Experimental study on severe convection forecast in Ningxia by nonlinear retrieval and variational a

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Experimental study on severe convection forecast
in Ningxia by non-linear retrieval and
variational assimilation using satellite data

• HU Wen-dong1,2 SHEN Tong-li3
• DING Jian-jun1 YANG You-lin1 LIU Jian-jun1
• CHEN Xiao-juan2WANG Chenwei3
• (1Key Laboratory of Meteorological Disaster
  Preventing and Reducing in Ningxia, 2Ningxia
  Meteorological Observatory, Yinchuan China,
  750002, 3Nanjing Institute of Meteorology,
  Nanjing China, 210044)

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1.      Introduction

• The application of satellite data is mainly
  confined to the synoptic, satellite
  meteorological conception model, and subjective,
  qualitative explanation in provincial
  meteorological agency.
• The numerical weather prediction (NWP) models are
  getting more and more perfected, their products
  have become one of the indispensable parts for
  modern meteorology and. But the problem of
  initial field remains unsolved, thus the
  meso-scale NWP cannot work efficiently.

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• The characteristics of meteorological satellite
  data make themselves play a very important role
  on data assimilation.
• The hardware performance, technical staff in
  provincial meteorological services are not good
  enough to support the operational implement of
  complicated retrieval and assimilation system.
• Simplicity and easy-going should be the basic
  features in provincial meteorological branch.

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2. Satellite data and derived elements

• The Geostationary Meteorological Satellite
  infrared data of 1999, 2000, and 2001 from May
  1st to Sept. 30 each year were used,the total
  samples is 6839.
• The gray-level data at every meteorological
  station in Ningxia were read correspondingly.
• The gray-level temporal change in a certain
  position was calculated as it did in the
  reference 1.
• Vk,i,jCk,i,j- Ck-1,i,j (1)
• Here C is gray-level, k is time (hour), and i,j
  means the coordinate of the station, or
  geographic position. This element indicates the
  change range of gray-level in a certain temporal
  interval, and reflects the stability of weather
  system.
• In the same data file, the spatial gradient was
  calculated as
• Gi,j (2)

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• This element reflects the consistency degree of
  the cloud. A small gradient means more similar
  near the taken pixel, and the weather tendency of
  cloud there is not obvious, vice versa.
• The bright temperature was calculated and both
  the change rate and gradient were derived.
• The hourly precipitations of 21 meteorological
  stations during that period were collected.
• The fields of relative humidity on surface and at
  different levels of atmosphere were calculated
  for the study using the surface observation and
  sonde data.

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3. Retrieval of meteorological satellite data

• 3.1 Assimilation and satellite data retrieved
  humidity
• Chou2, Charney3 conducted experiment using
  satellite data. Kou4 indicated that the
  precipitation forecast is very sensitive to the
  initial humidity. Because of the wide change of
  humidity both in space and time, and the sparsely
  location of meteorological observation, it is
  hard to describe the detail of moisture
  distribution and it is impossible to meet the
  need of NWP on initial condition. Shen5 studied
  the assimilation with limited area model using
  satellite data and improvement of precipitation
  was achieved. Cui6 adjusted the humidity at
  850400hPa and found the ability of rainfall
  prediction was elevated. Lin7, Zhu8
  researched the torrent rain NWP with satellite
  data retrieved humidity and obtained satisfactory
  results.
• In the light of the studies above, humidity
  retrieval using satellite was carried out to
  provide good initial field for NWP in Ningxia.

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• 3.2 Non-linear retrieval and optimal fitting
• Because of the non linear essential of atmosphere
  movement, the linear process is only an
  approximate approach under certain conditions.
• It is hard to acquire ideal effect based on this
  relation. Retrieval with satellite data is a
  complex issue and a nonlinear model is more
  reasonable.
• Regression mature technology and easy to be
  applied but linear only.
• If the very relation is nonlinear, the nonlinear
  regression can be done with special process. Here
  below are the cases of nonlinear regression.

