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LIU Jia-jun511 P.O.B. of HaiDian district in

BeijingBeijing, China

Liujiajun81@sohu.com

CHENG Liang511 P.O.B. of HaiDian district in

BeijingBeijing, China

chengliang@sohu.com

YU Dan-dan511 P.O.B. of HaiDian district in

BeijingBeijing, China

yudan@sohu.com

Abstract—The study of the saturation characteristic for the growth mode in the tropics has been done by the ensemble prediction using breeding growth mode(BGM) based on the T63L9 model.In the tropics and the extra tropics,the differences of the saturation characteristic for the size and configuration of the growth mode have been analysised in the “no rescaling” and “dynamic rescaling”,besides the influences on the size of growth mode are discussed when changing measurement of the initial mode.The result indictthat in the tropics,the growth mode can grow by the BGM, which can grow more rapidly in “dynamic rescaling” than “no rescaling” and can be saturated more easily.The different measurement of the initial mode have impact on the saturation of perturbation, so in different regions the size of mode should be selected suitably, the mode will take 2 3 days to be saturated in the tropics. In general, it is adaptive to choose 30%-50% of the model 24-hour forecast RMSE asthe initial mode.

Keywords-ensemble prediction; BGM;no rescaling; dynamic rescaling;growth rate;saturation

I. INTRODUCTION

The breeding growth method is brought forward by Toth and Kalnay [1 ~ 3] (1997) by analyzing the errors from the observation data as the forecast initial data and the proportion of other errors in all forecast errors. They consider that the errors of the analysis data mainly come from two parts, one is the random error from the observation data, another is the growth error from the instability of atmosphere. During the forecast process, the component of attenuation will quickly weaken, but the component of increase will grow rapidly. So even if the component of the growth error is small, it will also make an important contribution to the prediction error. The component of attenuation will be weakened more quickly from the initial random error by BGM. Comparatively the component of increase will been grown more rapidly. The previous numerous studies confirm [4 ~ 5], the error growth from the baroclinic instability in the middle and high latitude regions is reflected better by the breeding growth method(BGM),and the breeding vectors in a strong baroclinic zone can quickly grow. therefore, BGM get a better application to the ensemble prediction in the middle and high latitude regions. But the tropical weather situationis very different. In the tropical region, the barotropic instability, convective instability and the interaction of the two is leading mechanism. Whether the error growing rapidly or not by BGM in the tropical region has been

studies less. In the essay, the study of saturation characteristic of the growth mode by BGM has been done in the tropical zone.

II. THE DATA SELECTION AND EXPERIMENT DESIGN

The model initial data use NCEP / NCAR daily reanalysis data by 6 hours from 30 July,2005 to 9 August for the study period.

Using the medium-range numerical prediction modelT63, the ensemble prediction for 10 days will be performed by BGM from 30 July, 2005, the initial mode chooses the forecast RMSE of 24-hour from the model T63 multipliedby random numbers, which obey the [-1,1] of uniform distribution between[6]. This means that 50% of the forecast RMSE of 24-hour from the model T63 will be taken as the initial data (including which the initial mode of relative humidity will take 25% of the 24-hour forecast RMSE because of the too large RMSE relative to the actual error). The breeding cycle period takes 6 hours. At the end of each breeding cycle period, the growth mode is gotten by the forecast results of the disturbance forecast which uses the initial mode plus the observation data as the initial input data of the model T63 subtracting that of the control forecast at the same time. Then the initial mode plus the initial observation data at the next time to carry out the next breeding cycle forecast. Repeating the aboving process for 10 days, finally the 40 growth modes are available.

III. SATURATION CHARACTERISTICS ANALYSIS OF THE GROWTH MODE IN THE TROPICAL REGION

A. The growth rate and the field similitude degreeThe perturbation growth rate is defined as following [7

~ 11]:

1

( )( )

tt

t

E prE p -

= 1

In the formulation, )( tpE represent the size of the

growth mode after t breeding cycle periods.The perturbation growth rate response the speed of the perturbation growth. The perturbation which can grow rapidly maybe have more contributions to the ensemble prediction effect. When the growth rate is greater than

2010 Second IITA International Conference on Geoscience and Remote Sensing

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2010 Second IITA International Conference on Geoscience and Remote Sensing

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1,the perturbation is growing. Higher the growth rate is, the faster the perturbation will grow. The part of the perturbation which grow slowly or weaken will gradually be filtered in the breeding process, but the retaining part is the rapid growth perturbation. When the growth rate is stable by time, the size of the growth mode is close to saturation and the growth rate can be considered as the saturated growth rate. The greater the saturated growth rate is, the better the growth mode is. In theory, the perturbation mode has successfully captured the rapid growth of initial error in the model.

the field similitude degree is defined as following:

yyxxyyxx

xy -·->--<

=)(),(

r 2

In the formulation, x y represent the grid value of the two physical parameter, x y represent the grid

average value, òò ·>=<s

ydsxs

yx 1, is the norm

of yx, 2/1, >=< xxx 2/1, >=< yyy is the

inner product of yx, the field similitude degree shows

that the similarity of the two data grid field The process of BGM is more than one breeding cycle

period. The perturbation field will gradually become saturated in the breeding process. When the output mode is similar with the former input mode before breeding, the breeding cycle can be terminated because of the distribution pattern of the growth mode has become saturated.

