Introduction
Numerical simulation of a weather phenomenon requires an efficient numerical
model as well as an accurate initial state of the system. Data assimilation
is the technique used to estimate the optimal state of the atmospheric
system, utilising available meteorological observations as well as background
information. The background and the observation information are weighted
utilising their respective error covariances. Accurate specification of both
observation and background errors is important for the success of a data
assimilation system since these contribute to the improved analysis.
The observation error covariance matrix R is determined by instrument
errors and representation errors, the latter arising from the effect of
unresolved scales in a model as well as errors that arise from the
specification of the observation operator, which maps model space variables to
observation space. However, exact determination of a background error
covariance (BEC) matrix is not practically possible, as the “truth” is not
known, and hence is estimated in data assimilation systems using different
methods. Furthermore, for a typical numerical weather model with a state
space of dimension ∼107, the BEC matrix has a dimension of ∼107×107, which cannot be explicitly represented in a computing
system. Better estimates of the BEC matrix can, in principle, lead to more
accurate analyses. Hence the study of different methods of determination of
background errors has become an important research area, with substantial
literature available
There are three methods for diagnosing background error (BE) covariance,
namely (i) using innovation statistics ,
(ii) the National Meteorological Center (NMC) method
and (iii) the analysis-ensemble method
. Usage of innovation
(observation minus background) statistics has the limitation that this method
requires a good-quality, homogeneous observation network. Furthermore, this
method provides estimates of background error for observed quantities only.
The NMC method approximates the background error statistics using the
difference between two model forecasts of different lead times that are valid at the
same time. The analysis system is run several times using perturbed inputs in
the analysis-ensemble method. The difference between background fields in the
various runs provides a surrogate of background errors in this method.
Despite having its own shortcomings, the most commonly used method for generating the BEC is the NMC method. It is known that the NMC method
underestimates the variance of background error over data-sparse regions.
Also, the duration of forecasts used to generate BEC is typically 12 to
48 h. Since the background fields used in the assimilation system would
typically be of a shorter duration, the covariances of estimated background
error could become broader than the actual background error
. The popularity of the method, however, arises from
the fact that this method yields global statistics for BEC for model
variables at all levels. Moreover, it is less expensive to implement the NMC
method in an operational weather prediction environment since the forecasts
required to generate the differences would be already available.
The NMC method has been implemented to estimate the BEC in the Weather Research
and Forecasting (WRF) model's variational data assimilation system (WRFDA)
. This method employs a control variable transform
(CVT) in which the model variables are converted into the control variables of
the data assimilation system. This CVT renders the BEC matrix diagonal and
also imposes balance relations within the variables. The manner in which the
CVT is specified can impact the data assimilation results. In WRFDA3.5.1,
there are three choices for CVTs, referred to as the cv3, cv5 and
cv6 options. With cv3, the control variables are described in physical space,
while the control variables are defined in the eigenvector space in the cv5 and
cv6 options. While the cv3 option uses a vertical recursive filter to model the
vertical covariance, both the cv5 and cv6 option use an empirical orthogonal
function (EOF) approach to represent the vertical covariance. Previous
studies (e.g. ) have shown that the simulation of
mesoscale weather phenomena like monsoon depressions over India can be
improved using domain-specific BEC statistics calculated using the cv5 option
rather than BEC utilising the cv3 option in WRF. However, comparisons
of the impact of assimilating observations by three-dimensional
variation (3DVar) analysis using the cv5 and cv6 options for
simulating weather phenomena over the Indian region are not available in the
literature. The present study is an effort in that direction which examines
how the difference in the formulation of CVTs in BEC
formulation influences the impact of assimilating meteorological observations
in the WRF model.
The BEC statistics generated here using the NMC method are indeed
homogeneous, isotropic and stationary. Flow-dependent BEC statistics
generated using ensemble methods and ensemble-based data assimilation systems
provide improved analysis . However, generating
and maintaining a large-sized ensemble that can adequately sample the model's
uncertainty space is challenging and computationally expensive. This is
especially true in a limited-area model, where uncertainties in the model's
lateral boundary conditions are also significant.