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• 1. fit with polynomial. Take x,x2,x3xn as linear
  independent factors.
• 2. Transforming with some functions to linear
  regression, such as Gagins9, Bocchieris work
  10.
• 3. Normalize the variable as Bocchieri11 did
  with mathematic model and then to set up
  regression model.
• The method in this paper is, try to find out more
  precise relations between the independent and
  dependent variables with suitable mathematic
  model developed by fitting on the samples. The
  linear relations can be established for
  regression after transform, and the further study
  can be conducted.

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• In this case, the key to the problem is to find
  out the non linear relation.
• In fact, because of the widely scattering of the
  sample, it may not be a strict linear relation
  after the transform, but the linear degree will
  be improved and its beneficial for the quality
  of regression.
• Xie12, Chu13 adopted the fitting method on
  meteorological use, however it is quite rare.

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• The works 9-13 mentioned above assumed the
  fixed function and try to get the parameters
  only. It is limited and the function chosen may
  not an optimal one.
• In this paper, we try to find out a cluster of
  mathematic functions to meet the physics demands,
  and get the parameters. So the optimal function
  can be found out in a certain extent.
• Considering the shape of variables distribution,
  48 functions were designed to fit the samples.
• The functions chosen were sorted by the fitting
  effect, or residual error. The best 2 functions
  were listed in table 1.

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Table 1. The fitted functions
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• 3.3 Over fitting
• The coefficients were improved with the best
  functions. All the absolute coefficients of
  others were elevated more than 0.1.
• But overfitting phenomenon appeared for
  gray-level. Because the function pursued the
  fitness too much, indulged special details and
  the particular non typical samples, the fit
  function is too sensitive and caused violent
  vibration. (Runge phenomenon 14,15. )
• In order to keep the stability and avoid the
  overfitting, the 2nd function was taken for
  gray-level.
• The linearity improvement of bright temperature
  is the most remarked, the absolute correlation
  increased 0.135, and the others increased more
  than 0.1 except temporal change of bright
  temperature which increased 0.084.
• Generally speaking, the correlation improved to a
  better level. The lowest is 0.148 and the highest
  is 0.367.

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• 3.4 Nonlinear regression
• The regression can be conducted after the
  transform to set up the relation between humidity
  and the IR data of geostationary meteorological
  satellite. For concision, let
• V1gray-level
• V2temporal change of gray-level
• V3spatial gradient of gray-level
• V4bright temperature
• V5temporal change of bright temperature
• V6spatial gradient of bright temperature
• V7relative humidity
• Then
• V7a1?1(V1)a2?2(V2)a3?3(V3)a4?4(V4)a5?5(V5)a6
  ?6(V6)b (7)
• Here ai, b are coefficient of regression and ?i()
  are the nonlinear functions selected above and
  i1,2,3,6.

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Table 2. effect of regression before and after
transform.
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The regression with independent fitting transform
is obviously better than the original one. The
correlation enhanced 53.2 from 0.312 to 0.478,
the standard error decreased from 0.1928 to
0.1783 and the residual decreased 27.189, from
184.192 to 157.394.The f was employed to examine
the significance of the regression
(8)Here n number of samples and p number of
factorsThe bigger the correlation, the bigger
the f, and the better the regression. The f of
transformed regression is 2.75 times of that of
original one. Take degree of freedom as 6 and the
number of samples 8, a0.05, then F02.22?Both
fs of the 2 regressions developed are bigger than
F0, so the regression models are acceptable or
significant, and the nonlinear regression is
better.
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Table 3. Regression parameters, A original, B
fitting transformed.
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• 3.5 Retrieval of satellite data for heavy
  precipitation
• Geographically, Ningxia located in the northwest
  China, far inside the mainland and with an arid
  climate. Take Yinhcuan city, the capital as an
  example the annual precipitation is only about
  200mm. Heavy rainfall must go with severe
  convection. Without abundant moisture, even
  though the convection happens, lack of enough
  energy supply of latent heat of condensation
  provided by moisture, the convection will hardly
  develop, and the heavy rainfall will not occur.
• After all, heavy rainfall in Ningxia must
  accompany with severe convection and, the severe
  convection must be supported by plentiful
  moisture.
• For the torrent rainfall, moisture is the key
  condition. 990 samples were selected taking
  relative humidity as threshold and the criterion
  was set as 75 experimentally. With the nonlinear
  approach employed, the relative humidity
  retrieval models at different levels of
  atmosphere were developed and the accuracy was
  further improved.

