kalman filter–based cmorph

Kalman Filter–Based CMORPH

ROBERT J. JOYCE

NOAA/Climate Prediction Center, Camp Springs, Maryland, and Wyle, Inc., McLean, Virginia

PINGPING XIE

NOAA/Climate Prediction Center, Camp Springs, Maryland

(Manuscript received 22 February 2011, in final form 19 May 2011)

ABSTRACT

A Kalman filter (KF)-based Climate Prediction Center (CPC) morphing technique (CMORPH) algorithm

is developed to integrate the passive microwave (PMW) precipitation estimates from low-Earth-orbit (LEO)

satellites and infrared (IR) observations from geostationary (GEO) platforms. With the new algorithm, the

precipitation analysis at a grid box of 8 3 8 km2 is defined in three steps. First, PMW estimates of in-

stantaneous rain rates closest to the target analysis time in both the forward and backward directions are

propagated from their observation times to the analysis time using the cloud system advection vectors

(CSAVs) computed from the GEO–IR images. The ‘‘prediction’’ of the precipitation analysis is then defined

by averaging the forward- and backward-propagated PMW estimates with weights inversely proportional to

their error variance. The IR-based precipitation estimates are incorporated if the gap between the two PMW

observations is longer than 90 min. Validation tests showed substantial improvements of the KF-based

CMORPH against the original version in both the pattern correlation and fidelity of probability density

function (PDF) of the precipitation intensity. In general, performance of the original CMORPH degrades

sharply with poor pattern correlation and substantially elevated (damped) frequency for light (heavy) pre-

cipitation events when PMW precipitation estimates are available from fewer LEO satellites. The KF-based

CMORPH is capable of producing high-resolution precipitation analysis with much more stable performance

with various levels of availability for the PMW observations.

1. Introduction

Despite its crucial importance in many meteoro-

logical, hydrological, and water resources management

applications, accurate measurements of regional and

global precipitation remain a challenging task. In par-

ticular, precipitation variations of fine spatial and tem-

poral scales are not well observed over most of the

globe, although they represent a substantial portion of

the overall variability and play an important role in

hydrological cycle and land–atmosphere interactions

(Dai et al. 1999, 2007; Tian et al. 2007; Hong et al. 2007).

While precipitation products based on observations

from individual platforms and instruments (gauge, ra-

dar, satellites, etc.) have been widely utilized in a variety

of operational and research applications, integrating

information from multiple satellite sensors as well as

ground observations (gauges and radars) further im-

proves the quality and resolution of precipitation anal-

ysis (Adler et al. 1994; Huffman et al. 1997; Xie and Arkin

1996, 1997; Sapiano et al. 2008). Substantial progress has

been made in the past decade to generate precipitation

estimates at high spatial and temporal resolutions through

combined use of infrared (IR) and passive microwave

(PMW) observations from multiple satellites. Two cate-

gories of techniques have been developed to combine the

precipitation and/or cloud information from individual

satellite PMW and IR observations. The first category in-

cludes the Precipitation Estimation from Remote Sensing

Information using Artificial Neural Network (PERSIANN;

Hsu et al. 1997), the Naval Research Laboratory (NRL)

blended satellite precipitation estimates (Turk et al. 2003),

and the Tropical Rainfall Measurement Mission (TRMM)

Multisatellite Precipitation Analysis (TMPA; Huffman

et al. 2007, 2009). A temporally changing and regionally

Corresponding author address: Dr. Pingping Xie, NOAA/Climate

Prediction Center, 5200 Auth Road, Suite 605, Camp Springs, MD

20746.

