Barnes objective analysis scheme of daily rainfall over Maharashtra (India) on a mesoscale grid

Abstract

An objective analysis of daily rainfall over Maharashtra (India) by distance weighting function on a mesoscale grid is described. The Barnes scheme is applied to interpolate irregularly distributed daily rainfall data on to a regular grid. The spatial resolution of the interpolated arrays is 0.25 degrees of latitude by 0.25 degrees of longitude. Some objectively determined constraints are employed in this study: (i) weights are determined as a function of data spacing, (ii) in order to achieve convergence of the analyzed values, two passes through the data are considered, (iii) grid spacing is objectively determined from the data spacing. The case of a typical westward moving monsoon depression during the 1994 monsoon season is chosen for this study. Objective analyses of six days (16 to 21 August 1994) have been carried out using variable length scale two pass (V2P) and fixed length scale two pass (F2P) Barnes scheme. A length scale of 80 km for the outer pass and 40 km for the inner pass are considered. Analyses show moderate improvement of V2P scheme over F2P scheme. The bias of the analysis based on V2P is 2% lower than that of analysis based on F2P.

Full text

Atmósfera 19(2), 109-126 (2006)
Barnes objective analysis scheme of daily rainfall over
Maharashtra (India) on a mesoscale grid
S. K. SINHA, S. G. NARKHEDKAR
Indian Institute of Tropical Meteorology, Dr. Homi Bhabha Road, Pashan, Pune – 411008, India.
Corresponding author: S. K. Sinha; email: sinha@tropmet.res.in
A. K. MITRA
NCMRWF, DST, A-50, Institutional Area, Sector - 62, NOIDA, UP, 201 307, India
email: akm_delhi@yahoo.com
Received April 4, 2005; accepted December 9, 2005
RESUMEN
En este trabajo se describe un análisis objetivo de la precipitación diaria sobre Maharashtra (India) por medio
del peso de la función de la distancia en una red de mesoescala. Para interpolar en la red regular los datos de
precipitación diaria distribuidos irregularmente se aplica el esquema de Barnes. La resolución espacial de los
arreglos interpolados es de 0.25 grados de latitud por 0.25 grados de longitud. En este estudio se emplean
algunas restricciones determinadas objetivamente: (i ) los pesos se determinan como una función del
espaciamiento de los datos, (ii) para lograr la convergencia de los valores analizados se realizan dos pasos por
los datos, (iii) el espaciamiento de la red se determina objetivamente por el espaciamiento de los datos. Para
este estudio se escogió el caso de una depresión monzónica típica con movimiento hacia el oeste durante la
temporada de monzones de 1994. Se realizaron análisis objetivos de seis días (16 a 21 de agosto de 1994)
utilizando la escala de longitud variable de dos pasos (V2P) y la escala de longitud fija de dos pasos (F2P) del
esquema de Barnes. Se consideró una escala de longitud de 80 km para el paso externo y de 40 km para el paso
interno. Los análisis mostraron una mejora moderada del esquema V2P sobre el F2P. La tendencia del análisis
basado en V2P es 2 % menor que la del análisis basado en F2P.
ABSTRACT
An objective analysis of daily rainfall over Maharashtra (India) by distance weighting function on a mesoscale
grid is described. The Barnes scheme is applied to interpolate irregularly distributed daily rainfall data on to
a regular grid. The spatial resolution of the interpolated arrays is 0.25 degrees of latitude by 0.25 degrees of

110 S. K. Sinha et al.
longitude. Some objectively determined constraints are employed in this study: (i) weights are determined as
a function of data spacing, (ii) in order to achieve convergence of the analyzed values, two passes through
the data are considered, (iii) grid spacing is objectively determined from the data spacing. The case of a
typical westward moving monsoon depression during the 1994 monsoon season is chosen for this study.
Objective analyses of six days (16 to 21 August 1994) have been carried out using variable length scale two
pass (V2P) and fixed length scale two pass (F2P) Barnes scheme. A length scale of 80 km for the outer pass and
40 km for the inner pass are considered. Analyses show moderate improvement of V2P scheme over F2P
scheme. The bias of the analysis based on V2P is 2% lower than that of analysis based on F2P.
Key words: Barnes scheme, mesoscale analysis, rainfall, monsoon depression.
1. Introduction
The Indian community generally regards rainfall as the most important meteorological parameter
affecting its economic and social activities. Rainfall observations are needed to support a range of
services extending from the real time monitoring and prediction of flood events to climatological
studies of drought. For a wide range of applications, rainfall measurements over India are interpolated
or extrapolated to ungauged locations where the information is desired but not measured. Numerical
interpolation of irregularly distributed data to a regular N-dimensional array is usually called ‘‘objective
analysis’’.
The existing observational network and synoptic methods of forecasting cannot predict
mesoscale events except in very general terms. The meteorological data available on the Global
Telecommunication System (GTS) and at the India Meteorological Department (IMD), New
Delhi, raingauge data primarily cater to synoptic analysis and forecasting. These data do not
have the required resolution in space and time to resolve and define mesoscale systems. There is
an increasing demand for high resolution mesoscale weather information from different sectors
like aviation, air pollution, agro-meteorology and hydrology. Mesoscale meteorology is of special
importance as local severe weather events cause extensive damage to property and life. Lack of
data on the mesoscale is one of the primary reasons for the poor understanding of mesoscale
phenomena over the Indian region. Objectively analyzed data prepared by the National Centre for
Medium Range Weather Forecasting (NCMRWF), New Delhi and IMD are of 1.5° Lat./Long.
resolution, which is rather coarse for mesoscale NWP models having a resolution of 10 to 50 km.
(0.1 to 0.5° Lat./Long.).
Mesoscale analysis is an important prerequisite for mesoscale research and modelling work. It
has evolved into a specialized activity involving data acquisition, quality control checks, background
first guess from the model, data ingest and assimilation. As of today, objective gridded analysis of
mesoscale data is not available over the Indian region. Thus there is an urgent need to start work in
developing a mesoscale analysis system. Our aim is to prepare a high resolution rainfall data over
data rich regions. In this context we have tried to develop an objective analysis scheme of daily
rainfall on a mesoscale grid. Raddatz (1987) examined the spatial representativeness of point rainfall
measurements for Winnipeg (Canada) for two accumulation periods −one day and one month.
Bussieres and Hogg (1989) made objective analysis of daily rainfall on a mesoscale grid using four

