoid any overlapping of the forecast periods. The selection of initial days was based on northern hemisphere skill scores. The first case (1212-poor) has 12 December 1983 as initial day when the operational forecast was very poor in terms of anomaly correlation of geopotential height and when the time mean errors were large. The 16 January 1984 case (1601-good) can be regarded as an excellent forecast with small errors. In the third case, initial day 31 January 1984 (3101-mean), the mean error had a structure close to

SYSTEMATIC ERRORS INVESTIGATION 575

the mean error of the season, and the last case, initial day 18 February 1984 (1802-late) was chosen to cover the late winter season. Different types of experiments were carried out: these are listed in Table 1.

The number of cases which have been examined in this study is too small to cover all aspects of systematic errors. There are, however, error features in the selected cases, which are common to a large number of forecasts. Some of the most frequent errors are increases of upper-level westerlies in middle latitudes and easterly errors in the upper troposphere of the tropics.

TABLE 1. TYPES OF EXPERIMENT

Control experiment Global Relaxation Tropical Relaxation Land Relaxation Land Relaxation excluding the Himalayas Relaxation upstream the west coast of North America

Relaxation upstream the west coast of North America excluding the Rocky Mountains

including the Rocky Mountains

CON RG RT RL NOH

NOR

RR

3. GLOBAL RELAXATION

In this section we describe how the forecasts behaved when the relaxation of mass and wind was carried out over the full global domain. These experiments will be used as a reference in the experiments where the relaxation is restricted to certain areas like the tropics or mountainous regions. Therefore it is important to have an estimate of the residual errors (globally relaxed forecast minus analysis).

From a cross-section of the zonal mean wind (Fig. 1) we can see that the structure of the operational 12-hour forecast errors is similar to that of the residual errors averaged over a 10-day period. In general the magnitude of the residual errors is close to the magnitude of the 12-hour forecast errors as well. The success of the global relaxation method in keeping the forecast close to the analysis can also be measured in terms of anomaly correlation between the analysis and the forecast. In the globally relaxed experiments the correlation stays between 0.99 and 1.00 throughout the prediction period. However, in the first 12 hours of the forecast, the errors increase at a rate similar to that of the control forecast. This characteristic of the global relaxation experiments- an initial increase of errors followed by a levelling off after 12 hours-suggests the existence of a large constant error growth term competing with the error reduction forcing of the relaxation scheme.

4. RELAXATION IN THE TROPICS

Large upper-level wind errors are found in the operational forecasts in the tropics. The horizontal structure of these errors suggests a connection with an anticyclonic error circulation over the subtropical Pacific and Atlantic which extends as far north as 40"N. There is enough evidence from observational studies (Horel and Wallace 1981) and from theoretical investigations (Hoskins and Karoly 1981) to support the hypothesis that the tropical circulation has an important influence on the extra-tropical flow.

By relaxing the tropical forecast towards the analysis we can prevent the propagation of tropical errors into the extra-tropics and estimate the extra-tropical response to tropical errors. We have to keep in mind that the tropical analysis has errors of a size which is not known exactly, owing to the sparse data-coverage in the tropics. However, we can

576 E. KLINKER

LATITUDE 0 20 40 60 80

a) 200 200

w W 5 400 400 5 m in

600 600 IY n- a (1

800 800

1000 1000 0 20 40 60 80

LATITUDE

LATITUDE Figure 1. Northern hemisphere latitude-height (pressure in hPa) section of zonal mean wind errors. (a) Ensemble mean of 10-day errors for 4 globally relaxed forecasts (RG - ANA); (b) 12-hour mean operational

forecast errors for the winter season 1983/84 (112 days, H12 - ANA). Units: m s-' .

at least assume that the analysis errors are much smaller than the errors in the medium forecast range.