E-mail: [email protected]

DECEMBER 2011 J O Y C E A N D X I E 1547

DOI: 10.1175/JHM-D-11-022.1

� 2011 American Meteorological SocietyUnauthenticated | Downloaded 04/22/22 11:18 PM UTC

dependent empirical relationship between precipitation

intensity and cloud-top temperature is defined using col-

located IR and PMW data, assuming that PMW estimates

represent the ‘‘truth’’ of instantaneous precipitation rates at

the ground. This relationship is then applied to estimate

precipitation over the globe from the high-resolution IR

data observed from geostationary (GEO) platforms. In

some of the algorithms, the IR-based precipitation esti-

mates are further merged with PMW estimates from low-

Earth-orbit (LEO) satellites, wherever available, to form

the final satellite-based precipitation products. Key to this

category of techniques is the IR–precipitation relationship,

established through a sophisticated artificial neural net-

work system in the PERSIANN (Hsu et al. 1997) and

through matching the probability density function (PDF) of

IR against that of the PMW precipitation estimates in the

NRL (Turk et al. 2003) and TMPA (Huffman et al. 2003,

2007). While utility of the GEO–IR data ensures the pro-

duction of high-resolution precipitation estimates over a

quasi-global domain, lack of direct physical linkage be-

tween the precipitation and cloud-top temperature results

in substantial error in the IR-based precipitation estimates

and thereby the final PMW–IR merged analyses. Currently,

the official TRMM (Simpson et al. 1988; Kummerow et al.

2000) takes the 3-hourly precipitation analysis generated by

the TMPA algorithm (3B42) as its official level 3 product.

For convenience purposes, here we call the techniques of

this category ‘‘Euler approach’’ to reflect their common

feature that only the PMW and IR observations available

locally inside the target grid box are used directly in the

definition of analysis.

In the second category of techniques, called ‘‘Lagrangian

approach,’’ estimates of instantaneous rain rates from the

PMW observations from LEO are propagated and in-

terpolated in the combined time–space domain through

the use of the precipitating cloud system advection vec-

tors (CSAVs) computed from consecutive IR images

from the GEO platforms (Joyce et al. 2004; Ushio et al.

2009). PMW estimates are propagated along the advec-

tion vectors from the time of observation to that of the

target analysis. Since the IR observations are not used

directly to estimate precipitation, the error inherent in the

IR estimates (especially when PMW observations are

available around the target analysis time) is excluded as

a potential contaminate of the merged analysis. Recently,

Behrangi et al. (2010) proposed a conceptual model to

construct high-resolution precipitation analysis by prop-

agating PMW estimates along motion vectors defined by

cloud tracking with consideration of intensity changes

during the propagation.

The Lagrangian approach of propagating and morph-

ing high-resolution satellite precipitation estimates was

first adopted by Joyce et al. (2004) in the development of

their Climate Prediction Center (CPC) morphing tech-

nique (CMORPH). The success of CMORPH inspired

other agencies such as Japan Aerospace Exploration

Agency (JAXA) with their Global Satellite Mapping of

Precipitation (GSMaP) algorithm to follow CMORPH’s

methodology of using PMW rainfall in a Lagrangian

framework with IR-derived vectors as the method of

propagation (Ushio et al. 2009). Recent evaluation results

showed superior performance of CMORPH and GSMaP

compared to other high-resolution satellite precipitation

products derived using an Euler approach (Xie et al. 2007;

Ebert et al. 2007; Shen et al. 2009). The high temporal and

spatial resolution global precipitation estimates that are

created by these algorithms are applied in a wide variety

of research and operational applications.

While CMORPH consistently presents excellent

performance in estimating the spatial distribution and

temporal variations of precipitation over most of the

global regions and for all seasons, shortcomings exists in

the current version CMORPH and its high-resolution

precipitation products. Further improvements are needed

for the CMORPH technique to better meet the require-

ments of both science and societal communities.

First, the current CMORPH technique does not take

full advantage of precipitation information from PMW

observations and other sources. In the process of prop-

agating the PMW precipitation estimates, only data from

one scan closest to the target analysis time from each of

the forward and backward directions are included; IR-

based precipitation estimates are not used at all to adjust

the rainfall estimate. Despite their relatively poor accu-

racy, IR-based estimates may provide useful information

when no PMW estimates are available around the target

analysis time. The weights used to define the final analysis

from the propagated PMW estimates are approximated

as inversely proportional to the length of the propagation

time without consideration of the instrument dependency,

temporal propagation direction, surface type, season, lat-

itude, or the nonlinear nature of the estimation error. In

addition, the intensity of the precipitation is assumed un-

changed over the duration of both the forward and back-

ward propagation of the PMW estimates.