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4. Brief summary of experiment

• Using the models developed above, relative
  humidity retrieval can be processed easily with
  satellite data, and it can satisfy the
  requirement of provincial meteorological
  department.
• After the retrieval using the approach in this
  paper and neutral network, variational
  assimilation were conducted as reference 16
  did.
• Relative humidity quality control. In space, no
  introduction here.
• Then the retrieved humidity was put into MM5V3
  with other initial fields of T213 output, for a
  sudden occurred heavy rainfall in northern
  Ningxia on July 21 2003, which caused a flood.
• The results show that the precipitation region
  forecast with retrieved humidity is highly
  consistent with observation, and the
  precipitation products are helpful to the
  operational forecast, and spin up was improved
  25. While the forecast without retrieved data
  failed in this experiment.

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• Satellite data July 21 2003, 0800 am, FY-2 IR
• The grid is 60km west and 80km south to the
  actual position in the images. The information
  was read directly from satellite data after
  geographic calibration, in stead of from the
  images above.

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• Retrieved relative humidity after quality
  control and originals at 400 and 500hPa. Dot
  line(blue) humidity of T213, solid line(red)
  retrieved after quality control.
• It is clear that the retrieved relative
  humidity after quality control is consistent with
  the original in macroscale, so it is beneficial
  for the model to run stable.
• On the other hand, the mesoscale systems
  retrieved are much more obvious compared with the
  T213s.

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• A case of heavy rainfall
• a convective torrential rain was observed at
  1400-1500, July 21 2003in north part of
  Ningxia. Maximum hourly precipitation reported
  22.3mm, with 3.2, 1.6, 1.8 and 0.1mm in some
  other stations and the hour next.
• Spatial and temporal distribution of precipitation

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• MM5V3 precipitation without satellite data. The
  convective precipitation only, with a very tiny
  value 0.2128mm at the south end of Ningxia
  (hundreds km away) the maximum forecasted 4h
  later than the observation (spin-up)
• The MM5 can not indicate this convective rainfall
  at all without the assimilation.

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• The satellite data at different levels were
  retrieved and quality controlled (The relative
  humidity fields above), then they were put into
  the MM5v3.
• 1400, 1500, 1600 July
  21,2003

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• 1700
  1800 precipitation (mm)
• The precipitation got enhanced greatly, the
  convective rainfall was forecasted in north part
  of Ningxia since 1400, the exact area of
  observed, and middle part also, maybe false,
  without observation evidence. 1500 north
  stronger 0.2mm, middle disappear. North only.
  1600 0.8. 1700 1.1 mm, 1800 0.5mm and the
  area shrinking. 1900 stopped.

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5. Conclusion and discussion

• With optimal fitting, the mathematical relations
  between the relative humidity and meteorological
  satellite data were found out and, all of the
  relations are nonlinear.
• After the transform with these nonlinear
  functions, nonlinear regression was achieved, and
  the effect of regression was enhanced.
• For the heavy rainfall, the capability of
  retrieval improved further. Comparing with the
  traditional regression, it is not only much more
  reasonable, but achieved a rather high precision
  also.
• The primary experiment indicated the NWP forecast
  made a distinct advance with retrieved data for a
  sudden occurred severe convection with an
  intensive precipitation and caused a flood,
  meanwhile the NWP without assimilation failed to
  forecast.

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thanks for your attention??merci

• ???
• 1?????????????,????,750002,
• HU Wendong
• Key Laboratory of Meteorological Disaster
  Preventing and Reducing in Ningxia, Yinchuan
  China, 750002,
• hu.wendong_at_163.com, 86-951-5043015