The influence of the CVT's formulation in BEC modelling is demonstrated here
in the case of three monsoon depressions (MDs) that formed over the Indian
region. The amount of summer monsoon rainfall over central India depends
on the formation and passage of these systems. MDs are one of the most
significant synoptic-scale disturbances that occur during the Indian summer
monsoon season of June–September. Typically 6–7 MDs form over the Indian
region during this period each year. These systems, which have a horizontal
radial extent of 1000 km, contribute to heavy to very heavy rainfall over
India during their passage. Several previous studies (e.g. ; ; ; )
have reported that 3DVar assimilation of observations have resulted in
improved simulation of MDs using the WRF model. However, the inclusion of
additional multivariate correlation information in the background error
formulation in the cv6 option has not been investigated by any of the above-mentioned studies.
Section 2 provides further details on the cv5 and cv6 options available with
WRFDA and Sect. 3 describes the depression cases investigated here.
Experimental design details are provided in Sect. 4, with the results
discussed in Sect. 5. Section 6 briefly summarises the conclusions drawn
from the current study.
Background error covariance modelling
Let x∈Rn denote the state vector of the system. If
the true state of the system is represented as xt and a
background state is represented as xb, then the error in the
background state can be represented as ϵb=xt-xb. It is assumed that the background error is
unbiased, i.e. 〈ϵb〉=0 where the angular brackets
denote the expectation value. The 3DVar analysis is obtained by minimising a
cost function defined as
J(x)=Jb+Jo=12[(x-xb)TB-1(x-xb)+=(y-H(x))TR-1(y-H(x))].
The analysis x=xa represents a minimum variance
estimate of xt given the observations y∈Rm as well as the error covariances of background and
observations denoted by B and R respectively. The
observation operator H provides a mapping from the model's grid space to
the observation space.
The calculation of the background term Jb requires ∼O(n2)
calculations for a system with n degrees of freedom. For a numerical
weather model with typically 107 degrees of freedom, the direct
calculation of this term is not possible. To reduce the computational cost,
Jb is calculated in terms of control variables v defined via
the relation x′=Uv, where x′
denotes the analysis increment, x′=x-xb . Using the incremental formulation
and the control variables,
Eq. () can be rewritten as
J(v)=Jb+Jo=12vTv+12(y-HUv)TR-1(y-HUv).
The transformation matrix U is defined in such a way that the
background error matrix can be represented as UUT. In
WRF 3DVar system, the CVT is implemented in three
steps – a horizontal transform, Uh; a vertical
transform,
Uv; and a parameter transform, Up
.
i.e,x′=UhUvUpv
The CVT aims to convert the BEC matrix into
block-diagonal form. The horizontal transform Uh is represented
using recursive filters in
WRF 3DVar. There are two free parameters associated with each variable for
the recursive filter – the number of applications of the filter and the
correlation length scale of the filter. The correlation length scale is
estimated for each variable and vertical mode using the NMC method's
accumulated forecast difference data processed as a function of grid-point
separation . A tuning factor is applied to the length
scale in order to reflect the actual correlation length scales in a domain.
In the vertical transform, Uv, an empirical orthogonal function
decomposition is performed on the vertical component of the background error,
Bv. The analysis increments are projected onto the eigenvector
space and the eigenvalues specify the relative weights of increments in the
calculation of cost function. The parameter transform, Up, is
applied so that the errors in the control variables are not correlated with
each other and the BEC matrix is rendered block-diagonal. The increments in
model variables u (zonal wind), v (meridional wind), T (temperature),
p (pressure) and humidity (q) are converted into a new set of variables such as
stream function (ψ), velocity potential (χ), temperature (T),
surface pressure (ps) and relative humidity (rh). The WRF-Var system provides
the balance relations between the new set of variables using regression
relations. After the “balanced part” of analysis variables is estimated, the
“unbalanced part” is determined by subtracting the former from the full
fields. Hence, while some fields are analysed in full, for some other
variables the unbalanced parts are included in the analysis system. The
control variable options cv5 and cv6 differ from each other in the
specification of the balance relations between these control variables.