B. The saturation characteristic analysis of the growth mode in no rescaling in the tropical regions Typically, tropical region is defined as the area between

30 ° S ~ 30 ° N. The saturation characteristics of the growth mode in the tropical region will be discussed in the “no rescaling” and “dynamic rescaling” and meanwhile the comparisons with the saturation characteristic will be studied between in the tropical region and in the middle and high latitude regions of Southern Hemisphere ( 30 ° S ~ 90 ° S) and Northern Hemisphere(30 ° N ~ 90 ° N).

The analysis of the experiment results indicate that when 50% of the model 24-hour RMSE is used as the initial mode in no rescaling, the breeding process will experience a large amplitude adjustment of a longer period both in the tropical region and in the middle and high latitude regions. Except the wind velocity field, the perturbation growth rate in the tropical region is slightly less than in the middle and high latitude regions with an average of 1.0 ~ 1.05 / (6 hours).The growth rate of wind velocity field in low level is the highest, but it only reaches 1.1 / (6 hours). That is, the instability growth of the mode is slow in the tropics in no rescaling. The

perturbation size of potential height field in the tropics is more difficult to reach saturation in the middle and high latitude region. In the tropics, the perturbation size of potential height and wind velocity will take 3 4 days in the lower level and 2 3 days in the high level to reach saturation. Contrast with relative humidity, the perturbation size is saturated more easily, the breeding time shortens the average of 1 day.

C. The saturation characteristic analysis of the growth mode in no rescaling in the tropical regions

Dynamic rescaling means that the size of output mode at each breeding cycle period will be rescaled to the measurement of the initial mode in the sense of RMSE and then it is taken as the input mode at the next breeding cycle period.

· Figure 3 shows the evolution of the field similitude degree and the growth rate of the potential height with the breeding time increasing at 1000~100hPa in the tropical region. From the figure 3a the conclusion can be drawn that in the tropics the growth rate of potential height in dynamic rescaling is greater than that in no rescaling, at 600hPa ~ 200hPa the growth rate can be up to 1.4 / (6 hours). In addition, below the 800hPa the growth rate is less than 1 / (6 hours) so that the input mode need be enlarged at each breeding cycle period. The growth rate takes 2~3 days to reach saturated The saturation of the distribution pattern of the growth mode will take longer time in the higher level. The saturation time is 1 day below 800hPa and 2 days super 800hPa.

(a)

(b)

Figure 1. the evolvement of field similarity degree and

the growth rate of potential height.

(a) growth rate (b)field similitude degree

415

The growth rate in the middle and high latitude regions is slightly smaller than the 0.1 ~ 0.2 / (6 hours).The Saturation time of the distribution pattern in the middle and high latitude regions of northern hemisphere is ahead half a day than that in tropics(Figure omitted).

· Figure 4 shows the evolution of the field similitude degree and the growth rate of the wind velocity field with the breeding time increasing at 1000~100hPa in the tropical region. From the figure 4 the conclusion can be drawn that the growth rate is greater than 1 at each isotonic height but at near 300hPa and super 150hPa,where the growth rate is less than 1.The maximum growth rate is 1.5/(6 hours) at 850hPa and 1.1/(6 hours) at 500hPa and 200hPa. This evolvement of the growth rate shows the rate can grow rapidly in dynamic rescaling in the tropics. The saturated time of the growth rate and the distribution pattern require 2~3 days. And at 400hPa both of them are more difficult to reach saturation, the saturated time is 3 days.

·

(a)

(b)

Figure 2. the evolvement of field similarity degree and

the growth rate of wind velocity

(a) growth rate (b)field similitude degree The same as the potential height, the evolvement of

the wind velocity field in the tropics is similar to that in middle and high latitude regions. The difference lies in the former 1 to 5 days, the growth rate is greater over 0.1 ~ 0.2 / (6 hours) at 1000hPa ~400hPa in tropics than in the middle and high latitude regions. Besides, In the way of the distribution pattern, the growth mode in the tropics can reach higher saturation state than in the middle and high latitude regions.