111
Mesoscale analysis of daily rainfall
different types of objective analysis schemes and compared the merits and demerits of different
analysis techniques. Mitra et al. (1997) analyzed daily rainfall using the Cressman (1959) scheme
over the Indian monsoon region by combining daily raingauge observations with the daily rainfall derived
from INSAT IR radiances. The present study describes the details of the daily rainfall analysis on
a mesoscale grid over the Maharashtra (India) region.
2. Synoptic condition and data
2.1. Synoptic condition
Monsoon depression is very important so far as the distribution of rainfall in space and time over the
region of its influence is concerned. Generally, 24 h accumulated rainfall is 10-20 cm and isolated
falls can exceed 30 cm in 24 hours. On any particular morning heavy rainfall exceeding 7.5 cm
extends to about 500 km ahead and 500 km to the rear of the depression centre and this area has a
width of 400 km lying entirely to south of the track. The preferential rainfall is in the SW sector.
Contribution of total depression associated rainfall is 11 to 16% in the left sector along the track
(Mooley, 1973). During the summer monsoon short duration rainfall fluctuations are mainly due to
westward passage of depressions, fluctuations in the intensity, location of the monsoon trough, and
the low level westerly jet stream over the Arabian Sea. On an average, two to three monsoon
depressions are observed per month during the monsoon period. The months of July and August
experience the high frequency of these depressions. These systems have horizontal dimensions of
around 500 km and their usual life span is about a week (Das, 1986). For Indian region, the standard
deviation and the coefficient of variability for annual, summer monsoon (June to September total)
and monthly rainfall are reported in tabular form and/or charts by Rao et al. (1971) and the IMD
(1981). A general result in these reports is that rainfall amount and its relative variability are inversely
related.
Daily rainfall analysis for a six day period starting from August 16, 1994 was carried out. This
period was a very active phase of the monsoon, which caused heavy rainfall associated with the
monsoon trough and also along the west coast of India. On 17 August a monsoon depression
formed over the northwest of the Bay of Bengal and intensified into a deep depression on 18
August. Subsequently it moved in a northwesterly direction and lay over the northwestern part of
the country on 20 August. It weakened into a low-pressure area by 21 August.
2.2. Rainfall data
The domain of our analysis extends from 72°E to 83°E longitude and 15°N to 23°N latitude,
cast on a fine mesh of 0.25° by 0.25° latitude/longitude grid. This particular domain covers
all Maharashtra. The 24 hours’ accumulated (valid at 03UTC) rainfall values from IMD
raingauge observations coming through the GTS were collected. The GTS rainfall data over
Maharashtra were supplemented by additional rainfall data obtained from the Agriculture
Department of the Government of Maharashtra. Figure 1a shows the distribution of about 267
raingauge observations on a typical day. Latitudes and longitudes of different rainfall stations

112 S. K. Sinha et al.
over Maharashtra are given in Table 1. Sub-division wise climatological normal rainfall values
based on 1871-2003 over India for the monsoon season (June-September) have been given in the
Table 2 and the locations of different sub-division of India are shown in Figure 1b. This will help to
understand the characteristics of rainfall over Indian region.
Fig. 1a. Locations of rainfall
stations over Maharashtra.
22N
20N
18N
16N
72E 74E 76E 78E 80E
Maharashtra
Table 1. Latitude and longitude (degrees) for different observing stations over Maharashtra.
Station Lat. Long. Station Lat. Long. Station Lat. Long.
Achalapur 21.27 77.52 AheriTahs 19.40 80. 00 AhmedpurT 18.70 76.93
AiraTahsi 16.12 74.22 Akkalakot 17.53 76.20 Akkalkuwa 21.75 74.00
AklujTahs 17.88 75.03 AkolaTahs 19.55 74.02 AkotTahsi 21.10 77.07
AlibagTah 18.63 72.87 AmalnerTa 21.05 75.03 AmbadThas 19.62 75.80
AmbegaonT 19.05 73.83 Ambejogai 18.73 76.38 AmravatiT 20.93 77.78
Anjangaon 21.17 77.32 ArniTahsi 12.68 79.28 ArviTahsi 20.98 78.23
AshitTahs 18.80 75.18 AshtiTahs 21.22 78.25 AsolaTahs 20.25 79.85
Aurangaba 19.88 75.33 SataraTah 18.25 76.50 Babhulgao 20.38 78.13
Badalkasa 21.37 80.05 BadneraTa 20.87 77.73 BalapurTa 20.67 76.78
Continues in the next page.