In the following paragraphs we describe the effect of tropical relaxation on the evolution of errors in the northern hemisphere. The investigation will be based on three types of experiment (see also Table 1):

RG-globally relaxed forecasts: CON-control forecasts: RT-tropical relaxed forecasts:

contain small errors contain errors of extra-tropical and tropical origin contain errors mainly of extra-tropical origin.

By looking at differences between forecasts of types RG, CON and RT we are able to distinguish between errors of extra-tropical and tropical forecast origin in extra-tropical latitudes. Thus in the extra-tropics

Forecast CON minus RG-shows the total forecast errors Forecast RT minus RG-shows the forecast errors of extra-tropical origin Forecast CON minus RT-shows the forecast errors of tropical origin.

The relaxation boundaries are at 20"N and 20"s with a smooth transition zone between latitudes 15" and 25" from full relaxation in the tropics to no relaxation in the extra- tropics.

( a ) Error propagation The first question we wanted to answer was whether there are preferred regions

from which tropical errors propagate into the extra-tropics. In trying to identify error


tracks we investigated error propagation on daily error maps using vorticity as a con- venient tracer. No clear signs of a preferred track could be found at upper levels. However, at 1000hPa the propagation of vorticity errors made it possible to identify an error track in the Pacific and in the Atlantic as well. These vorticity errors have a wavelike structure with wavenumber 8 to 10 and a phase speed between 12 and 15 m s-'. Locally the vorticity errors have an oscillation with a period close to 3 days. A time spectral analysis of vorticity errors supported our findings based on examination of consecutive maps. The high-frequency variance (periods smaller than 3.3 days) of the transient vorticity errors calculated from the difference between the tropically relaxed and the control forecasts shows two major tracks (Fig. 2). The Pacific track starts south of Japan and follows closely the storm track across the north Pacific to the north-west coast of Canada. The Atlantic error track is completely separated from the Pacific one. It appears first in the extra-tropical flow close to Florida and follows a path close to the Atlantic storm track.

go"# 90"E

Figure 2. Track of tropical errors at 1000 hPa, averaged over 4 sets of experiments. The figure shows the high- frequency variance (periods smaller than 3.3 days) for the vorticity differences between control experiments and

tropically relaxed experiments (CON - RT). Units: 10-I" s - ~ ,

From the starting points of the two error tracks we conclude that tropical errors in the Caribbean region and the area of south-east Asia probably have the most important influence of tropical errors on the extra-tropical flow. This result agrees well with barotropic model experiments by Simmons et al. (1983) which show that forcing in these areas produces a maximum response in extra-tropical regions north-east of the source location.

(b) Time mean height errors The results of the tropical relaxation experiments have been summarized by applying

an ensemble mean over each set of experiments in the same category (RG,CON,RT: see Table 1). We investigate mainly the time mean error over a 10-day period (taking twice-daily model output values from 12 to 240 hours into account).

578 E. KLINKER

The 10-day mean height errors of the four control experiments (Fig. 3(a)) have a horizontal structure which is typical for the operational forecast errors for the complete winter season, with a dipole structure of too low heights over Alaska and the Norwegian Sea. Major features of this pattern are already established by day 1. In the forecast where we have relaxed the tropics towards analyses (Fig. 3(b)) the errors (extra-tropical origin) have grown to almost the same magnitude as in the control forecasts.

Figure 3. Mean height errors at 500 hPa, averaged over 10 days and 4 cases, spectral truncation T20. (a) Total errors (CON - RG); (b) errors of extra-tropical origin (RT - RG); (c) errors of tropical origin (CON - RT).

Units: dam.


The errors of tropical origin (Fig. 3(c)) have reached in certain places about 60% of the total errors. However, they only contribute to a shift of the total errors compared to the extra-tropical errors in most regions. This is particularly apparent in the Pacific where the position of the dipole of the cyclonic and anticyclonic error pattern in the total error field is more to the east than in the extra-tropical error field. The wavelike structure of the tropical error contribution suggests little impact of tropical errors on the zonal mean error statistic in the extra-tropics for the four cases considered.