The objective of this work is to develop a prototype

model of the Kalman filter (KF)-based CMORPH that

is capable of producing high-resolution global pre-

cipitation analysis with improved accuracy through the

incorporation of additional IR-based information and

through the integration of all PMW- and IR-based in-

formation available using more precise weights. Section

2 of this paper describes the current CMORPH algo-

rithm and individual datasets used as inputs to the merg-

ing process, sections 3 and 4 present the development of

the prototype model of KF-based CMORPH over the

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conterminous United States (CONUS) and its implemen-

tation over the globe, and a summary and discussion is

provided in section 5.

2. Input data to the CMORPH processing system

a. A brief description of the current CMORPHalgorithm

CMORPH derives high-resolution (8 3 8 km2) half-

hourly precipitation analyses over a quasi-global domain

(608S–608N) through the integration of PMW estimates

from all available LEO satellites in a Lagrangian frame-

work. First, advection vectors of precipitating systems over

the globe are determined by computing spatially lagged

correlation between consecutive IR images observed by

GEO satellites. The CSAVs are then further refined as a

proxy to rainfall propagation through adjustments de-

termined from comparison studies against radar rainfall

motion. Precipitating cloud systems detected from PMW

satellite observations are then propagated along the ad-

vection vectors from the orbit observation time to the

target analysis time under the assumption that precipi-

tation intensity remains the same over the period. This

propagation is performed in both forward and backward

directions in time. The final precipitation analysis is de-

fined as the weighted mean of the propagated PMW es-

timates with the weights inversely proportional to the

length of propagation.

b. PMW precipitation estimates

Previously the only source of the information used

by CMORPH to define global high-resolution precip-

itation analyses was the level 2 instantaneous rain-rate

products retrieved from PMW observations of LEO

satellites (Ferraro 1997; Ferraro et al. 2000; Kummerow

et al. 2001). At the time of this writing, PMW pre-

cipitation estimates from up to nine LEO satellites are

available and utilized as inputs to the CMORPH pro-

cessing system. The most recent Goddard profiling algo-

rithm (GPROF; Kummerow et al. 1996; Olson et al. 1999)

is used to derive rainfall from PMW imagers. The tech-

nique used to retrieve precipitation from the PMW Ad-

vanced Microwave Sounding Unit (AMSU)/Microwave

Humidity Sounder (MHS) is the latest National Environ-

mental Satellite, Data, and Information Service (NESDIS)

algorithm (Vila et al. 2007), which reduces the error as-

sociated with the over- or underestimation of rainfall over

nadir–limb beam positions of the cross-track scanners

observed in the previous version of the algorithm. Fairly

well spaced in orbit time, observations from these plat-

forms combined provide critical information in defining

precipitation analysis around the diurnal cycle.

A series of innovative preprocessing procedures are

developed and implemented to prepare the PMW pre-

cipitation estimates to be used in the morphing process.

First, level 2 PMW estimates of instantaneous rain rates

generated at individual retrievals [or field of view (FOV)]

are mapped onto a global grid of 0.07278 latitude–longitude

(8 3 8 km2, at equator). Multiple 8-km grid boxes cov-

ered by a single satellite retrieval are assigned with the

same rain-rate value to ensure the spatial completeness and

representativeness of the resulting 8-km gridded fields of

PMW estimates.