113
Mesoscale analysis of daily rainfall
BaramatiI 18.15 74.58 Barshitak 20.50 77.10 BarshiTah 18.23 75.70
BasmathTa 19.32 77.17 BeedIMDTa 19.00 75.77 BhadgaonT 20.67 75.23
BhiraTahs 18.45 73.40 BhiwandiT 19.30 73.05 BhokarTah 19.22 77.68
Bhokardan 20.25 75.77 BhorTahsi 18.13 73.85 Bramhapur 20.60 79.87
BhusawalT 21.07 75.78 BiloliTah 18.77 77.73 BolthaneT 20.20 74.92
BuldhanaT 20.53 76.18 Chalisgao 20.45 75.02 Chamorshi 19.95 79.90
ChandagadT 15.93 74.18 ChandorTa 20.33 74.25 Chandrapu 19.95 79.95
ChadurBa 21.25 77.73 ChandurRl 20.82 77.97 Chikaltha 19.85 75.40
ChikhaliT 20.35 76.25 ChimurTah 20.50 79.38 ChiplunTa 17.53 73.52
ChopdaTah 21.25 75.30 ChousalaT 18.72 75.70 DahanuTah 19.98 72.72
DahiwadiT 17.70 74.55 DapoliTah 17.77 73.20 DaryapurT 20.93 77.33
DeglurTah 18.55 77.58 DeogadTah 16.37 73.37 DeoliTahs 20.62 78.62
DeoriTahs 21.07 80.37 DeorukhTa 17.05 73.62 DeolgaonR 20.03 76.03
DhadgaonT 20.33 75.50 DharniTah 21.57 76.88 DharwhaTa 20.17 77.77
DhondTahs 18.47 74.60 DhuleTahs 20.90 74.78 DigrasTah 20.12 77.72
DindoriTa 20.20 73.83 EdlabadTa 21.07 76.07 ErandolTa 20.93 75.33
Gadchirol 20.18 80.00 Gadhimgla 16.22 74.35 Gaganbava 16.55 73.83
Gangakhed 18.92 76.75 GangapurT 19.68 75.02 GargoitBh 16.30 74.13
GarmoshiT 19.95 79.90 GeoraiTah 19.25 75.75 Ghorazeri 20.53 79.63
GuhagarTa 17.47 73.20 HadgaonTa 19.50 77.68 HarnaiIMD 17.82 73.10
Hatkangal 16.75 74.43 Hingangha 20.55 78.83 HingoliTa 19.72 77.15
IndapurTa 18.12 75.03 JalgaonJa 21.05 76.53 JalnaTahs 19.85 75.88
JamkhedTa 18.73 75.32 JamnerTah 20.82 75.78 JawharTah 19.92 73.23
JejuriTah 18.28 74.17 JinturTah 19.62 76.70 JunnerTah 19.22 73.88
KagalTahs 16.58 74.32 nKalamKal 18.58 76.02 KalwanTah 20.50 74.03
KalyanTah 19.25 73.12 KamteeTah 21.43 79.30 KandharTa 18.87 77.20
Kanakavli 16.27 73.70 KannadTah 20.25 75.13 KaradTahs 17.28 74.18
KaranjaTa 20.47 77.53 KarjatTah 18.55 75.00 KarmalaTa 18.40 75.20
KarveerTa 16.70 74.23 KhamgaonT 20.72 76.57 KhandalaT 17.98 74.03
KhariTahs 20.27 79.77 KhatavVad 17.60 73.40 KhedTahsi 17.72 73.40
Khuldabad 20.00 78.20 Khyrband 21.48 80.07 KinwatTah 19.62 78.20
KolegaonM 19.92 74.17 KolhapurI 16.70 74.23 Kopargaon 19.90 74.48
KoregaonT 17.70 74.17 KotalTahs 21.27 78.58 KudalTahs 16.02 73.70
KurkhedaT 19.58 79.83 LanjaTahs 16.87 73.55 LaturTahs 18.40 76.58
LohaTahsi 19.08 77.33 LonarTahs 19.98 76.55 MadhaTahs 18.03 75.52
MahadTahs 18.08 73.42 MalegaonT 20.55 74.53 MalsirasT 17.87 74.92
MalwanMal 16.05 73.47 Mandangad 17.98 73.25 Mangalwed 17.50 75.45
MangaonTa 18.23 73.28 Mangrulpi 20.32 77.35 Manjlegao 19.15 76.22
MaregaonT 20.07 78.95 MatheranT 18.98 73.28 MavalTahs 18.73 73.65
Table 1. Latitude and longitude (degrees) for different observing stations over Maharashtra (continued).
Station Lat. Long. Station Lat. Long. Station Lat. Long.
Continues in the next page.