· Figure 5 shows the evolution of the field similitude degree and the growth rate of the relative humidity field with the breeding time increasing at 1000~100hPa in the tropical region. From the figure 5 the conclusion can be drawn that the growth rate in the tropics is far greater in dynamic rescaling than in no rescaling. With the height rising upwards, the growth rate continues to decrease. however, the growth rate is still high average of 2.0 / (6 hours) in middle and high level, its growth rate is far greater than that of the potential height field and the whole wind velocity field. Although the growth rate reached a certain value, but variation is unstable and difficult to determine the saturation time. In the tropics the distribution pattern is easier to reach saturation in the lower level than in middle and high level. Below 600hPa the similitude degree can achieve 0.8 after breeding 1 day and 0.9 after breeding one-half days. At 500hPa the similitude degree is 0.7 after breeding 2 days. That can be considered to have reached saturation.

(a)

(b)

Figure 3. the evolvement of field similarity degree and

the growth rate of relative humidity

(a) growth rate (b)field similitude degree

IV. THE SIZE INFLUENCE OF THE INITIAL GROWTH MODE IN THE TROPICS

According to the study from Toth and Kalnay [12 ~ 13] shows that the growth rate and distribution patterns is closely related to the size of the initial mode.The previous section has discussed the saturation characteristics when taking 50% of 24-hour RMSE as the initial mode(25% in relative humidity) in tropical areas. In this section, the initial model will get 0.5%, 10%, 30%, 50%, 70% and 90%

416

of 24-hour forecast RMSE(corresponding to 0.25%, 5%, 15% 25%, 35% and 45% in relative humidity).

A. No Rescaling In no rescaling, when the initial mode takes less than

10% of 24-hour forecast rmse or greater than 50% of 24-hour forecast rmse, the growth rate and distribution pattern saturated had no significant effect with the initial mode. When taking more than 50% as the initial mode, the growth rate remain at 1.0 ~ 1.03 / (6 hours) or so and the perturbation grow less. When taking 10%~50% as the initial mode, the greater the initial mode ,the smaller the growth rate and easier the distribution pattern saturated, then growth rate can achieve 1.05 ~ 1.1 / (6 hours).

B. Dynamic Rescaling When the size of initial mode used is very small, the

perturbation of physical quantities will be in the statue of high growth rates and low distribution pattern saturation, in which the growth rate of potential height and wind velocity field has been up to 4.6 / (6 hours), but that of relative humidity is even up to 5 ~ 35 / (6 hours). For the saturated pattern, the maximum similitude degree of all physical quantities can only reach 0.5 ~ 0.6.

When the initial mode takes 10% to 50% of 24-hour forecast RMSE, in the lower levels of the tropics, the initial mode has little effect on the growth rate of potential height. With the size of the initial mode increasing, the growth rate of wind velocity and relative humidity will continue to decrease. In the middle and high levels of the tropical regions, the growth rate can reach the maximum value when the initial mode takes 30% of the 24-hour forecast RMSE. For the saturated pattern, the higher the size of the initial mode used, the easier the distribution pattern saturated. In the middle and high level, when 30% of the 24-hour RMSE is taken as the initial mode, the saturated pattern is lowest.When taking more than 50%,the size of initial mode has little effect on the growth rate and distribution pattern of physical quantities in every isotonic height( Figure 6, the figure thick solid line represents 50% of 24-hour forecast RMSE taken as initial mode ;circle solid line represents 10%; thin solid line represents 30%; circle dotted line represents 70% of the mold; dotted line represents 90%).

V. THE CONCLUSION Using the medium-range numerical prediction model

T63L9, the sensitivity experiments are done by the model T63L9 and the growth rate of the mode and the field similitude degree in different breeding times are calculated, the differences of the saturation character for the growth mode are been contrasted and analyzed in the “no rescaling” and “dynamic rescaling”, besides the influences on sizes of breeding mode are discussed when changing sizes of the initial mode.

· In the tropics, the perturbation can grow by the BGM, which can grow more rapidly in “dynamic rescaling” than “no rescaling” and can saturate more obviously. The initial mode of different sizes have impact on the saturation of perturbation, so in different regions the mode of different sizes should

be selected. In general, it is adaptive to choose 30%-50% of the model 24h rms for the initial mode.

· The impact of physical process on the perturbation growth relate to the size of initial mode. In the breeding process, the too large or the too small initial mode can’t reflect convective instability very well in the tropics. It is adaptive to choose 30%-50% of the model 24h rms for the initial mode. In the tropics on the middle and high levels, when the smaller initial mode was selected, the main growth mechanism of the perturbation is Cumulus convection and wet process. With selecting larger size of the initial mode, the impact of Cumulus convection and wet process on the perturbation growth is less. When the size of initial mode is larger than 70% of the model 24h rms, the impact of that on the perturbation growth is very little, however physical process is more important for the perturbation growth, the effect of Cumulus convection and wet process to the perturbation growth is not obvious from the size of initial mode when breeding for 5-6 days.

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