<p><b>hsiao</b> 2007-01-21 20:53:28 -0700 (Sun, 21 Jan 2007)</p><p>add radar chapter file radar.tex<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/wrfvar/technote/description.bbl
===================================================================
--- trunk/wrfvar/technote/description.bbl 2007-01-19 16:13:16 UTC (rev 38)
+++ trunk/wrfvar/technote/description.bbl 2007-01-22 03:53:28 UTC (rev 39)
@@ -1,5 +1,9 @@
\begin{thebibliography}{}
+\bibitem[Asai(1965)]{asai65}%
+Asai, T., 1965: A numerical study of the air-mass transformation
+over the Japan Sea in winter. {\em J. Meteor. Soc. Japan}, {\bf 43}, 1-15.
+
\bibitem[Barker et al.(2003)]{barker03}%
Barker, D. M., W. Huang, Y.-R. Guo, and A. Bourgeois, 2003: A Three-Dimensional
Variational (3DVAR) Data Assimilation System For Use With MM5.
@@ -7,12 +11,12 @@
Box 3000, Boulder, CO, 80307.].
\bibitem[Barker et al.(2004)]{barker04}%
-Barker, D. M., W. Huang, Y.-R. Guo, A. Bourgeois, and X. N. Xiao, 2004:
+Barker, D. M., W. Huang, Y.-R. Guo, A. Bourgeois, and Q. Xiao, 2004:
A Three-Dimensional Variational Data Assimilation System for MM5:
Implementation and Initial Results
{\em Mon. Wea. Rev.}, {\bf 132}, 897--914.
-\bibitem[Barker (2005)]{barker05}%
+\bibitem[Barker(2005)]{barker05}%
Barker, D. M., 2005: High Southern-Latitude Ensemble Data Assimilation in the Antarctic
Mesoscale Prediction System.
{\em Mon. Wea. Rev.}, {\bf 133}, 3431--3449.
@@ -22,6 +26,11 @@
satellite data to a hurricane simulation.
{\em Quart. J. Roy. Meteor. Soc.}, {\bf 130}, 801--825.
+\bibitem[Courtier et al.(1994)]{courtier94}%
+Courtier, P., J. N. Thepaut, and A. Hollingsworth, 1994: A strategy for
+operational implementation of 4D-Var using an incremental approach.
+{\em Quart. J. Roy. Meteor. Soc.}, {\bf 120}, 1367-1387.
+
\bibitem[Cucurull et al.(2004)]{cucurull04}%
Cucurull, L., F. Vandenberghe, D. Barker, E. Vilaclara, and A. Rius, 2004: 3DVAR assimilation
of GPS and meteorological observations in MM5 during the December 14th 2001 storm event
@@ -48,6 +57,11 @@
in a variational assimilation.
{\em Quart. J. Roy. Meteor. Soc.}, {\bf 127}, 1433--1452.
+\bibitem[Dudhia(1989)]{dudhia89}%
+Dudhia, J., 1989: Numerical study of convection observed during the winter
+monsoon experiment using a mesoscale two-dimensional model.
+{\em J. Atmos. Sci.}, {\bf 46}, 3077-3107.
+
\bibitem[Faccani et al.(2003)]{faccani03}
Faccani, C., R. Ferretti, R. Pacione, F. Vespe, L. Cucurull, and D. M. Barker, 2003: Near real-time
data assimilation of GPS ZTD and PW into a non-hydrostatic model.
@@ -68,8 +82,14 @@
{\em Seminar on Recent Development in Data Assimilation for Atmosphere and Ocean},
45--63, ECMWF.
+\bibitem[Fujiyoshi et. al.(1990)]{fujiyoshi90}
+Fujiyoshi, T., T. Endoh, T. Yamada, K. Ksuboki, Y. Tachibana,
+and G. Wakahana, 1990: Determination of a Z-R relationship for snowfall using
+a radar and high sensitivity snow gauges. {\em J. Appl. Meteor.},
+{\bf 29}, 147-152.