114 S. K. Sinha et al.
MedhaTags 17.78 73.83 MehkarTah 20.17 76.55 MhasalaTa 18.13 73.12
MhaswadTa 17.63 74.78 MohgaonTa 19.58 77.70 MoholTahs 17.82 75.65
MokhadaTa 19.93 73.33 MorshiTah 21.33 78.02 MukhedTah 19.15 77.52
MulTahsil 20.07 79.68 MurbadTah 19.40 73.40 Murtizapu 20.73 77.38
MurudTahs 18.33 72.97 NagpurCit 21.15 79.12 NalesarTa 20.05 79.47
NandedTah 19.13 77.33 NandgaonT 20.32 74.67 NanduraTa 20.83 76.47
Nandurbar 21.33 74.25 NarkhedTa 21.45 78.53 NasikTahs 20.00 73.78
NawapurTa 21.15 73.80 NerTahsil 20.48 77.87 NilangaTa 18.08 76.75
NiphadTah 20.08 74.12 Osmanabad 18.17 76.05 PachoraTa 20.67 75.37
PaithanTa 19.47 75.38 PalgharTa 19.65 72.72 Pandharka 20.02 78.55
Pandharpu 17.65 75.33 PangriTah 21.42 80.10 PanhalaTa 16.80 74.12
PanvelTah 18.98 73.12 PaoniTahs 20.78 79.65 ParandaTa 18.27 75.45
ParbhaniI 19.27 76.77 ParnerTah 19.00 74.45 ParolaTah 20.88 75.12
ParseoniT 21.37 79.15 ParturTah 19.58 76.22 PatanTahs 17.37 73.90
PathardiT 19.17 75.17 PathriTah 19.25 76.43 PaturTahs 20.45 76.95
PaudTahsi 18.53 73.62 PenTahsil 18.73 73.10 PhaltanTa 17.98 74.43
Pimpalgao 20.17 73.98 Pimpalner 20.95 74.12 PoladpurT 17.92 73.42
PotodaTah 18.80 75.48 PuneIMDTa 18.53 73.85 PusadTahs 19.92 77.58
Radhanaga 16.33 73.98 RahuriTah 19.40 74.65 RajapurTa 16.65 73.52
RajuraTah 19.77 79.37 RalegaonT 20.40 78.55 RamtekTah 21.40 79.33
Ratnagiri 16.98 73.33 RaverTahs 21.25 75.03 RisodTahs 19.97 76.80
RohaTahsi 18.43 73.12 RotiTahsi 18.80 75.12 SakoliTah 21.08 80.00
SakriTahs 21.00 74.30 Sangamner 19.57 74.22 SangliIMD 16.87 74.57
SangolaTa 17.43 75.20 SaonerTah 21.38 78.92 SaswadTah 18.35 74.03
SatanaTah 20.60 74.20 SataraIMD 17.68 73.98 Sawantwad 15.90 73.82
ShahadaTa 21.55 74.47 ShahapurT 19.45 73.33 Shahuwadi 16.88 74.00
ShegaonTa 20.80 76.70 ShevgaonT 19.33 75.22 Shindkhed 21.28 74.75
ShirolTah 16.74 74.60 ShirpurTa 21.35 74.88 Shrirampu 19.62 74.67
Shriwardh 18.05 73.02 SillodTah 20.18 75.77 Sindewahi 20.28 79.68
SinnerTah 19.85 74.00 SironchaT 18.83 79.97 SirurTahs 18.83 74.38
SolapurTa 17.67 75.90 SomthaneT 19.93 74.23 SudhagadP 18.53 73.03
SurganaTa 20.55 73.63 TalegaonT 18.65 74.15 TalodaTah 21.57 74.22
TelharaTa 21.03 76.83 RisodTahs 19.97 76.80 ThaneTahs 19.20 72.98
TiroraTir 21.43 79.93 TrimbakTa 19.95 73.53 TuljapurT 18.02 76.07
TumsarTah 21.40 70.80 UdgirTahs 18.40 77.12 UmarkhedT 19.58 77.68
UmrerTahs 20.85 79.33 UranTahsi 18.90 72.92 VadaTahsi 19.65 73.13
VasaiTahs 19.35 72.80 VelheTahs 19.12 74.18 VengarlaT 15.87 73.63
VaijapurT 19.93 74.73 Visarwadi 21.18 73.97 Wai Tahsil 17.93 73.90
WanawadiT 18.50 73.90 WaniTahsi 20.05 78.95 WardhaTah 20.75 78.60
WaroraTah 20.22 79.02 WarudTahs 21.47 79.27 WashimTah 20.12 77.13
YavalTahs 21.17 75.70 YeolaTahs 20.05 74.48 YeotmalTa 20.38 78.13
Table 1. Latitude and longitude (degrees) for different observing stations over Maharashtra (continued).
Station Lat. Long. Station Lat. Long. Station Lat. Long.