In the cv5 option, the analysis variables consist of the full fields
corresponding to stream function and relative humidity and the unbalanced
parts corresponding to the other variables included in the analysis. However,
in the cv6 option, only stream function is analysed in full, while relative
humidity and other variables comprise both balanced and unbalanced
parts.
The control variables specified in the cv5 option are related as given below,
χu(i,j,k)=χ(i,j,k)-αψχ(i,j,k)ψ(i,j,k),Tu(i,j,k)=T(i,j,k)-∑l=1NkαψT(i,j,k,l)ψ(i,j,l),psu(i,j)=ps(i,j)-∑l=1Nkαψps(i,j,l)ψ(i,j,l).
Here, i and j denote the horizontal dimension index, k and l indicate the
vertical sigma levels, and α represents the various regression coefficients
between the variables represented using the respective subscripts. The unbalanced
parts of the fields are denoted using the subscript u.
The relations specified by Eq. () indicate the manner in which the
various
analysis control variables are related in the WRF-Var system. Here, the balanced part
of velocity potential is related to the stream function alone and hence the possible
relations that the divergent component of wind could have with other variables are
not properly considered. Similarly, in cv5, temperature and surface pressure are
neither related to each other nor to the moisture variable. Relative
humidity field is not influenced by any of the model variables like
temperature or wind, as per the relations in Eq. ().
The balance relations defined in the cv6 option, on the other hand, include additional
correlations between model variables. The cv6 option has the following balance
relations:
χu(i,j,k)=χ(i,j,k)-αψχ(i,j,k)ψ(i,j,k)Tu(i,j,k)=T(i,j,k)-∑l=1NkαψT(i,j,k,l)ψ(i,j,l),-∑l=1NkαχuT(i,j,k,l)χu(i,j,l)psu(i,j)=ps(i,j)-∑l=1Nkαψps(i,j,l)ψ(i,j,l),-∑l=1Nkαχups(i,j,l)χu(i,j,l)rhu(i,j,k)=rh(i,j,k)-∑l=1Nkαψrh(i,j,k,l)ψ(i,j,l),-∑l=1Nkαχurh(i,j,k,l)χu(i,j,l)-∑l=1NkαTurh(i,j,k,l)Tu(i,j,l)-∑l=1Nkαpsurh(i,j,k)psu(i,j).
Here, additional correlation coefficients connect model variables in more ways than are
available in the cv5 option. For example, the balanced parts of temperature and surface pressure
are now also correlated with the unbalanced velocity potential. Hence, temperature and
surface pressure are influenced by the divergent component of wind in the cv6 option
unlike in the cv5 option. Similarly, additional correlations defined in the moisture
variable make the moisture analysis multivariate in nature in the cv6 option .
In both the cv5 and cv6 option, the estimation of BECs proceed in the following five
stages:
Calculation of standard perturbations from forecast differences. In the NMC method, this
is calculated as x′=xT2-xT1, where xT2
and xT1 are forecast difference times (e.g. 48 and 24 h for global, 24 and 12 h for regional).
Time/bin mean for each variable/level is removed so that zero-mean fields are
obtained.
Regression analysis is performed and the various correlations are determined between
the control variable fields. The unbalanced components of the fields are calculated.
The vertical component of the CVT is applied.
Recursive filter is used to provide horizontal correlations.
The cv5 and cv6 options in WRF-Var differ from each other in the step (iii) mentioned above.