( c ) Mean wind errors in the upper troposphere We began this investigation with the suspicion that much of the wind errors in extra-

tropical latitudes might be forced by wind errors in the tropics. Heckley (1985) argues that the horizontal structure of the time mean wind errors suggests a forcing from the tropics. A noticeable impact of tropical errors on the extra-tropical flow was shown by Haseler (1982) using a similar relaxation technique for the tropical forecast. She found the largest effect when tropical features interacted with deep mid-latitude troughs.

The ensemble error pattern of the control forecasts (Fig. 4(b)) would support the assumption of a close connection between errors in the tropics and extra-tropics as the large upper-level wind error pattern off the west coast of Peru has a poleward branch in both hemispheres in the mid-Pacific. The northern hemisphere branch is part of an anticyclonic-cyclonic error pattern reaching as far north as 65"N. The wind errors in the Pacific imply a shift of the jet axis to the north and an extension to the north-east, the latter indicating insufficient deceleration in the jet exit region. The map of extra-tropical errors (Fig. 4(c)) shows that the Pacific wind error pattern during the first 5 days is largely independent of the tropical influence. Though the tropical errors (Fig. 4(d)) contribute to the anticyclonic-cyclonic error pattern in the north Pacific, their relative contribution to the total error north of 40"N is only in the order of 10 to 20%. In the North Atlantic the contribution of errors of tropical origin to the anticyclonic error pattern is noticeable as well, but is much weaker there than in the Pacific.

When we examine the mean wind errors averaged over the full forecast period of ten days the propagation of tropical errors to higher latitudes becomes apparent. In Fig. 5 we compare the total errors (a: CON - RG), the errors of extra-tropical origin (b: RT - RG), and the errors of tropical origin (c: CON - RT). Especially over the Pacific, tropical errors cause modifications of the cyclonic-anticyclonic error structure. Adding together errors of tropical and extra-tropical origin yields only a small increase in magnitude, but a noticeable shift from the Bering Strait to a region south of Alaska. In the North Atlantic little impact is felt from the tropical relaxation.

From the results of the four experiments we can conclude that in the Pacific the error forcing from the tropical region contributes a relatively small amount to an anticyclonic-cyclonic error pattern which seems to be mainly produced by extra-tropical error forcing. This suggests that the main error sources for the time mean errors in the north Pacific are of extra-tropical origin. Errors penetrating from the tropics into the extra-tropics interact with the extra-tropical errors by shifting the error structures. The influence of tropical forcing on errors in the extra-tropical latitudes of the Atlantic seems to be weaker than in the Pacific.

( d ) Zonal mean wind errors and errors of transient waues The structure of the zonal mean wind errors for the full winter season can be detected

in most individual forecasts. Typical features are an increase of westerlies at middle latitudes and a decrease at high and low latitudes with strong easterlies at upper levels in the tropics. The 10-day and ensemble mean for all four cases shows this error

580

+ 60 m i s

E. KLINKER

D 60"N 60"N

30% 30'N

c" 0"

3 0 5 305

60"S 605

3 60°N

30"N

3"

30"5

50'8

Figure 4. Mean winds and wind errors at 200 hPa, averaged over 5 days and 4 cases, spectral truncation T20. (a) Wind field for globally relaxed forecasts (RG); (b) total errors (CON - RG); (c) errors of extratropical

origin (RT - RG); (d) errors of tropical origin (CON - RT). Units: ms-'.


- , i m s a 0" 90"E

a) 60°N 60"N

30"N

0" 0"

30"s 30"s

6C"S 60"s

90"E

a 90"W 90"E b) 60"N 60"N

3WN

00 0"

30"s 30"s

60"s 60"s

9 V W 0" 9O"E 0" a 90nw

60"N

30"N

0"

30"s

60"s 90"W 0" 90"E

Figure 5 . Mean wind errors at 200hPa, averaged over 10 days and 4 cases, spectral truncation T20. (a) Total errors (CON - RG); (b) errors of extra-tropical origin (RT - RG); (c) errors of tropical origin (CON - RT).