115
Mesoscale analysis of daily rainfall
1. Andaman and Nicobar Islands
2. Arunachal Pradesh
3. Assam and Meghalaya
4. Naga, Mani, Mizo and Tripura
5. Sub-Him W. Bengal and Sikkim
6. Gangetic West Bengal
7. Orissa
8. Jharkhand
9. Bihar
10. East Uttar Pradesh
11. West Uttar Pradesh
12. Uttaranchal
13. Haryana, Chandigarh and Delhi
14. Punjab
15. Himachal Pradesh
16. Hammu and Kashmir
17. West Rajasthan
18. East Rajasthan
19. Madhya Pradesh
20. Chattisgarh
21. Gujarat
22. Saurashtra, Kutch and Diu
23. Konkan and Goa
24. Madhya Maharashtra
25. Marathwada
26. Vidarbha
27. Coastal Andhra Pradesh
28. Telanmgana
29. Rayalaseema
30. Tamil Nadu and Pondicherry
31. Coastal Karnataka
32. North Interior Kamataka
33. South Interior Kamataka
34. Kerala
35. Lakshadweep
Fig. 1b. Map showing different meteorological sub-divisions of India.
40
35
30
N
25
20
15
10
70 80 90 100
5 E
Table 2. Sudivision wise climatological normals (seasonal) based on 1871 to 2003 rainfall data.
Subdivision Rainfall (mm) Subdivision Rainfall (mm)
North Assam 1448.59 Gujarat 861.75
South Assam 1443.33 Saurashtra and Kutch 428.95
Sub-Hima W. Bengal 1996.19 Konkan and Goa 1994.80
Gangetic W. Bengal 1156.26 Madhya Maharashtra 576.83
Orissa 1165.09 Marathwada 690.28
Jharkhand 1097.22 Vidarbha 942.55
Bihar 1034.97 Chattisgarh 1196.11
East Uttar Pradesh 906.74 Coastal Andhra Pradesh 507.66
West U. P. Plains 766.86 Telangana 711.24
Haryana 461.01 Rayalseema 424.66
Punjab 499.58 Tamil Nadu 308.60
West Rajasthan 257.22 Coastal Karnataka 1867.51
East Rajasthan 629.01 North Interior Karnataka 594.77
West Madhya Pradesh 867.77 South Interior Karnataka 500.87
East Madhya Pradesh 1123.53 Kerala 1809.20

116 S. K. Sinha et al.
3. Methodology
Barnes (1964, 1973) proposed an analysis scheme, which has probably replaced the Cressman
analysis scheme (1959). The Cressman scheme corrects the background grid point values by a
linear combination of residuals between predicted and observed values. These residuals are then
weighted according to their distances from the grid point. The background field at each grid point
is successively adjusted on the basis of nearby observations in a series of scans (usually three to
four) through the data. The cutoff radius CR (the radius of the circle containing the observations
which influence the correction) is reduced on successive scans in order to build smaller scale
information into the analyses where data density supports it. Cressman (1959) and Barnes (1973)
objective analysis schemes are both weighted average techniques. One important difference is
the choice of cutoff radius CR. Cressman weights do not approach zero asymptotically with
increasing distance as they do in the Barnes technique, but instead abruptly become zero at
distance equal to CR. This aspect of the Cressman scheme causes a serious problem when the
data distribution is not uniform. The Barnes technique has gained wide importance in mesoscale
analysis (e.g. Doswell, 1977; Maddox, 1980; Koch and McCarthy, 1982). This analysis produces
a rainfall field on a regular grid from irregularly distributed observed rainfall stations. The rainfall
estimated at a grid point ‘‘g’’ is a weighted average of surrounding observations, which are
weighted according to the distance from the grid point. Achtemeier (1987) used a successive
correction method so that an estimate of the rainfall fields is made on the first pass (iteration) and
refined on successive passes. Inner passes, which yield incremental changes to the initial rainfall
field, use shorter length scales so that relatively greater weight is assigned to observations close
to an analysis grid point.
The analysis is performed using Barnes two pass successive correction system (Barnes,
1973; Koch et al., 1983). If a variable S(xm, ym) is observed at a location designated by m, then the
first pass analysis at a grid point ‘‘g’’ is described by:
()
∑
∑
=
=
=N
m
m
mm
N
m
m
g
w
yxSw
S
1
1
1
,
(1)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−
=2
2
exp c
d
wm
m
(2)
where the weight applied to the mth observation is given by:
The length scale c controls the rate of fall-off of the weighting function. Since the weight
approaches zero asymptotically, there is no need to specify a radius of influence. However, the
number of observations N should be chosen large enough so that the observations far away from

117
Mesoscale analysis of daily rainfall
the grid point receive a small weight. c exerts control over the filtering properties of the analysis.
The analysis after the second pass is given by:
()()
1
1
21
'
1
,,
N
mmm mm
m
gg N
m
m
'
wsxy sxy
ss
w
=
=
⎡⎤
−
⎣⎦
=+
∑
∑(3)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−
=2
2
exp c
d
wm
m
'
γ
(4)
The analysis from the first pass provides a background field for the second pass. The weights
produced by this function are in the range 0 to 1.
γ
is a numerical convergence parameter that
controls the difference between the weights on the first and second passes, and lies between 0 and
1 (0 <
γ
< 1). Thus the weighting function has a steeper fall-off on the second pass in an attempt to
build smaller scales into the analysis. Barnes (1964) objective analysis scheme without
γ
is convergent,
but it requires several more passes to reach the same degree of convergence as compared to
Barnes (1973) version with
γ,
which requires only two passes through the data.
A simple bilinear interpolation between the values of Sg1 at four surrounding grid points can be
used to obtain an estimate for s1(xm, ym) at each data location. If the average spacing of the data
and the grid points is small compared to some wavelength λ, then the representation of that wavelength
(response function) after the second pass is given by (Barnes, 1973):
R = R0(1 + R0
γ
− 1 − R
γ
0)
where R0 = exp(−
π
2 c2/λ2) is the response after the first pass. The response function R is the
measure of the degree of convergence after a second pass through the data. The shape of the
response curve is illustrated in Figure 2.
4. Results and discussion
4.1. Length scale and grid resolution
Objective determination of the analysis length scale (c) and grid resolution parameters (∆x) used in
the analysis scheme is made from the method of Koch et al. (1983). The choice of both parameters
is based on the average station separation, ∆n and is given as:
∆n = √area/number of stations
where:
(5)