+
\bibitem[Gu et al.(2005)]{gu05}
-Gu, J., Q. -N. Xiao, Y. -H. Kuo, D. M. Barker, J. Xue, and X. Ma, 2005: A Case Study Of
+Gu, J., Q. Xiao, Y. -H. Kuo, D. M. Barker, J. Xue, and X. Ma, 2005: A Case Study Of
Typhoon Rusa (2002) On Its Analysis And Simulation Using WRF 3DVAR And The WRF
Modeling System.
{\em Adv. In Atmos, Sci.}, {\bf 22}, 415--425.
@@ -94,6 +114,15 @@
the Met. Office global 3-D variational data assimilation scheme.
{\em Quart. J. Roy. Meteor. Soc.}, {\bf 127}, 209--232.
+\bibitem[Jorgenson and Wills(1982)]{jorgenson82}%
+Jorgenson, D. P., and P. T. Wills, 1982: A Z-R relationship for hurricanes.
+{\em J. Appl. Meteor.}, {\bf 21}, 356-366.
+
+\bibitem[Kessler(1969)]{kessler69}%
+Kessler, E., 1969: On the distribution and continuity of water substance
+in atmospheric circulation. {\em Meteor. Monogr.}, {\bf 10}, No. 32,
+Amer. Metreor. Soc., 84pp.
+
\bibitem[Lee et al.(2005)]{lee05}%
Lee, M. -S., and D. M. Barker, 2005: Preliminary Tests of First Guess at Appropriate Time
(FGAT) with WRF 3DVAR and WRF Model.
@@ -118,6 +147,27 @@
Dimensional Variational Data Assimilation Scheme.
{\em Quart. J. Roy. Meteor. Soc.}, {\bf 126}, 2991--3012.
+\bibitem[Mohr and Vaughan(1979)]{mohr79}%
+Mohr, C. G., and R. L. Vaughan, 1979: An economical procedure for Cartesian
+interpolation and display of reflectivity data in three-dimensional space.
+{\em J. Appl. Meteor.}, {\bf 18}, 661-670.
+
+\bibitem[Mohr et al.(1981)]{mohr81}%
+Mohr, C. G., L. J. Miller, and R. L. Vaughan, 1981: An interactive software
+package for the rectification of radar data to three-dimensional Cartesian
+coordinates. Preprints, 20th Conf. On Radar Meteorology, Boston,
+Amer. Meteor. Soc., 690-695.
+
+\bibitem[Navon et al.(1992)]{navon92}%
+Navon, I. M., X. Zou, J. Derber, and J. Sela, 1992: Variational data
+assimilation with an adiabatic version of the NMC spectral model.
+{\em Mon. Wea. Rev.}, {\bf 120}, 1433-1446.
+
+\bibitem[Oye et al.(1995)]{oye95}%
+Oye, R., C. Mueller, and S. Smith, 1995: Software for radar translation,
+visualization, editing, and interpolation. Preprints: 27th Conference on
+Radar Meteorology, Vail, Amer. Meteor. Soc., 359-361.
+
\bibitem[Parrish and Derber(1992)]{parrish92}%
Parrish, D. F., and J. C. Derber, 1992: The National Meteorological Center's Spectral
Statistical Interpolation analysis system.
@@ -134,38 +184,92 @@
experiments with a four-dimensional variational assimilation system.
{\em Quart. J. Roy. Meteor. Soc.}, {\bf 124}, 1861--1887.
+\bibitem[Ray et al.(1980)]{ray80}%
+Ray, P. S., C. L. Ziegler, W. Bumgarner, and R. J. Serafin, 1980: Single- and
+multi-Doppler radar observations of tornadic storms. {\em Mon. Wea. Rev.},
+{\bf 108}, 1607-1625.