Units: m s-'.

distribution for the control forecasts (Fig. 6(b)). From the error maps of the wind we have seen large local contributions from tropical errors in extra-tropical latitudes, but because of their wavelike nature they contribute rather little to the zonal mean errors. Therefore the mean zonal-flow errors away from the tropics are little affected by tropical relaxation (Fig. 6(c)). Zonal mean errors of tropical origin are clearly restricted to a latitude band with boundaries around 30"s and 30"N only ten degrees away from the relaxation boundaries (Fig. 6(d)).

In line with the small changes of the mean errors due to tropical relaxation, the effect on the transient errors is also small. The decrease of high-frequency variance of the meridional wind in the control forecasts (Fig. 7(b)) corresponds to changes of transient wave activity already known from earlier work on operational forecasts (Klinker and Capaldo 1986). In the tropically relaxed forecast (Fig. 7(c)) a slightly larger variance error indicates that extra-tropical errors are larger than the total errors. It suggests that,

582 E. KLINKER

LArlTUDE 80 -60 -40 -20 0 20 40 60 SO

a) 200

W 5 400 v, I/) W 600 LY

800

1000

a

-

LATITUDL

-80 -60 -40 -20 0 20 40 60 80 LATITUDE

LATITUDE -

d)

5 400 200

W

Ln

LK a 600

800

1000 -80 -60 -40 -20 0 20 40 60 80

LATITUDE

Figure 6 . Latitude-height (pressure in hPa) cross-section of zonal mean winds and wind errors, averaged over 10 days and 4 cases (a) Zonal mean wind for globally relaxed forecast (RG), (b) total errors (CON - RG),

(c) errors of extratropical origin (RT - RG), (d) errors of tropical origin (CON - RT) Units. m s


a) 300

Y 00

500

600

I00

BDO

900

b) 300

900

500

600

700

900 - I 30 YO so 60 70

Figure 7. Latitude-height (pressure in hPa) cross-section of high-frequency variance and variance errors of the meridional wind (periods smaller than 3.3 days). (a) Variance of the globally relaxed forecast (RG); (b)

control forecast errors (CON - RG); (c) errors of tropically relaxed forecasts (RT - RG). Units: m2s-2,

in the control forecasts, transient errors in the shorter time-scale were partly compensated by errors originating from the tropics. This effect will be noticeable as well in the scores for the total fields of the geopotential when we look at the anomaly correlation of forecasts with analyses in the next section.

The compensation effect is important when considering proposals for changes in the physical parametrization package. Noticeable improvements in the tropics might have detrimental effects in the extra-tropics, though this should not necessarily prevent the implementation of improved physical parametrization, as better forecasts in the tropics might then help to uncover errors in the extra-tropics.

( e ) Scores of the tropically relaxed forecasts The impact of the relaxation on the verification scores varied from case to case in

the four cases selected. Differences between the control forecast and the tropically relaxed forecast become noticeable after three days (Fig. 8). The largest improvements

0

P8Z081 1.;; I- OE

Oh -- 05

09 OL 08 06

--

.............. - -- -- --

(PI

Itlo 01, 6 , , 8 , , L , , 9 , , S ~ , fi , , r , , 7. , , I , , 0 , 0 01

-t;91091

.............. ................... 05 09 OL 08 06

lt10 01 , 6 8 L 9 S fi f z I 0

f z I 0 :!.,,,,,,, D

E8ZlZl ,”: L 9 S

OE Oh 0s

DL 08 06

............... .... 09

-.._ -. N... _-_--------_

--______....