118 S. K. Sinha et al.
In the case of a daily rainfall network of about 267 stations over Maharashtra, ∆n was found to
be 0.6 degrees (approximately 60 km). Peterson and Middleton (1963) stated that a wave whose
horizontal wavelength does not exceed at least 2∆n cannot be resolved, since five data points are
required to describe a wave. Hence ∆x should not be larger than half of ∆n. Since a very small grid
resolution may produce an unrealistic noisy derivative and if the derivative fields are to represent
only resolvable features, the grid length should not be much smaller than ∆n. Thus a constraint that
∆n/3 ≤ ∆x ≤ ∆n/2 was imposed by Barnes in his interactive scheme. The analysis length scale (c)
is fixed by the data spacing and is given as
Fig. 2. Response functions
after two passes of the Barnes
analysis. The illustrated
curves are for γ = 1.0, first
pass (°−°) and for γ = 0.3,
second pass (*−*) corres-
ponding to C2 = 6400 km2.
⎟
⎠
⎞
⎜
⎝
⎛∆
=
π
n
c2
052.5
Response
Wavelength (km)
(Koch et al., 1983) which is roughly 80 km in this experiment, so that waves shorter than 2∆n are
strongly filtered. Table 3 shows the values of different input parameters used in this experiment.

119
Mesoscale analysis of daily rainfall
4.2. Analysis
Analyses of daily rainfall (16 to 21 August 1994) are carried out using a 2-pass (iteration) variable
length scale Barnes scheme (here after referred to as V2P) and the standard 2-pass (iteration)
fixed length scale Barnes (F2P) scheme. F2P and V2P are two ways of analysis. Pass here implies
iteration, both (F2P and V2P) involve two passes. In the case of first pass (outer pass)
γ
= 1.0 and
in the second pass (inner pass)
γ
= 0.3 are considered. F2P and V2P differ from each other in the
sense that in F2P length scale (c) is fixed during both the iterations whereas in V2P length scale
changes from first pass to second pass. Although analyses were made for six days, in Figure 3 the
analyzed rainfall with V2P as well as F2P from 17 August to 20 August are shown, when the
monsoon depression was passing in north-westerly direction from Bay of Bengal to North-West
India. For 2-pass scheme, Koch et al. (1983) required
γ
to be in the range of 0.2 to 1.0, while
Barnes (1973) suggested 0.2 <
γ
< 0.4. For the present study we have chosen length scale of 80 km
for the outer pass (first iteration,
γ
= 1.0) and the inner pass (second iteration) length scale of 40 km
corresponding to
γ
= 0.3 is chosen to add a reasonable amount of detail to the analyzed rainfall. On
17 August when the depression was over North-West Bay, analysis with F2P shows maximum
rainfall of 40 mm whereas analysis with V2P shows maximum amount of 50 mm of rainfall over the
same area. The contours are drawn at a regular interval of 10 mm. On 18 August when the system
intensified into a deep depression, F2P shows a maximum amount of 30 mm rainfall at two places:
one at 20° N, 74° E and other along the west coast. But the analysis with V2P shows 50 mm of rain
at 20° N, 74° E and 30 mm of rain at three different places at a lower latitude along the west coast
of Maharashtra. Around 20°N and 78.5°E, F2P shows 10 mm of rain whereas at the same place
V2P shows 20 mm of rain. On 19 August the depression further moved landward. Comparing both
the analyses (V2P and F2P), F2P shows rainfall maxima of 70 mm near 21°N and 80°E, whereas
V2P shows a maxima of 90 mm in the same region. In addition to this there are a number of regions
along the west coast where V2P shows enhanced rainfall when compared to F2P (e.g. 20.5°N,
74.5°E; 16.5°N, 74.0°E). On 20 August (i.e. a day before the depression dissipated) F2P shows
rainfall of about 20 mm at 20°N and 74°E, whereas V2P shows 40 mm of rain at the same place
and at lower latitude along the west coast about 60 mm of rain is observed (V2P) compared to only
30 mm of rain (F2P). Thus it can be concluded that analyzed rainfall values with V2P are always
higher than the F2P.
Table 3. Characteristics of different parameters used in the analysis.
Input Weighting Initial Interpolation Number Maximum Length scale (c)
parameters function guess from grid to of number of in km
station iterations data points
Barnes Exp (−dm2/γc2) Not 4−point 2 No limit Outer pass − 80
scheme required average Inner pass − 40