+
+\bibitem[Ray et al.(1981)]{ray81}%
+Ray, P. S., B. C. Johnson, K. W. Johnson, J. S. Bradberry, J. J. Stephens,
+K. K. Wagner, R. B. Wilhelmson, and J. B. Klemp, 1981: The morphology of
+several tornadic storms on 20 May 1977. {\em J. Atmos. Sci.},
+{\bf 38}, 1643-1663.
+
+\bibitem[Richardson(1922)]{richardson22}%
+Richardson, L. F., 1922: Weather Prediction by Numerical Process.
+Cambridge University Press, London, 1922, 236pp.
+
\bibitem[Skamarock et al.(2005)]{skamarock2005}%
Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, W. Wang, and J. G. Powers,
2005: A Description Of The Advanced Research WRF Version.
NCAR Tech Note, NCAR/TN-468+STR, 88 pp. [Available from UCAR Communications, P.O.
Box 3000, Boulder, CO, 80307.].
+\bibitem[Sun and Crook(1997)]{sun97}%
+Sun, J., and N. A. Crook, 1997: Dynamical and microphysical retrieval from
+Doppler radar observations using a cloud model and its adjoint.
+Part I: Model development and simulated data experiments. {\em J. Atmos. Sci.},
+{\bf 54}, 1642-1661.
+
+\bibitem[Sun and Crook(1998)]{sun98}%
+Sun, J., and N. A. Crook, 1998: Dynamical and microphysical retrieval from
+Doppler radar observations using a cloud model and its adjoint.
+Part II: Retrieval experiments of an observed Florida convective storm.
+{\em J. Atmos. Sci.}, {\bf 55}, 835-852.
+
+\bibitem[Sun and Crook(2001)]{sun01}%
+Sun, J., and N. A. Crook, 2001: Real-time low-level wind and temperature
+analysis using single WSR-88D data. {\em Weather and Forecasting},
+{\bf 16}, 117-132.
+
+\bibitem[Tuttle and Foote(1990)]{tuttle90}%
+Tuttle, J. D., and G. B. Foote, 1990: Determination of the boundary layer
+airflow from a single Doppler radar. {\em J. Atmos. and Oceanic Technol.},
+{\bf 7}, 218-232.
+
\bibitem[Wang et al.(2004)]{wang04}%
Wang, W., D. Barker, C. Bruy\`ere, J. Dudhia, D. Gill, and J. Michalakes, 2004:
WRF Version 2 modeling system user's guide.
{\em http://www.mmm.ucar.edu/wrf/users/docs/user$\_$guide/}.
+\bibitem[Weygandt et al.(2002a)]{weygandt02a}%
+Weygandt, S. S., A. Shapiro, and K. K. Droegemeier, 2002a: Retrieval of
+model initial fields from single-Doppler observations of a supercell
+thunderstorm. Part I: Single-Doppler velocity retrieval.
+{\em Mon. Wea. Rev.}, {\bf 130}, 433-453.
+
+\bibitem[Weygandt et al.(2002b)]{weygandt02b}%
+Weygandt, S. S., A. Shapiro, K. K. Droegemeier, 2002b: Retrieval of model
+initial fields from single-Doppler observations of a supercell
+thunderstorm. Part II: Thermodynamic retrieval and numerical prediction.
+{\em Mon. Wea. Rev.}, {\bf 130}, 454-476.
+
+\bibitem[White(2000)]{white00}%
+White, A., 2000: A View of the Equations of Meteorological Dynamics and
+Various Approximations. Forecasting Research Scientific Paper,
+No. 58. UK Met Office.
+
\bibitem[Wu et al.(2002)]{wu02}%
Wu, W. -S., R. J. Purser, and D. F. Parrish, 2002: Three-Dimensional Variational
Analysis with Spatially Inhomogeneous Covariances.
{\em Mon. Wea. Rev.}, {\bf 130}, 2905--2916.
-\bibitem[Xiao et al.(2004)]{xiao04}%
-Xiao, Q. N., Y. H. Kuo, J. Sun, W. C. Lee, E. Lim, Y. R. Guo, and D. M. Barker, 2004:
- Assimilation of Doppler Radar Observations with a Regional 3D-Var System: Impact of
- Doppler Velocities on Forecasts of a Heavy Rainfall Case.