Experimental
The Advanced Research WRF (ARW) model version 3.5.1 is configured with
two-way nested domains as shown in Fig. . The outer
domain has 350 × 350 grid cells in the east–west and north–south
directions with a horizontal resolution of 27 km, while the inner domain is
configured with 451 × 451 grid points with a horizontal resolution of 9 km. There are 36 vertical levels in both domains. Physics
parametrisation schemes utilised in this study are the same as in
for simulating monsoon depressions. Further
details on WRF model formulation and implementation are available in
and . All results
discussed in this study are from the inner, higher-resolution domain.
Model domains used in the study.
The initial and boundary conditions for the model are obtained from the
National Center for Environmental Prediction (NCEP) Global Forecast System
(GFS) forecast fields of horizontal resolution 0.5∘×0.5∘. Here,
data assimilation is performed in the outer domain only. The inner domain has
been initialised from the outer, coarse-resolution domain. For determining
BEC using the NMC method, 12 and 24 h forecasts are generated for a period
of 1 month during the 2013 summer monsoon period (1 June to 1 July 2013) for the outer domain. In the WRF 3DVar system, the forecast differences of
24 and 12 h forecast times are typically used for calculating background
error using NMC method in the regional domain . The
forecast perturbations generated using the differences of these forecasts are
used for calculating BECs using both the cv5 and cv6 option. The
conventional surface and upper air observations from the NCAR Computational and Information Systems Laboratory (CISL) Research Data
Archive (http://rda.ucar.edu/datasets/ds337.0) are utilised here for assimilation.
Also, Advanced Microwave Sounding Unit-A (AMSU-A) radiances
are assimilated in this study. In
all three depression cases investigated here, the WRF model is integrated for
12 h without any assimilation for model spin-up. Using this model forecast
as a background, 3DVar analysis is performed using both the cv5 and cv6 option once,
with a specified observation window of ±3 h around the analysis time,
followed by free forecast (no assimilation of observations) for the next 48 h. Figure 2 shows the all observations typically available in the domain at
the assimilation time. In order to bring out clearly the effect of data
assimilation, a control (CTRL) run is performed with no assimilation of
observations.
Observations available typically over the domain.
Analysis increment for zonal wind (a, e), meridional wind (b, f),
potential temperature (c, g) and water vapour mixing ratio (d, h) when a
single u-wind observation is assimilated at the middle of the domain at model
level 19. Panels (a–d) are for the cv5 run and (e–h) for the cv6 run.
Assimilation of a single observation is a convenient and useful way to
diagnose the properties of the BEC matrix. Let us suppose that we have the observation of
the kth element of the state x. That is, here the observation
is a scalar. Let the observation error be σ2 and the single
observation be denoted as y. The observation operator H and its Jacobian
H become row vectors of zeroes apart from their kth element,
which becomes 1. Calculating the gradient of J in Eq. (1) and rearranging
the terms, we get the analysis increment at an element l as
xla-xlb=Blky-xkbBkk+σ2.
That is, the analysis increment is proportional to the element Blk of the BEC matrix,
which denotes the covariance between elements at k and l. Hence, assimilating a single observation provides
information regarding the structure of the BEC matrix. To investigate the impact of the formulation of control
variables of BEC matrix, several single-observation assimilations have been performed.
The European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis data available at a
horizontal resolution of 0.125∘×0.125∘ are used to evaluate the
model forecasts here. Furthermore, a high-resolution analysis is also
utilised here. The high-resolution analysis has been determined as follows.
The GFS global analysis and all the observations (conventional and AMSU
radiances) over the model domain are subjected to the 3DVar methodology using
the cv5 option, throughout the model forecast period, with assimilation performed
every 6 h. This uses the same horizontal and vertical resolution of the model
grids as indicated in Sect. 4.
Analysis increment at model level 1 in zonal wind (a, e) meridional
wind (b, f), temperature (c, g) and water vapour mixing ratio (d, h) for the cv5
option (a–d) and the cv6 option (e–h) for the first depression case due to
assimilation of all available observations.