PI


were found in the poorest forecast (12 Dec. 1983) and a modest overall improvement was found even in the best scoring one (16 Jan. 1984). The ‘average case’ (31 Jan. 1984) showed poorer scores in the medium range indicating that errors of tropical origin compensated for parts of the errors of extra-tropical origin. In terms of r.m.s. vector wind errors (integrated over 1000 to 200 hPa) the error reduction by tropical relaxation in the medium range was around 10%.

5 . RELAXATION OVER THE CONTINENTS

As the relaxation experiments suggest that tropical forecast errors have only a secondary effect on errors at mid-latitudes in the cases chosen, we now concentrate our efforts on the extra-tropics to locate the most important error source there. Regions with high terrain are well-known source areas for errors in numerical forecasts. The sensitivity of model errors to mountain forcing has been shown by Fawcett (1969) and Wallace et al. (1983).

We address the mountain-forcing problem by selectively including or excluding mountainous regions in the relaxation area. In a stepwise procedure we first partition the forecast errors into errors originating from continental and oceanic areas by relaxing the forecasts over the continents only. We can further partition the mountain-forcing errors from the continental errors by including or excluding mountainous regions in the relaxation.

When we switched on the relaxation over the continents (Fig. 9) a distinct difference in the error growth over the Pacific and the Atlantic emerged. Over central parts of the North Pacific positive errors in the height field reached almost the same level in the relaxation forecasts as in the control forecasts (see Fig. 3(a)). Despite the relaxation over land the negative height errors near the coast of Alaska are only slightly smaller than in

Figure 9. over land

0” Mean 10-day height errors at 500 hPa. ‘Sea errors’, defined as differences between forecasts relaxed

and globally relaxed forecasts (RL - RG). Mean over 10 days and 4 sets of experiments, spectral truncation T20. Units: dam.

586 E. KLINKER

the control forecast. By contrast the relaxation over the American continent has led to a substantial reduction of the Atlantic errors. These results suggest that errors over the Pacific are dominated by errors originating from oceanic regions whereas the Atlantic errors are mainly of continental origin.

6. RELAXATION OVER THE ROCKIES

As we have found a large sensitivity of the Atlantic error pattern to error forcing over North America we want to isolate the main error source region even further. The Rocky Mountains, which constitute a major barrier for the zonal flow, are the most likely candidate for error production.

With the relaxation technique we can examine the mountain-forcing problem under conditions in which the flow meeting the mountain barrier is almost error free (to within the accuracy of the analysis). We made two types of experiments, NOR and RR. In both experiments we relaxed the forecast a long way upstream of the Rockies (Fig. 10). In experiment NOR there is no relaxation west of the Rockies and east of the Ural Mountains. By placing the boundary of the relaxation in this experiment on the windward side of the mountains we allowed the errors originating from the Rockies to develop and propagate downstream. In a second experiment (RR) the Rockies were included in the relaxation area and thereby we excluded errors from mountain forcing. The differences between these two experiments (NOR - RR) then reveal the role of mountain-forcing

relaxation on:RR / relaxation off: NOR

relaxation always on Figure 10. Relaxation mask for the Rocky Mountain experiments.


errors downstream of the Rockies. Additional experiments were carried out in which the effect of gravity-wave drag on errors over the Atlantic were tested. Only a small impact on 10-day errors in these four cases was seen from the gravity-wave drag scheme which went into operation at ECMWF in 1986.

(a) Transient errors As a first step in our error analysis we investigate if there are preferred error tracks

and if there are regions which can be identified as starting points of error propagation. Similar to the tropical relaxation experiments we use the vorticity as a parameter to examine error propagation.

From consecutive maps of vorticity differences between relaxation experiments, excluding and including the Rocky Mountains in the relaxation area, we followed the propagation of differences downstream in the flow. In addition, a spectral analysis of the vorticity differences was performed. The horizontal distribution of high-frequency variance at 500 hPa (Fig. 11) clearly depicts the major error track originating from the low-latitude region of the Rocky Mountains. The error track follows closely the usual storm track across southern parts of North America and the Atlantic, and splits into a northern and southern branch over Europe.