- {\em J. Appl. Met.}, {\bf 44(6)}, 768--788.
+\bibitem[Xiao et al.(2005)]{xiao05}%
+Xiao, Q., Y. H. Kuo, J. Sun, W. C. Lee, E. Lim, Y. R. Guo, and D. M. Barker,
+2005: Assimilation of Doppler radar observations with a regional 3D-Var
+system: Impact of Doppler velocities on forecasts of a heavy rainfall case.
+{\em J. Appl. Met.}, {\bf 44(6)}, 768--788.
-\bibitem[Xiao et al.(2006)]{xiao06a}%
-Xiao, Q., Y.-H. Kuo, Y. Zhang, D. M. Barker, and D.-J. Won, 2006: A tropical cyclone bogus data
- assimilation scheme in the MM5 3D-Var system and numerical experiments with Typhoon
- Rusa (2002) near landfall.
- {\em J. Meteor. Soc. Japan}, {\bf 84(4)}, 671--689.
+\bibitem[Xiao et al.(2006)]{xiao06}%
+Xiao, Q., Y.-H. Kuo, Y. Zhang, D. M. Barker, and D.-J. Won, 2006:
+A tropical cyclone bogus data assimilation scheme in the MM5 3D-Var system
+and numerical experiments with Typhoon Rusa (2002) near landfall.
+{\em J. Meteor. Soc. Japan}, {\bf 84(4)}, 671--689.
-\bibitem[Xiao et al.(2006)]{xiao06b}%
-Xiao, Q., Y.-H. Kuo, J. Sun, W.-C. Lee, D. M. Barker, and E. Lim, 2006: An approach of Doppler
- reflectivity data assimilation and its assessment with the inland QPF of Typhoon Rusa (2002) at
- landfall.
- {\em J. Appl. Meteor.}, Revised.
+\bibitem[Xiao et al.(2007)]{xiao07}%
+Xiao, Q., Y.-H. Kuo, J. Sun, W.-C. Lee, D. M. Barker, and E. Lim, 2007:
+An approach of radar reflectivity data assimilation and its assessment
+with the inland QPF of Typhoon Rusa (2002) at landfall.
+{\em J. Appl. Meteor. Climat.}, {\bf 46}, 14-22.
\end{thebibliography}
Modified: trunk/wrfvar/technote/description.tex
===================================================================
--- trunk/wrfvar/technote/description.tex 2007-01-19 16:13:16 UTC (rev 38)
+++ trunk/wrfvar/technote/description.tex 2007-01-22 03:53:28 UTC (rev 39)
@@ -76,7 +76,7 @@
\include{be_modeling}
\include{obs}
\include{radiances}
-%\include{radar}
+\include{radar}
\include{gps}
\include{diagnostics}
%\include{suites}
Modified: trunk/wrfvar/technote/radar.tex
===================================================================
--- trunk/wrfvar/technote/radar.tex 2007-01-19 16:13:16 UTC (rev 38)
+++ trunk/wrfvar/technote/radar.tex 2007-01-22 03:53:28 UTC (rev 39)
@@ -23,14 +23,14 @@
Doppler radar observation is an important data source for mesoscale and
microscale weather analysis and forecasting. Early work on Doppler radar
data analysis mainly focused on two aspects: one is rainfall analysis
-using radar reflectivity via Z-R relation (Jorgenson and Willis 1982;
-Fujiyoshi et al. 1990), and the other is synthesis of two independent
-Doppler velocities (Ray et al. 1980; 1981). Techniques to estimate
+using radar reflectivity via Z-R relation \citep{jorgenson82,fujiyoshi90},
+and the other is synthesis of two independent
+Doppler velocities \citep{ray80,ray81}. Techniques to estimate
the velocity field by objectively determining the motion of radar echo
-patterns have also received much attention (Tuttle and Foote 1990).