Results and discussion
Single-observation experiment
Figure shows the analysis increments in u,v, θ
and q when a single u wind observation is assimilated at the middle of the
domain at model sigma level 19 (same model level as in
). The u-wind observation which differs from the
background with a magnitude of 1 m s-1 is assimilated using both the cv5 and
cv6 option of the BEC matrix. Figure a–d provide the analysis
increment in u,v,θ and q respectively for the cv5 option, while Fig. e–h show the same for the cv6 options. The analysis
increment patterns for the cv5 option is similar to that obtained by
for the regional BE option, with a double maxima
over the ocean region in the C(u,u) pattern (Fig. a and
e). The inclusion of additional correlation functions in cv6 has resulted in
a non-vanishing increment in moisture field on assimilation of wind
information. Furthermore, the additional correlation coefficient
αχuT in the expression for Tu has resulted in a changed
temperature field (Fig. g) for the cv6 option. Also, the
location of the maximum impact of the observation is shifted in the cv6 run as
compared with that in the cv5 run. Since the covariance matrix is symmetric,
assimilation of a single temperature observation will result in a relative
rotation of increment pattern in the u field . Hence,
the single-observation experiments reveal that the difference in formulation
of control variables has resulted in different analysis increment structures
in the cv6 option as compared to that in the cv5 option.
Track error in kilometres for the three depression cases with respect to IMD data.
Case 1
Case 2
Case 3
Forecast hour
CTRL
cv5
cv6
CTRL
cv5
cv6
CTRL
cv5
cv6
00:00
414.9
73.14
82.2
137.1
110.0
110.0
230.9
41.3
139.6
06:00
320.4
113.5
122.5
74.9
19.8
22.9
422.1
494.4
512.5
12:00
165.3
123.9
132.9
257.4
239.3
293.6
360.3
360.3
378.3
18:00
120.8
159.3
168.4
368.6
434.5
440.8
449.9
391.5
499.9
24:00
118.04
253.2
271.3
515.9
390.7
506.9
675.9
594.5
543.0
Vertical profiles of temperature anomaly (a, b, c), moisture
divergence (d, e, f), relative vorticity (g, h, i), horizontal
divergence (j, k, l)
and relative humidity (m, n, o) at the analysis time of the cv5/cv6 sensitivity
experiments over the depression centre for case 1 (left column), case 2 (middle column)
and case 3 (right column) depressions.
Assimilation results
Figure shows the analysis increment for the cv5 and cv6 options at
the model level 1 for zonal wind (a and e), meridional wind (b and f),
temperature (c and g) and humidity (d and h) with all observations assimilated
for the case 1 depression. Assimilation of all available observations
(conventional and AMSU-A radiances) has yielded different impacts in the cv5 and
cv6 cases as seen from the differing analysis increment patterns. The
increments in u-wind shows a larger positive region over the oceans in the
cv5 run as compared with the cv6 run. This indicates that the strength of the
zonal wind has increased due to assimilation in the cv5 run as compared with
the cv6 run. While the increment patterns in meridional winds and temperature at
the surface level are fairly similar, assimilation of all observations has
impacted the water vapour mixing ratio differently in the cv5 and cv6 cases.
Additional correlation information in the BEC matrix formulation has resulted
in larger increments in the cv6 option as compared with the cv5 option. The above
results indicate that differing formulation of BEC matrix indeed impacts the
assimilation of observations in the WRF 3DVar system.
The impact of assimilation on the structure and movement of the depressions
is investigated by estimating the depression track errors for a 24 h forecast
period with respect to India Meteorological Department (IMD) track reports.
The track errors for the CTRL, cv5 and cv6 runs are shown in Table 1. In
general, both the cv5 and cv6 run perform better than the CTRL run in terms of lower track
errors. Here, the cv5 run has lower track errors as compared to the cv6 run. From
Fig. we can infer that the analysis increments between the cv5 and
cv6 options are significantly different for the water vapour mixing ratio only.
Therefore, it may be unrealistic to expect that the simulation of mean sea
level pressure and hence the track errors will be improved by utilising
the cv6 option instead of cv5.