To remove the systematic differences between PMW

estimates derived from observations of different instru-

ments using different algorithms, PMW estimates from

the TRMM Microwave Imager (TMI) are selected as

the reference standard and those from all other plat-

forms are calibrated against the TMI estimates through

matching the rain-rate PDF. The TMI estimates are cho-

sen as the normalization standard because of the finer

spatial resolution and emission detection (over ocean) of

the imaging sensors along with the dynamic ability of the

TRMM satellite to underfly all polar orbiting satellites,

allowing precise temporal and spatial matching of the re-

spective estimates. Data pairs of collocated TMI and tar-

get PMW estimates observed within 30 min or closer are

collected from the mapped 8 3 8 km2 grid fields for a

10-day period up to the target date. Accumulated PDF

tables are then constructed and utilized to adjust the target

PMW estimates. The PDF tables are created for the land

and oceanic regions separately and for each 108 latitude

band, using collocated data pairs over a wide domain of 308

in latitudes centering at the target band. Since the TMI

PMW estimates are available only from 408S to 408N, cali-

bration for PMW estimates from other satellites beyond the

408 parallels is performed against the PMW estimates from

the Advanced Microwave Scanning Radiometer (AMSR).

A preliminary examination showed very close agreements

in rain-rate PDF between the AMSR and TMI over tropics

and subtropics. PMW estimates from the future PMM core

satellite are expected to provide an improved calibration

standard especially over extratropics. Figure 1 illustrates

an example of the PDFs for the PMW instantaneous rain

rates from the TMI (green), original (blue), and cali-

brated (red) AMSU estimates for June–August 2005. The

PDF of the calibrated AMSU estimates matches much

better with that of the TMI than the original AMSU.

While the procedures described above work effec-

tively for the calibration of PMW estimates from most

LEO satellites, an additional calibration must be applied

for oceanic precipitation estimates derived from the PMW

observations of AMSU/MHS aboard National Oceanic

and Atmospheric Administration (NOAA) polar orbiting

platforms and the Meteorological Operational Satellite



(MetOp). Because of the limitations of the PMW sensors,

the AMSU/MHS is unable to detect some of the light

precipitation over water, resulting in a PDF of sub-

stantially reduced raining frequency (Vila et al. 2007).

Performing no correction for cases of zero rainfall, the

PDF matching procedure described in the last para-

graph would generate corrected AMSU precipitation

estimates with negative bias in overall magnitude com-

pared to the TMI estimates. To solve this problem,

a recursive filter is developed and applied to revise the

correction table slightly until the bias between the re-

sulting adjusted AMSU and TMI estimates is negligible.

c. Cloud system advection vectors

Key to the CMORPH technique is the propagation of

PMW observations of instantaneous rain rates in the

combined time–space domain along the CSAVs. Follow-

ing Smith and Phillips (1972) and Purdom and Dills (1994),

the CSAVs are derived by computing the displacements

of cloud systems detected from full-resolution (4 3

4 km2) GEO–IR images in 30-min intervals. Spatially

lagged correlation is calculated for the brightness tem-

perature (Tb) arrays on two consecutive GEO–IR im-

ages and the displacement with the highest correlation

is used to define the CSAV. Assuming the CSAVs do not

present substantial variations on small spatial scales,

definition of the CSAVs is performed on a 2.58 latitude–

longitude grid over the globe from 608S to 608N using the

GEO–IR data over a 58 latitude 3 58 longitude domain

centering at the target grid point.

Early versions of CMORPH used CSAVs directly to

propagate PMW-derived precipitation. However, it was

soon determined that the west–east and south–north

advection rates were too fast in the North Hemisphere

midlatitudes (Joyce et al. 2004). To correct this, a speed

adjustment procedure was developed. First, rainfall

system advection vectors were computed by spatially

lagging hourly U.S. Next Generation Weather Radar

(NEXRAD) stage II (Klazura and Imy 1993) radar

rainfall (mapped to the same 8 3 8 km2 grid) in the exact

same dimensions and manner CSAVs are computed from

IR. The frequency distribution of CSAV and radar rain-

fall advection rates indicated that north–south rates are

quite similar but that west–east CSAV speeds were about

3–4 times as fast compared to the radar-derived vectors,

and south–north rates were twice as fast (Joyce et al.