+patterns have also received much attention \citep{tuttle90}.
In recent years, assimilation of Doppler radar data for short-term
numerical weather forecasting or nowcasting has become a focal point of
-research (Sun and Crook 2001; Weygandt et al. 2002a, b).
+research \citep{sun01,weygandt02a,weygandt02b}.
There are several technical and scientific challenges in Doppler radar
data assimilation. First of all, the radar data are normally at the
@@ -52,7 +52,7 @@
Although there are challenges, radar data assimilation could be
very promising for short-range numerical weather prediction.
To assimilate Doppler radial velocities, the WRF 3D-Var has been included
-vertical velocity ($w$) increments (Xiao et al. 2006). This is important
+vertical velocity ($w$) increments \citep{xiao05}. This is important
when radar data are included in the analysis and for small-scale
convective weather systems. Mixing ratios of cloud water ($q_c$) and
rainwater ($q_r$) are included in the background fields. When 3D-Var
@@ -60,21 +60,29 @@
alleviate the spin-up problems for the subsequent forecast.
For radar reflectivity assimilation, the inclusion of the analyses
(increments) of rainwater and cloud water mixing ratios in the
-3D-Var system is vital (Xiao et al. 2007). In the continuous
+3D-Var system is vital \citep{xiao07}. In the continuous
cycling mode, 3D-Var assimilation of radar reflectivity data can
produce relatively rational analyses of the hydrometeor fields.
+A case study for Typhoon Rusa (2002) in East Asia showed very
+positive impact of the Doppler radar data assimilation.
+Although 3D-Var without radar data could improve the typhoon forecast
+\citep{gu05,xiao06}, inclusion of Doppler radar data further improved
+the forecast of the typhoon track and intensity \citep{xiao07}.
+
A significant advantage of 3D-Var is its greater computational
efficiency than other assimilation techniques (e.g. 4D-Var or
-ensemble Kalman filter).
-
-In this chapter, we will briefly introduce the radar data preprocessing
+ensemble Kalman filter). This makes 3D-Var more feasible in real-time
+or operational forecasting. In this chapter, we will
+briefly introduce the radar data preprocessing
procedure, including data quality control, data thinning, and a
-simple observation error statistics in Section 2. This description of the
-preprocessing is in conceptual level, and the users should have their
+simple observation error statistics in Section \ref{radar-prep}.
+The description of the preprocessing is in conceptual
+level, and the users should have their
own preprocessing of the radar data before assimilation. However, we
will present details of the techniques for Doppler radar data
assimilation. The assimilation of Doppler radial vedlocity will be
-described in Section 3, and that of reflectivity will be in Section 4.
+described in Section \ref{radar_rv}, and that of reflectivity will
+be in Section \ref{radar_rf}.
\section{Preprocessing of Doppler Radar Data}
\label{radar-prep}
@@ -91,7 +99,7 @@
ground clutter, second trip echo, sea clutter and other noise.
We should conduct quality control using manual editting or automatic
software. For example, the radar data can be interactively edited
-using NCAR SOLO software (Oye et al. 1995) to conduct the data
+using NCAR SOLO software \citep{oye95} to conduct the data
quality control. Each scan was carefully examined in order to
identify unwanted radar echoes. These unwanted echoes were either
recovered (e.g., velocity folding) or removed
@@ -123,7 +131,7 @@
The thinning of radar data can be performed using NCARs software
SPRINT (Sorted Position Radar INTerpolation) and CEDRIC (Custom
Editing and Display of Reduced Information in Cartesian space)
-developed by Mohr and Vaughan (1979) and Mohr (1981). Data for each
+developed by \citet{mohr79} and \citet{mohr81}. Data for each
Cartesian grid are interpolated using the surrounding eight points
from the four beams (two on either side, above and below). Each
volume data are put at the same time. To get rid of grid data that
@@ -154,24 +162,23 @@
observations and related errors are calculated, they are converted
to 3D-Var input format.