Monsoon depressions are known to have cold core lows at the lower levels and
warm core highs at the upper levels. It is known that systems with a cold core
at lower levels typically intensify with increasing height, indicating that
the monsoon depression has higher intensity at the lower to middle troposphere
. To investigate how the various experiments have
simulated this observed thermal structure of depressions, the profile of the
temperature anomaly has been calculated over the depression centre at the
initial time. For this a 3∘×3∘ box has been considered around
the depression centre. The difference in average temperature in this box to
that outside it is calculated. Figure a, b, and c show the
vertical profile of the temperature anomaly at the analysis time at the
depression centre for the case 1, case 2 and case 3 depressions respectively.
All assimilation runs have simulated the thermal structure of the depression
well with respect to the high-resolution analysis as compared with the CTRL
run, in all three cases. However, as compared with the ECMWF reanalysis,
the simulated temperature anomalies have stronger cold cores at lower levels.
For the case 1 depression, the ECMWF reanalysis reveals a system whose cold
core, which is indicative of its intensity, weakens with height at the lower levels. This is different from
the typically observed thermodynamic structure of the monsoon depressions. In
all three depression cases, the cv6 runs have simulated a relatively stronger
cold core at the lower levels, as compared to the CTRL and cv5 runs as well as the
ECMWF and high-resolution analyses. This indicates that the thermodynamic
structure of the monsoon depressions is modified by the cv6 analysis.
Water vapour mixing ratio at level 1 compared with the ECMWF
reanalysis at the analysis time of the cv5/cv6 sensitivity experiments at
level 1 for case 1 (a–e), case 2 (f–j) and case 3 (k–o) depressions for ECMWF
reanalysis (a, f, k), high-resolution analysis (b, g, l), CTRL run (c, h, m), cv5
run (d, i, n) and cv6 run (e, j, o).
48 h accumulated precipitation for case 1 (a–d), case 2 (e–h) and
case 3 (i–l) depressions from TRMM (a, e, i), CTRL run (b, f, j), cv5 run (c, g, k) and
cv6 run (d, h, l).
Figure d–f show the vertical profile of
moisture divergence at the centre of the depression cases at the initial time
of the forecast (+0 h forecast). Figure d shows that the cv6 run
has contributed to higher moisture convergence values that are closer to the
high-resolution analysis in the lower levels at the depression centre as
compared with both the CTRL and cv5 run for the first depression case. In the
second depression case shown in Fig. e, the cv6 run shows
higher moisture convergence value close to the surface and relatively higher
divergence values in the higher levels as compared with the cv5 run. Figure f, which shows the third depression case, indicates that
surface moisture convergence values of cv6 are closer to the high-resolution
analysis. The cv6 run simulated moisture convergence is closer to the ECMWF
reanalysis as compared to the cv5 run at low levels for the first depression
case.
Figure g–i show the vertical profile of relative vorticity
at the centre of the depression for all the depression cases at analysis time
of the cv5/cv6 sensitivity experiments (+0 h forecast). For the second and
third depression cases, at lower levels, the relative vorticity values for
the cv6 runs are closer to the high-resolution analysis as compared to the cv5 and
CTRL runs. The difference in relative vorticity profiles between the cv5 and cv6
options is not marked for all depression cases. However, the CTRL run's
results for the first depression are very far from the analysis values at all
levels. ECMWF reanalysis of the relative vorticity profile for the first
depression case also shows a weaker vortex at all the levels.
Vertical profiles of horizontal divergence over the depression centre at
analysis time of the cv5/cv6 sensitivity experiments (+0 h forecast) for
all three depression cases are shown in Fig. j–l
respectively. For the first and third depression cases considered here, the
cv6 option has simulated stronger convergence at the lower levels than the
cv5 option. In the first case the simulated profile is closer to the ECMWF
reanalysis.