2004, their Fig. 7). These systematic differences are con-

sistent with several case studies that show the tendency of

IR features to quickly stream to the northeast on the east

side of long-wave troughs, with the actual rainfall also

moving in this direction but at a slower rate. The CSAVs

computed from the IR images over midlatitudes are ad-

justed accordingly based on the comparison results. For

consistency with the Northern Hemisphere, the meridio-

nal adjustment is applied to vectors of the opposite sign

in the Southern Hemisphere. The incorporation of this

adjustment procedure into the CMORPH processing has

resulted in improved propagation of precipitation features.

d. IR-based precipitation estimates

In the first-generation CMORPH algorithm (Joyce

et al. 2004), the GEO–IR data are utilized only to com-

pute the CSAVs for propagating the PMW instantaneous

precipitation estimates toward the targeted analysis time.

In developing the KF-based CMORPH, precipitation

estimates derived from GEO–IR observations will also be

incorporated to improve the quantitative accuracy of the

integrated precipitation analysis when PMW observations

are not available over an extended period of time. To this

end, a new technique is developed to estimate precipi-

tation from the full-resolution global GEO–IR data of

Janowiak et al. (2001) by matching the PDF of Tbs from

GEO–IR observations to that of the PMW instantaneous

rain rates.

First, combined PMW precipitation estimates

(MWCOMB) are defined in a 30-min interval on the 8 3

8 km2 global grid system by averaging the calibrated

PMW rain rates from individual LEO satellites. Mean-

while, global arrays of IRTb are created on the same

time–space resolution by utilizing the full-resolution

(4 km–30 min) GEO–IR data of Janowiak et al. (2001).

Collocated pairs of the IRTb and MWCOMB rainfall

data are then collected and used to create PDFs. An

FIG. 1. The cumulated PDF of instantaneous rain rates for the

original (blue) and calibrated (red) PMW estimates from the

AMSU aboard the Polar-orbiting Operational Environmental

Satellites (POES), and the PMW estimates from the TRMM TMI

(green) over Northern Hemisphere land for 1 Jun–31 Aug 2005.

The cumulated PDF is plotted as the contribution to the mean

rainfall (mm day21, y axis) from all cases with instantaneous rain

rates equal to or larger than a selected intensity (mm hr21, x axis).



estimation of 30-min precipitation over an 8 3 8 km2

grid box is assigned by matching the cumulated PDF of

the IRTb with that of the MWCOMB rain rates. To

ensure statistical stability and temporal–spatial conti-

nuity for the estimation of global precipitation, the PDF

tables are constructed for each 30-min time step and for

each 58 3 58 latitude–longitude grid box using collocated

data pairs collected over a 158 3 158 latitude–longitude

region centered at the target 58 latitude–longitude grid

box and covering a 9.5-hr time window centered at the

target estimation time. The short time window is used to

capture the current location in the diurnal cycle. Esti-

mation procedures are performed separately for land

and ocean to account for the differences in the IRTb–

precipitation relationship. Called IR rainfall frequency

(IRFREQ), precipitation estimates generated by this

technique are capable of capturing the spatial distribution

and temporal variations of precipitation with reasonable

quality over tropical and subtropical regions during warm

seasons (Fig. 2). A comprehensive evaluation of several

IR-based precipitation algorithms revealed superior per-

formance of the IRFREQ precipitation estimates com-

pared to other IR-based products (R. Kuligowski 2009,

personal communication).

3. Development of the prototype KF-basedCMORPH over CONUS

a. Conceptual model of the KF-CMORPH

Utilized widely in the atmospheric and oceanic data

assimilation community, the Kalman filter is an efficient

and effective recursive data processing algorithm to es-

timate the state of a linear system from a series of obser-

vations with different error characteristics. In general,

a Kalman filtering process consists of two sequential steps:

a ‘‘forecast step’’ that creates the ‘‘forecast’’ of the final

analysis as well as the error variance for the forecast, fol-

lowed by an ‘‘analysis step’’ that modifies the forecast with

the observations (Kalnay 2003).