-\section{Doppler Radial Velocity Assimilation}
+\section{Assimilation of Doppler Radial Velocities}
\label{radar_rv}
The configuration of the WRF 3D-Var system is based on a multivariate
-incremental formulation (Courtier et al. 1994). The preconditioned
+incremental formulation \citep{courtier94}. The preconditioned
control variables are described in Chapter 2. For radail velocity
assimilation, we added a new balance equation, the Richardson's
-equation, for generating the vertical velocity increments (Xiao et al.
-2005).
+equation, for generating the vertical velocity increments \citep{xiao05}.
\subsection{Vertical velocity increments}
In order to include a capability to assimilate the vertical component of
Doppler radial velocity data, the WRF 3D-Var includes vertical velocity
-increments. Based on Richardson (1922) and White (2000), a balance
+increments. Based on \citet{richardson22} and \citet{white00}, a balance
equation that combines the continuity equation, adiabatic
thermodynamic equation, and hydrostatic relation is derived. Details of
-the derivation can be seen in Xiao et al. 2005.
+the derivation can be found in \citet{xiao05}.
\begin{equation}
{\gamma p} {\partial w \over \partial z} =
@@ -185,8 +192,8 @@
heat capacities of air at constant pressure/volume, $p$ pressure,
$\rho$ density, $T$ temperature, $c_p$ specific heat capacity of air
at constant pressure, $z$ height, and $g$ the acceleration due to
-gravity. For simplicity, hereafter Eq. (1) will be referred to as
-Richardsons equation. Linearizing Eq. (1) by writing each variable
+gravity. For simplicity, hereafter Eq. (\ref{richdson_b}) will be referred to as
+Richardsons equation. Linearizing Eq. (\ref{richdson_b}) by writing each variable
in terms of a basic state (overbar) plus a small increment (prime)
gives
@@ -199,14 +206,16 @@
& + g \int _z ^\infty {\bf </font>
<font color="black">abla}
\cdot (\overline \rho {\bf V_h}') dz + g \int _z ^\infty {\bf </font>
<font color="gray">abla}
\cdot ({\rho}' {\bf \overline V_h}) dz
+\label{r_l}
\end{eqnarray}
-The basic state (overbar) variables satisfy Eq. (1). They also
+The basic state (overbar) variables satisfy Eq. (\ref{richdson_b}). They also
satisfy the continuity equation, adiabatic equation and hydrostatic
-equation. The linear equation (2) is discretized, and its adjoint code
+equation. The linear Richardson's equation (\ref{r_l})
+is discretized, and its adjoint code
is developed according to the code of the linearized equation. The
correctness of the adjoint check following the method proposed by
-Navon et al. (1992) is verified.
+\citet{navon92} is verified.
The Richardsons equation is chosen due to the following reasons:
a). It is a higher order approximation of the continuity equation
@@ -251,7 +260,7 @@
water and rainwater information. In the Doppler radial velocity
operator, rainwater terminal velocity is included, and terminal
velocity is calculated based on the rainwater mixing
-ratio (Sun and Crook 1998).
+ratio \citep{sun98}.
\subsection{Observation operator for Doppler radial velocity}
@@ -269,7 +278,7 @@
and $v_T$ is terminal velocity. For radar scans at nonzero
elevation angles, the fall speed of precipitation particles has
to be taken into account. There are different ways to calculate
-terminal velocity. Here, we use the algorithm of Sun and Crook (1998)
+terminal velocity. Here, we use the algorithm of \citet{sun98}
to calculate terminal velocity $v_T$ (m/s),
\begin{equation}
@@ -288,7 +297,7 @@
</font>
<font color="gray">oindent where $\overline p$ is the base-state pressure and $p_0$
is the pressure at the ground.