Figure m–o show the vertical profiles of relative humidity
at analysis time of the cv5/cv6 sensitivity experiments over the depression
centre for all three depression cases. For the first depression case, the
CTRL run simulates relatively drier atmosphere until the mid-troposphere, while
the assimilation runs are closer to the high-resolution analysis and are
moister. ECMWF reanalysis also indicates a drier atmosphere. This is
consistent with the warmer core at around 900 hPa present in the ECMWF
reanalysis. The ECMWF reanalysis also shows large relative humidity values
for all depressions at the upper levels. For the first and second depression
cases, the cv6 option simulates higher values of relative humidity at lower
levels as compared to the high-resolution analysis as well as the CTRL and cv5
runs. In the case of the third depression, despite having lower relative
humidity values at the initial time at lower levels, relative humidity
simulated by the cv6 run is closer to the high-resolution analysis and the ECMWF
reanalysis as compared to the cv5 and CTRL runs, especially in the middle levels.
Differences in 48 h accumulated precipitation (in mm) from TRMM
rainfall observation for case 1 (a–c), case 2 (d–f) and case 3 (g–i)
for the CTRL (a, d, g), cv5 (b, e, h) and cv6 (c, f, i) runs.
Location and intensity of maximum precipitation (cm) as obtained from TRMM for all three depressions together with location and magnitude error of maximum precipitation for the CTRL, cv5 and cv6 runs.
TRMM
CTRL
cv5
cv6
location
magnitude (cm)
location
magnitude
location
magnitude
location
magnitude
of max.
of max.
error (km)
error (cm)
error (km)
error (cm)
error (km)
error (cm)
rainfall
rainfall
of max.
of max.
of max.
of max.
of max.
of max.
precipitation
precipitation
precipitation
precipitation
precipitation
precipitation
Depression 1
89.13∘ E,
35.7
1173
-11.8
257
-4.9
146
-4.4
20.88∘ N
Depression 2
80∘ E,
24.1
218
-21.6
211
-11.4
183
-2.1
21.25∘ N
Depression 3
79.65∘ E,
29.9
1325
-13.5
937
-15.2
943
-13.3
20.88∘ N
The differences between the vertical profiles between the cv5 and cv6 runs with
respect to the CTRL run at each model level at the beginning of the free
forecast period are calculated. To estimate whether the assimilation has
significantly altered the model fields, a Student t test
has been performed by considering these
differences. It is found that the differences in the vertical profiles of
moisture convergence and relative vorticity between the reference (CTRL) run
and the cv5/cv6 analyses are significant at the 95 % confidence level. The
differences in relative humidity are found to be 95 % significant over the
first 15 model levels only. However, the divergence profiles are found
to be statistically significant at the 65 % level only.
Comparison of vertical profiles at the depression centre at analysis time of
the cv5/cv6 sensitivity experiments shows that, in comparison with the cv5
option, the cv6 option has simulated the following:
Stronger cold core low at lower levels (up to 800 hPa) for all three depression
cases.
Stronger low-level moisture convergence for two of the three cases at the initial
time.
Stronger low-level horizontal wind convergence for two of the three depression
cases.
Higher values of relative humidity at lower levels in two out of three depression cases.
Considering the above, it is clear that utilising the cv6 option has modified
the vertical structure at the depression centre at the initial time in two
out of three cases considered here, resulting in higher relative humidity
values, higher low-level moisture convergence and higher low-level horizontal
convergence values. However, to infer definite and broad conclusions, more
depression cases have to be investigated.
Skill scores of 48 h accumulated precipitation (mm) with regard to TRMM for
case 1 (a–d), case 2 (e–h) and case 3 (i–l) depressions. Equitable threat score
is shown in (a, e, i). Bias scores (b, f, j), false alarm
ratio (c, g, k) and probability of detection (d, h, l).