The forecast of a state variable at step i (Fi) is com-

puted from the analysis at the previous step (i 2 1) Ai21

through a forecast model M:

Fi 5 Mi21(Ai21), (1)

while the error variance for the forecast (sfi )2 can be

defined as

(sfi )2

5 P2 1 Q2, (2)

where P2 is the error variance attributable to the prop-

agation of the error in the initial condition over the

forecast process and can be computed using the forecast

model. The Q2, meanwhile, is the error variance created

in the forecast process with the perfect initial condition.

The final analysis Ai is defined by updating the fore-

cast (Fi) with the observations (Oi):

Ai 5 Fi 1 Ki(Oi 2 Fi), (3)

where Ki is the Kalman gain computed as a function of

the forecast error variance (sfi )2 and the observation

error variance (s0i )2:

Ki 5 (sfi )2=[(s0

i )21 (s

fi )2]. (4)

In our application to the modification of CMORPH,

a simplified implementation of the KF approach has

been taken as a first step to demonstrate the effective-

ness of the statistical framework in integrating pre-

cipitation from multisensors. PMW estimates from

multiple LEO platforms are first propagated backward

and forward from their observation times to the analysis

time. Weighted mean of the propagated PMW estimates

are then defined as the forecast at the analysis time, with

the weights inversely proportional to the error variance

for the propagated PMW estimates. The model adopted

here therefore only forecasts the precipitation by propa-

gating PMW estimates, assuming no changes in the pattern

and intensity of the precipitating systems. The forecast is

then refined by incorporating information from IR-based

precipitation estimates at the analysis time to form the fi-

nal precipitation analysis.

The forecast error, as defined in Eq. (2), should be

composed of two portions: i) propagation of the error in

the input PMW estimates composed mainly of the level

2 PMW retrieval error, and ii) KF-CMORPH model

error arising in the process of defining the forecast from

the PMW estimates caused by, among many other fac-

tors, inaccurate estimation of the propagation vectors

and unrealistic assumption of unchanged precipitating

systems (pattern and intensity) over the period of propa-

gation. In the development of this conceptual model,

however, the error for the forecast is simplified as a func-

tion of the propagation time and defined separately for

PMW estimates of different sensor types (section 3b). It is

critically important that future work will quantify the error

in the PMW estimates, its propagation in the processing,

and the error caused by various imperfect assumptions and

estimations in the integration process to further improve

the quantitative accuracy of the combined satellite pre-

cipitation estimates.

Our final goal is to construct a KF-based system

to produce high-resolution pole-to-pole global pre-

cipitation analysis through integration of information

from satellite IR, PMW observations, numerical model



simulations, and other available sources. As a first step,

we have developed a prototype model of the KF-based

CMORPH to combine precipitation estimates derived

from PMW and IR observations over a global domain

from 608S to 608N. The IR-based estimates are included

only when no PMW data are available within a window

of 90 min centered at the target analysis time.

b. Development of the prototype model over CONUS

Key to the development of the KF-CMORPH is the

definition of error structure for the propagated PMW- and

IR-based estimates as a function of instrument type,

propagation time and temporal direction, location, and

season. A preliminary test is first performed to define the

error through comparison of the IRFREQ and the PMW

estimates propagated through various lengths of time

against the stage-II radar observations (Klazura and Imy

1993) over CONUS for summer 2007. Estimation error

is expressed here as the correlation between the satellite

estimates and the stage-II radar data. Correlation for the

PMW estimates degrades sharply as they are propagated

from their observation time (Fig. 3). The magnitude and

FIG. 2. Evolution of hourly precipitation in association with the development of a severe

weather system over CONUS from (top to bottom) 2200 UTC on 4 Aug through 0100 UTC on

5 Aug 2009, as depicted by the current version of CMORPH (Joyce et al. 2004) based on (left)

PMW observations and by (right) the IRFREQ.



the degradation rate of the correlation, however, differ

for different instruments, indicating the importance of

defining the error separately for estimates from different

platforms. During this summertime study over land, the

IR-based precipitation estimates outperform the PMW

estimates when the propagation time is longer than 90 min

or so, suggesting potential improvements in the final anal-

ysis through the inclusion of IR estimates to fill in PMW

observation gaps.