The existence of a well-defined error track suggests that the relaxation had a noticeable impact on the transient wave errors. To concentrate our discussion on the baroclinic waves we have selected the meridional wind as a parameter and calculated the variance in a frequency band which contains periods of up to 3-3 days only. The variance distribution at 5OOhPa in the analysis (Fig. 12(a)) shows the Atlantic storm track extending from the lee of the Rocky Mountains into western Europe. Though this storm track represents only 40 days (four 10-day experiments) of the winter season we find a close agreement to the seasonal mean storm track of the winter 1983/84 (not shown).

180"

0.. .

Figure 11. Track of mountain-forcing errors at 500 hPa, averaged over 4 sets of experiments. The figure shows the high-frequency variance (periods smaller than 3.3 days) for the vorticity differences between experiments

excluding and including the Rocky Mountains in the relaxation (NOR - RR). Units: s-*.

588 E. KLINKER

Figure 12. High-frequency variance and variance errors for the meridional wind (periods smaller than 3.3 days) at 500 hPa, averaged over 4 sets of experiments. (a) Variance of the globally relaxed forecasts (RG); (b) control forecast errors (CON - RG); (c) difference between the experiments excluding the Rocky Mountains

in the relaxation (NOR - RR). Units: m2s-’.

In the control forecasts the baroclinic waves suffer a weakening which amounts to a reduction of variance in the order of 40% (Fig. 12(b)) in the North American and west Atlantic part of the storm track. Though the spectral technique using only 20 write-up times in the time series suffers from poor spectral resolution, we found a good agreement to the seasonal day-3 forecast errors for the 1983/84 season. (See Arpe and Klinker 1986, Fig. 16). The differences in high-frequency variance between the two experiments,


excluding and including the Rocky Mountains in the relaxation domain (NOR - RR, Fig. 12(c)), show a strong weakening of the baroclinic waves in the lee of the Rockies and further downstream over the Atlantic. This result suggests that errors from the main mountainous region of North America cause a damping of the baroclinic waves in the Atlantic storm track.

(b) Time mean errors The effect of mountain-forcing errors on the time mean flow pattern can be estimated

from error maps at 500 hPa showing the difference between the experiments excluding and including the Rockies in the relaxation (Fig. 13). For the 10-day mean we find a large similarity to the control forecast error structure (see Fig. 3(a)). Noticeable are the positive height errors over central and northern parts of North America and negative height errors over the Norwegian Sea.

The north-south gradient in the height error field north-west of Britain corresponds to an erroneous westerly flow which extends the Atlantic jet eastward into western Europe. It is remarkable that this error feature, which has its origin in the Rocky Mountain area, is so similar to the seasonally averaged day-10 forecast error (see Arpe and Klinker 1986, Fig. 4).

7. RELAXATION OVER THE HIMALAYAS

To investigate the impact of errors in the Himalayan area on the flow further downstream we modified our land-only relaxation experiment (RL). In this experiment (NOH) we excluded, additionally, a region downstream from the windward side of the Asian mountains (see Fig. 14). In the experiments where forecasts were relaxed towards analyses over land (RL) we found only a small impact on the evolution of errors over

180"

0" Figure 13. Mean height errors at 500 hPa, averaged over 10 days and 4 sets of experiments, spectral truncation T20. Units: dam. Errors are defined as differences between experiments excluding and including the Rocky

Mountains (NOR- RR).

590 E. KLINKER

0 relaxation on:RL / relaxation off: NOH

0 relaxation always on Figure 14. Relaxation mask for the Himalayas experiments

the Pacific. Therefore we can only expect small effects of mountain errors over east Asia on the flow further downstream.