120 S. K. Sinha et al.
17.08.94
V2P F2P
Fig. 3. Objective analysis of August 17 and 18, 1994 with V2Pand F2P.
Continues in the next page.
18.08.94

121
Mesoscale analysis of daily rainfall
19.08.94
V2P F2P
Fig. 3. Objective analysis of August 19 and 20, 1994 with V2P and F2P (continued).
20.08.94

122 S. K. Sinha et al.
For the quantitative analysis of the rainfall root mean square (rms) errors for the six days are
computed by comparing the analyzed rainfall against independent data not used in the analysis. This
process is called cross validation approach and has been used widely dating back to Gandin (1963).
That is, out of 267 observations 95% of data are used in the analysis and the verification is done
on the remaining 5%. In the verification the analyzed values have been interpolated to the observation
locations. The root mean squares (RMS) errors are generally between 8.15 to 16.58 mm for the
V2P scheme, whereas for F2P they are in the range of 8.34 to 17.0 mm showing moderate
improvement of the V2P scheme over F2P. As the distribution of rainfall amounts is positively
skewed (non-normal) and the rainfall is highly variable, the rms error can give a misleading picture
of rainfall analysis errors. This means a small number of large errors can unreasonably dominate
rms statistics. Tapp et al. (1986) have shown that sometimes rms statistics on the cube root of
rainfall amounts (which are less skewed) can sometimes give a better picture of the analysis error.
Often a mean absolute error is a more reasonable measure of rainfall analysis accuracy than rms
error. Table 4 shows the different types of errors and the standard deviations of rainfall on different
days for the present study. It has been observed that when the standard deviation (SD) of the
observed rainfall values is high, on those days the rms errors of the analyzed rain are also high. In
many cases, bias is a more important measure of analysis accuracy since the total rainfall over an
area, rather than the variation within the area, is often required from the analysis. Analyses based
on V2P have been found to be more accurate than analyses using F2P. The bias of the analyses
based on V2P is 2 % lower than that of analyses based on F2P.
Table 4. Analysis of errors for different days (mm) August 1994.
Scheme V2P F2P V2P F2P V2P F2P V2P F2P V2P F2P V2P F2P
Date 16 17 18 19 20 21
RMS error 8.15 8.34 10.27 10.40 12.02 12.61 16.58 17.00 9.85 10.43 8.29 8.96
RMS error of cubic 0.88 0.88 1.01 0.01 1.09 1.09 1.13 1.13 0.94 0.95 0.92 0.95
root of rainfall
Mean absolute 4.43 4.62 6.52 6.80 8.69 9.23 12.31 13.04 7.10 7.62 6.10 6.65
error
S D 9.70 12.25 13.24 19.97 12.44 9.63
In order to examine how the analysis changes with the variation of convergence
parameter (
γ
), analysis with V1P (
γ
= 1.0, c = 80 km, Fig. 4a) and V2P (
γ
= 1.0, c =80 km;
γ
= 0.3, c = 40 km, Fig. 4b) are performed and displayed for 19 August. Figure 4b, which is for
γ
= 0.3, shows a rainfall maxima of 80 mm over northeast Maharashtra. But analysis with
γ
=1.0 (Fig.
4a) shows maximum of 45 mm of rain over the same region. Also Figure 4a shows only 10 mm
of rain over 20.5°N and 74.5°E whereas over the same region Figure 4b shows 40 mm of rain.
At lower latitude along the west coast Figure 4a shows a maximum of 25 mm of rain but Figure 4b
shows 40 to 60 mm of rain. Analysis of rainfall produced by V2P shows more number of maxima
with lot of spatial variability, whereas analysis with V1P shows a very smooth distribution of rainfall.

123
Mesoscale analysis of daily rainfall
Thus we find that analysis with V2P (
γ
= 0.3) produces superior. Figure 5a shows the analysis of
total of six days (16 to 21 August) rainfall with V2P. Analyzed rain for the same period with F2P is
shown in Figure 5b. Maximum rainfall of about 160 mm (F2P) is seen along the west coast (Fig.
5b). But V2P (Fig. 5a) shows 150 to 200 mm of rain along the west coast. Contours are drawn at
an interval of 20 mm. Average of daily rainfall (16 to 21 August 1994) at each grid point is computed
for both the analyses V2P as well as F2P and following Mills et al. (1997) analysis of the absolute
difference between the average daily rainfall fields in mm (V2P-F2P) is shown in Figure 6. Thus it
can be concluded that V2P produced a better analysis.
Fig. 4. Variation in the analysis with
γ
: (a) for
γ
= 1.0 and (b) for
γ
= 0.3 for 19 August 1994.
(a) (b)
Fig. 5. Analysis of total rainfall (16-21 August 1994) with (a) V2P and (b) F2P.
(a) (b)