Using these error statistics, a prototype model KF-

CMORPH is developed to construct high-resolution

precipitation estimates over CONUS. The IR-based pre-

cipitation estimates are included as part of the inputs to

the KF-based CMORPH when no PMW observations are

available within a window of 90 min.

c. Evaluation of the prototype KF-CMORPHmodel over CONUS

To assess the performance of the KF-CMORPH anal-

yses relative to the original CMORPH analyses, we

compared both analyses with estimates of precipitation

from radar over CONUS during July–August 2009. The

radar data used for this comparison is the surface rain-rate

estimation at 1-km/5-min resolution over CONUS gen-

erated by the National Mosaic and Quantitative Pre-

cipitation Estimation (QPE) system (NMQ/Q2; Zhang

et al. 2009) developed at the NOAA National Severe

Storms Laboratory (NSSL) and the University of Okla-

homa. The NMQ/Q2 system combines information from

all ground-based radars constituting the NEXRAD

network and calibrates the radar rain rates with gauge

observations. The Q2 radar rainfall data at its original

resolution are integrated to define mean rain rates at

a space–time scale of 0.258 latitude–longitude and 30 min

to compare against the CMORPH satellite estimates over

CONUS.

Figure 4a illustrates time series of pattern correlation

between the radar observations and three sets of satel-

lite precipitation estimates: the IR-based IRFREQ, the

original CMORPH, and the KF-based CMORPH. Cor-

relation used here is Pearson’s correlation coefficient

between two variables, defined as the covariance of the

two variables divided by the product of their standard

deviations:

rX,Y 5cov(X, Y)

sXsY

5E[(X2 mX)(Y2 mY)]

sXsY

. (5)

The KF-CMORPH performs consistently better than

the original CMORPH throughout the two-month pe-

riod. The improvements in the overall pattern correla-

tion, however, are marginal. The correlation computed

over the combined space–time domain is 0.717 and 0.725

for the original and KF-CMORPH, respectively (Table 1,

first line from bottom). Since the majority of PMW ob-

servations used as inputs to the CMORPH are from

LEO platforms that fly over different geographical lo-

cations at fixed local times, performance of the satellite-

based precipitation estimates are evaluated according to

different local hours (Fig. 5a). Pattern correlations for

both the original and KF-CMORPH estimates present

wave-shaped variations, showing higher correlation over

the half-hourly slots with frequent PMW flights (0214,

0618, and 0921 LST; see Table 2), a reflection that PMW

retrievals with shorter propagation time contain less error,

as shown in Fig. 3. The KF-CMORPH presents substantial

improvements upon the original CMORPH over the half-

hourly slots existing in PMW observation gaps, reflecting

the relative additional skill gained in the KF-CMORPH

through the incorporation of IR-based estimates.

Both the number and the configuration of the LEO

satellites are sensitive to the performance of satellite

precipitation estimates derived through the integration

of individual PMW estimates through a Lagrangian

approach. As shown in Table 1 and Fig. 4, while corre-

lation for both the original and KF-CMORPH improves

with increased number of LEO–PMW satellites, corre-

lation differences for precipitation estimates based on

four- and seven-satellite configurations are very small. A

careful examination (results not shown) revealed that

this ‘‘level off’’ in performance is caused primarily by the

orbit patterns for the seven-satellite configuration,

which contains a ‘‘hole’’ between 19:30 and 01:30 local

time in sampling the diurnal cycle (Table 1). By opti-

mizing diurnal sampling, the skill of the four-satellite

FIG. 3. Correlation for the IR-based and PMW-propagated 0.258

latitude–longitude precipitation estimates as a function of in-

strument type and propagation time computed by comparisons

with stage-II radar data over CONUS for June–September (JJAS)

2007. Positive and negative propagation times indicate forward and

backward propagation, respectively.



configuration offsets the addition of PMW satellites in

a poorly designed seven-satellite configuration. Turk et al.