( a ) Transient errors The downstream propagation of errors from the Himalayan region can again be

identified from local spectral analysis of vorticity errors for the full forecast period, in the same way as for the Rocky Mountain experiments. The distribution of the high- frequency variance of vorticity errors shows the major error track (Fig. 15). The key region for downstream-propagating errors turns out to be in north-west China on the lee side of the Altai-Sajany mountains. This is known to be an area where the largest frequency of cyclogenesis occurs (Chung 1977). The error track then follows the usual storm track north of the subtropical jet axis across the Pacific and ends where the relaxation dampens all errors over the American continent.

The main activity of the baroclinic waves in the Pacific is closely connected to the subtropical jet stream. These baroclinic waves follow a track about five degrees north of the jet axis (see Fig. 12(a)). In the control forecasts the baroclinic waves are weakened over almost the entire Pacific with the strongest damping taking place in the centre of the wave activity (Fig. 12(b)). The errors, as they appear in the difference between the experiments excluding and including Himalayas in the relaxation (NOH - RL), show a dipole structure with increasing values south of the storm-track centre and decreasing to

SYSTEMATIC ERRORS INVESTIGATION

180" I I

591

90"E

Figure 15. Track of mountain-forcing errors at 500 hPa. averaged over 4 sets of experiments. The figure shows the high-frequency variance (periods smaller than 3.3 days) for the vorticity differences between experiments

excluding and including the Himalayas in the relaxation (NOH-RL). Units: 1 0 ~ " ' ~ ~ ~ .

the north (Fig. 16). This structure differs from the control forecast errors, and its magnitude is only a third of the control forecast errors. This suggests that errors generated in the Himalayan region have a smaller influence on the transient waves further downstream than errors over the Rocky Mountains have for the baroclinic waves in the Atlantic storm track.

(6) Time mean errors The fact that errors from the Asian continent do not change the typical time mean

error pattern over the Pacific was demonstrated with the relaxation over land (see Fig. 9). The dipole structure of too low heights close to the coast of Alaska and too large heights just south of 40"N in the control forecast is little affected by relaxing the forecast over land. The differences between the forecasts including and excluding the Himalayas in the relaxation region are shown in Fig. 17. The errors originating from the Himalayan region are much more localized near the mountains compared to errors evolving from the Rocky Mountain area. Further downstream over the Pacific the magnitude of the 'mountain errors' is comparatively small.

8. SUMMARY AND CONCLUSIONS

From the winter period 1983/84 four forecasts have been selected to investigate the systematic errors of the ECMWF forecast model with the main emphasis on the northern hemisphere. The method of relaxing forecasts towards analyses appears to be a very useful tool to identify regions from which errors evolve and spread into neighbouring areas.

By relaxing the forecasts towards analyses in the tropics we could separate large errors generated in the extra-tropics from comparatively small errors propagating from

592 E. KLINKER

90"\ 30"E

Figure 16. High-frequency errors for the meridional wind (periods smaller than 3.3 days) at 500-hPa, averaged over 4 sets of experiments. Difference between experiments including and excluding the Himalayas in the

relaxation (NOH- RL). Units: mz SK'.

180" 0

90"W

NOH-RL

90"E

0"

Figure 17. Mean height errors at 500-hPa, averaged over 10 days and 4 sets of experiments, spectral truncation T20. Units: dam. Errors are defined as differences between experiments excluding and including the Himalayas

in the relaxation (NOH - RL).


the tropics into the extra-tropics. Some forecasts showed that baroclinic wave errors of tropical origin partly compensate extra-tropical errors, resulting in smaller errors in the control forecasts than in the tropically relaxed forecasts. This error compensation process means that improvements in tropical forecasts (probably by improved parametrization schemes for physical processes) could lead in some cases to a deterioration of extra- tropical forecasts.

Error tracks show that the largest interactions of tropical errors with the extra- tropical flow take place where the two major storm tracks have a rather low latitude position near the south-east coasts of Asia and North America. The effect of these errors on the upper-level flow is rather weak in the Atlantic. In the north-west Pacific they show a clear effect on the upper-level wind errors when they reach the exit region of the jet. Even though at that stage errors of tropical origin are locally relatively large, they contribute only to a shift of errors. Their wavelike structure has almost no effect on the mean zonal flow north of 30"N.