124 S. K. Sinha et al.
Fig. 6. Analysis of absolute
difference between average daily
station rainfall (V2P-F2P).
5. Conclusions
No worthwhile mesoscale research and modelling work can be carried out without good quality
of mesoscale data for the Indian region. The present study to analyze daily rainfall over
Maharashtra is an effort in this direction. Daily rainfall analysis over Maharashtra has been
produced using an interactive Barnes (1973) objective analysis scheme. Length scale and grid
resolution are objectively determined from the average data spacing. Analyses with V2P as well
as F2P Barnes scheme have been performed to examine the performance of the two schemes.
Length scale of 80 km corresponding to
γ
= 1.0 for the outer pass and length scale of 40 km for
the inner pass with
γ
= 0.3 are considered in this experiment.
It has been found that improvement in the analysis with V2P over F2P is moderate. Bias with
V2P analysis is 2% less than F2P. Barnes (1994) has shown that analysis accuracy depends on
the regularity of observation spacing. He found that in an objective analysis based on 77 randomly
distributed observations mean absolute errors could be 40% higher than for an analysis based on
23 uniformly distributed observations. Thus for producing better quality of rainfall analysis we
require more uniformly distributed rainfall observations. This scheme has the following advantages.
(i) There is no need to specify an influence radius.
(ii) Two to three passes are required to reach convergence.
(iii) Background field (first guess) is not required. Therefore analysis can be performed without
the use of a model.
Objective analyses for the six-day period were made using two passes (
γ
= 1.0 and
γ
= 0.3).
Errors were computed by comparing the analyses with the observations using a cross validation
technique. Mesoscale analysis involves assimilation of data from different sources and sensors.
Plans are ahead to include satellite data to complement the existing raingauge data and the length

125
Mesoscale analysis of daily rainfall
scale used in this study can then be adjusted accordingly. Satellite data will also extend the analysis
area over oceans and also over data sparse regions. Our main task is to combine optimally the
raingauge data with data from other sources. Currently we are in the process of analyzing daily
rainfall for longer periods over a larger region (whole India) and with number of different synoptic
situations.
Acknowledgements
The authors are extremely grateful to Dr. G. B. Pant, Director, Indian Institute of Tropical Meteorology,
Pune, for the necessary facilities. We are thankful to Shri P. Seetaramayya, Head, FRD for his
encouragement. We also express our gratitude to the anonymous referees for the constructive
comments and suggestions. Thanks are also due to India Meteorological Department and the
Agriculture Department of Government of Maharashtra for providing us with the rainfall data. Last
but not least we extend our thanks to Miss Anindita for her technical support.
References
Achtemeier G. L., 1987. On the concept of varying influence radii for a successive corrections
objective analysis. Mon. Wea. Rev. 115, 1760-1771.
Barnes S. L., 1964. A technique for maximizing details in a numerical weather map analysis. J.
Appl. Meteorol. 3, 396-409.
Barnes S. L., 1973. Mesoscale objective map analysis using weighted time-series observations.
NOAA Tech. Memo. ERL NSSL-62, National Severe Storms Laboratory, Norman, OK 73069,
60 pp. [NTIS COM-73-10781].
Barnes S. L., 1994. Applications of the Barnes objective analysis scheme. Part I: Effects of
undersampling, wave position and station randomness. J. Atmos. Oceanic Tech. 11, 1433-1448.
Bussieres N. and W. Hogg, 1989. The objective analysis of daily rainfall by distance weighting
schemes on a mesoscale grid. Atmosphere-Ocean. 27, 521-541.
Cressman G. P., 1959. An operational objective analysis system. Mon. Wea. Rev. 87, 367-374.
Das P. K., 1986. Monsoons. WMO monograph No. 613, WMO, Geneva, 155 pp.
Doswell C. A., 1977. Obtaining meteorologically significant surface divergence fields through the
filtering property of objective analysis. Mon. Wea. Rev. 105, 885-892.
Gandin L. S., 1963. Objective analysis of meteorological fields (in Russian). Israel Program for
Scientific Translation. 242 pp.
India Meteorological Department, 1981. Climatological atlas of India. Part I: Rainfall, New Delhi,
69 charts.
Koch S. E. and J. McCarthy, 1982. The evolution of an Oklahoma dry line. Part II Boundary-layer
forcing of mesoconvective systems. Mon. Wea. Rev. 39, 237-257.
Koch S. E., M. desJardins and P. J. Kocin, 1983. An interactive Barnes objective map analysis
scheme for use with satellite and conventional data. J. Clim. Appl. Meteorol. 22, 1487-1503.

126 S. K. Sinha et al.
Maddox R. A., 1980. An objective technique for separating macroscale and mesoscale features in
meteorological data. Mon. Wea. Rev. 108, 1108-1121.
Mills G. A., G. Weymouth, D. Jones, E. E. Ebert, M. Manton, J. Lorkin and J. Kelly, 1997. A
National objective daily rainfall analysis system. BMRC Techniques Development Report No.1
30 pp.
Mitra A. K., A. K. Bohra and D. Rajan, 1997. Daily rainfall analysis for Indian summer monsoon
region. Int. J. Clim. 17, 1083-1092.
Mooley D. A., 1973. Some aspects of Indian monsoon depressions and associated rainfall. Mon.
Wea. Rev. 101, 271-280.
Peterson D. P. and D. Middleton, 1963. On representative observations. Tellus 15, 387-405.
Raddatz R. L., 1987. Mesoscale representativeness of rainfall measurements for Winnipeg.
Atmosphere- Ocean, 25, 267-278.
Rao K. N., C. J. George and V. P. Abhyankar, 1971. Nature of the frequency distribution of Indian
rainfall (monsoon and annual). Rep. No. 168, India Meteorological Department, Pune, India.