-\section{Assimilation of Radar Reflectivity}
+\section{Radar Reflectivity Assimilation}
\label{radar_rf}
Radar reflectivity measures the radar signal reflected by
@@ -300,14 +309,14 @@
zero errors in most of the domain grid points. Instead, we chose
total water mixing ratio $q_t$ as a control variable and
conducted background error statistics for the WRF 3D-Var when
-radar reflectivity is to be assimilated (Xiao et al. 2007).
+radar reflectivity is to be assimilated \citep{xiao07}.
\subsection{Partitioning of moisture and hydrometeor increments}
Because total water mixing ratio $q_t$ is used as a control variable,
partitioning of the moisture and hydrometeor increments is necessary
in the 3D-Var system. We introduced the warm rain process of
-Dudhia (1989), which includes condensation of water vapor into
+\citet{dudhia89}, which includes condensation of water vapor into
cloud ($P_{CON}$), accretion of cloud by rain ($P_{RA}$), automatic
conversion of cloud to rain ($P_{RC}$), and evaporation of rain to
water vapor ($P_{RE}$). These are the major processes of hydrometeor
@@ -318,14 +327,16 @@
The autoconversion term, $P_{RC}$, is represented by
\begin{equation}
-P_{RC} = \cases{ \ k_1 (q_c - q_{crit}),
- &if $q_c \ge q_{crit}$; \cr
- \ 0. &if $q_c < q_{crit}$, \cr}
+P_{RC} =
+ \begin{cases}
+ k_1 (q_c - q_{crit}), &if\ q_c \ge q_{crit}; \\
+ 0. &if\ q_c < q_{crit},
+ \end{cases}
\label{P_rc}
\end{equation}
</font>
<font color="gray">oindent where $q_c$ is the cloud water mixing ratio. According to
-Kessler (1969), $k_1=10^{-3}\ s^{-1}$, $q_{crit}=0.5 g\cdot kg^{-1}$.
+\citet{kessler69}, $k_1=10^{-3}\ s^{-1}$, $q_{crit}=0.5 g\cdot kg^{-1}$.
The accretion of cloud water by rain is parameterized by
\begin{equation}
@@ -358,7 +369,8 @@
for water vapor, and specific heat at constant pressure for moist air,
respectively.
-The tangent linear and its adjoint of the scheme were developed and
+The tangent linear and its adjoint of the warm rain scheme
+(\ref{P_rc}) - (\ref{P_con}) were developed and
incorporated into the WRF 3D-Var system. Although the control variable
is $q_t$, the $q_v$, $q_c$ and $q_r$ increments are produced through the
partitioning procedure during the 3D-Var minimization. The warm rain
@@ -373,8 +385,8 @@
Once the 3D-Var system can produce $q_c$ and $q_r$ increments, the setup
of the observation operator for assimilation of reflectivity is
-straightforward. Simply, we adopted the observation operator from Sun
-and Crook 1997:
+straightforward. Simply, we adopted the observation operator from
+\citet{sun97}:
\begin{equation}
Z = 43.1+17.5log(\rho q_r),
@@ -382,14 +394,15 @@
\end{equation}
</font>
<font color="gray">oindent where $Z$ is reflectivity in the unit of $dBZ$ and $q_r$ is
-the rainwater mixing ratio. The relation is derived analytically
+the rainwater mixing ratio. The relation (\ref{Z_operator})
+is derived analytically
by assuming the Marshal-Palmer distribution of raindrop size.
\subsection{Summary of the implementation procedure}
Great efforts were made to incorporate the reflectivity assimilation into
the WRF 3D-Var system. The flow chart of computations in the WRF 3D-Var
-minimization procedure can be found in Xiao et al. 2007. For clarity of
+minimization procedure can be found in \citet{xiao07}. For clarity of
the procedure, we summarized some implementation details in the following.
First of all, the control variable transform was built to bridge
@@ -418,4 +431,3 @@
converges, the increments of $q_c$, $q_r$, $q_v$ and $T$ are
produced by the reflectivity assimilation. The radar reflectivity
observations is therefore assimilated into the 3D-Var analusis.
-
</font>
</pre>