Relaxing the forecast only over land gave different responses in the error devel- opment in the Pacific and in the Atlantic. Whereas the Pacific error pattern was changed only by a small amount through relaxation over land, errors over the Atlantic were almost totally suppressed.

The Atlantic errors showed a large sensitivity to errors generated in the Rocky Mountain region. The downstream propagation of errors forms a well-defined error track which corresponds closely to the Atlantic storm track for the period under investigation. The mountain-forcing errors are substantial contributors to the weakening of the baroclinic waves.

In the 10-day forecast, mountain-forcing errors propagate through the jet and produce a horizontal error structure in the upper-level wind field which explains large parts of the erroneous acceleration pattern in the exit region of the Atlantic jet. As many features of mountain-forcing errors correspond to prominent errors in the operational forecasts, we can conclude that one of the main sources of systematic errors over the Atlantic and Europe is located in the Rocky Mountain region.

As errors in the Pacific are much less dependent on errors generated over land, only a small impact of errors in the Himalayan region could be found downstream over the Pacific. We can therefore conclude that neither tropical errors nor upstream errors over land, including mountain-forcing problems, explain the large errors occurring in the Pacific. Further investigations are necessary to locate error sources there.

ACKNOWLEDGMENTS

We are very grateful to A . Hollingsworth for his suggestions to improve this paper. We also wish to thank R. Mureau for his comments on the final draft.

Arpe, K and Klinker, E.

Chung, Y. S.

Cubasch, U. and Wiin-Nielsen. A. C.

REFERENCES 1986 Systematic errors of the ECMWF operational forecasting

model in mid-latitudes. Q. J . R. Meteorol. Soc., 112,181- 202

On the orographic influence and lee cyclogenesis and airflow in the Andes, the Rockies and the East Asian Mountains. Arch. Meteorol. Geophys. Biok., A2, 26, 1-12

Predictability studies with the ECMWF spectral model for the extended range: the impact of horizontal resolution and sea surface temperature. Tellus, 38A, 25-41

1977

1986

594 E. KLINKER

Fawcett. E. B. 1969

Haseler. J . 1982

Heckley, W. A. 1985

Horel, J . D. and Wallace, J . M. 1981

Hoskins, B. and Karoly, D. 1981

Klinker, E. and Capaldo, M. 1986

Simmons, A. J . , Wallace, J. M. and 1983

Tibaldi, S. 1987 Branstator, G. W.

Wallace, J . M., Tibaldi S. and 1983 Simmons, A. J.

Systematic errors in operational baroclinic prognoses of the National Meteorological Centre. Mon. Weather Reu. , 97, 67Ck682

An investigation of the impact at middle and high latitudes of tropical forecast errors. Tech. Rep. No. 31, ECMWF, Reading, UK.

Systematic errors of the ECMWF operational forecasting model in tropical regions. Q. J . R. Mefeorol. Soc., 111,

Planetary scale atmospheric phenomena associated with the interannual variability of sea-surface temperature in the equatorial Pacific. Mon. Weather Reu., 109, 813-829

The steady linear response of a spherical atmosphere to thermal and orographic forcing. J . Afmos. Sci., 38, 1179-1196

Systematic errors in the baroclinic waves of the ECMWF model. Tellus, 38A, 215-235

Barotropic wave propagation and instability, and atmospheric teleconnection patterns, J . Afmos. Sci., 40, 1363-1392

Envelope orography and maintenance of the quasi-stationary circulation in the ECMWF global models. Aduances in Geophysics, Vol. 29

Reduction of systematic forecast errors in the ECMWF model through the introduction of an envelope orography. Q. 1. R. Mereorol. Soc. 109. 683-717

709-738

investigation of systematic errors by relaxation experiments

Documents