Figure shows the surface level water vapour mixing ratio of
the CTRL (c, h, m), cv5 (d, i, n) and cv6 run (e, j, o) compared with the ECMWF
reanalysis (a, f, k) and the high-resolution analysis (b, g, l) for all three
depressions. In general, all the model simulations indicate more moisture
than the ECMWF reanalysis. The cv6 run has simulated moderately higher mixing
ratio values as compared with the CTRL and cv5 runs over the land region in two
out of the three cases considered. With more moisture being simulated over
land, both in spatial and vertical profiles along with larger horizontal
moisture convergence, the cv6 run is expected to simulate rainfall better
than the cv5 and CTRL runs.
The model-simulated 48 h accumulated rainfall is compared with Tropical Rainfall Measurement Mission (TRMM) rainfall
observations to analyse the impact of BEC formulation on rainfall simulation
in Fig. . The accumulated precipitation from TRMM and the CTRL, cv5 and cv6 runs for the three depressions considered here is shown in
Fig. a–l. The top row (Fig. a–d)
shows the first depression case, the middle row
(Fig. e–h) shows the second depression case and the bottom
row (Fig. i–l) shows the third depression case
considered in this study. For all three cases, accumulated rainfall
values indicate heavy rainfall over the Indian region due to the monsoon
depressions. In the first depression case the model simulates excess rainfall
over the head of the Bay of Bengal and northeastern regions of India. The TRMM
observations show that the location of maximum precipitation is over the head
of the bay. Furthermore, the CTRL run simulates erroneous rainfall maximum off the
west coast of India, which is not seen in either the TRMM observations or assimilated runs. All the model runs show similar spatial pattern of
precipitation for the second depression case. However, the intensity of
rainfall is different in the cv6 run as compared with the CTRL and the cv5 runs. For
the third depression case, the observed rainfall maximum over oceans is
reproduced by all the model runs in terms of location and intensity. However,
both the cv5 and cv6 run simulate rainfall closer to TRMM observations as
compared to the CTRL run. The differences in 48 h accumulated rainfall
simulated by the three model runs with respect to the TRMM observation are
shown in Fig. . For all the depression cases, the maximum
differences between TRMM observation and model simulations in the CTRL, cv5 and
cv6 runs occur over the regions where TRMM observations show maximum
accumulated rainfall.
Table 2 gives the location and magnitude of maximum 48 h accumulated rainfall
from TRMM observations as well as the location error (in km) and magnitude
error (in cm) in the model simulations of the same for the CTRL, cv5 and cv6
runs. The results show that in all the depression cases considered here, the
model-simulated location and intensity of maximum accumulated rainfall has
errors when compared with TRMM observations. It is also found that the cv6 run
has lower error in the location as well as magnitude of maximum rainfall when
compared with both the CTRL and cv5 run in two out of three depression cases.
For quantitative verification of rainfall forecast skill, various skill
scores like equitable threat score (ETS), bias score, false alarm ratio
(FAR) and probability of detection (POD) have been calculated for 48 h
accumulated rainfall with respect to TRMM observations for all three
depression cases and are shown in Fig. . Towards this, model-simulated 48 h accumulated rainfall was regridded to the resolution of TRMM
rainfall observations. The skill scores are calculated using the contingency
table considering whether a forecast occurs or not
. The ETS estimates how well the observed event
is forecast, taking into account the correct forecasts that can occur by
chance. Bias score estimates the ratio of frequency of forecast events to the
frequency of observed events, indicating whether there is over- or underprediction by the model. The FAR gives the fraction of false alarms (model-simulated rainfall that is not observed) and POD gives the fraction of
correctly forecast events. In general, assimilated runs perform better than
the CTRL run in all rainfall thresholds with higher ETS values, lower FAR and higher POD in all three cases. In the
second and third depression cases, the cv6 runs have higher ETS score, lower bias, lower FAR and larger POD as compared with the cv5 and CTRL runs in the higher
threshold regions. The higher ETS score, higher POD and lower FAR scores for
all cases in the high rainfall thresholds also support the earlier
inference (refer Table 2) that the cv6 runs perform better than the CTRL and cv5 runs
for higher-intensity rainfall.