(2010) performed a similar experiment and found that

performance for precipitation estimates based on an Euler

approach will degrade when all cross-track sounders or the

morning local time crossing satellites were removed. While

it is not the central topic of this work to examine the sen-

sitivity of integrated precipitation estimates to the avail-

ability, quality, and configuration of input PMW and IR

satellite observations, future work is planned to address

this critically important issue to get a better understanding

of how the integration algorithm should be designed for

the estimation of precipitation for periods observed with

fewer satellites.

A set of synthetic experiments are designed and im-

plemented to further understand the performance of the

KF-CMORPH in generating integrated precipitation es-

timates from various LEO–PMW configurations. To this

end, high-resolution precipitation estimates over CONUS

are generated for the two-month period in 2009 using the

original and the KF-based CMORPH algorithms with

input PMW observations from only one, two, four, and

seven satellites selected from the all nine available plat-

forms (Table 2). The selection of the satellite configura-

tion is to mimic the PMW instrument availability over the

entire time span from 1987 to the present.

With fewer PMW observations available as inputs,

pattern correlation for the original CMORPH degrades

sharply from 0.717 for the nine-satellite configuration to

0.469 for the one-satellite simulation (Table 1). The

correlation for the original CMORPH is especially low

for the half-hourly local time slots precisely between two

consecutive LEO orbit times (Figs. 5b–e). The pattern

correlation for the original CMORPH degrades linearly

with the propagation time and falls down to ;0.1 for

estimates defined by propagating PMW by more than

5.0 h (Fig. 6, top).

The KF-CMORPH shows much less degradation in

correlation with PMW observations from a reduced

TABLE 1. Correlation of daily Q2 radar rainfall with the original

and Kalman filter CMORPH with input PMW estimates from

various LEO satellite configurations. Comparisons were made for

daily 0.258 latitude–longitude rainfall over the CONUS for a two-

month period from 1 Jul to 31 Aug 2009.

PMW satellite

configuration CMORPH

Kalman filter

CMORPH

One satellite 0.469 0.653

Two satellites 0.562 0.673

Four satellites 0.663 0.704

Seven satellites 0.659 0.702

Nine satellites 0.717 0.725

FIG. 4. Time series of correlation between the Q2 radar-estimated precipitation and

IRFREQ (red), the original CMORPH (black), and the prototype KF-CMORPH (green).

Comparisons are for daily 0.258 latitude–longitude precipitation over the CONUS for July–

August 2009. Results for CMORPH with (a) nine-, (b) seven-, (c) four-, (d) two-, and (e) one-

satellite configurations.



number of platforms (Table 1, Figs. 4b–e), thanks to the

contribution from the IR-based precipitation estimates.

The daily 0.258 pattern correlation, computed using all

data for the two-month period and over all grid boxes

over CONUS, is 0.725 and 0.653, respectively, for the

KF-CMORPH with the nine- and one-satellite configu-

rations (Table 1). Thirty-minute 0.258 pattern correlation

for KF-CMORPH decreases initially as the propagation

time extends and then becomes stabilized at ;0.45 for

propagation time of 1.5 h and longer (Fig. 6, bottom),

a substantial improvement upon that for the original

CMORPH.

The PDF of the rainfall intensity generated by the

original and KF-based CMORPH is virtually identical

for estimates defined with propagation time within

30 min and it is very close to that of the IR-based esti-

mates (Fig. 7a). All of the three satellite-based products

(the two versions of CMORPH and the IRFREQ), how-

ever, exhibit overestimation for events of precipitation

(.25 mm h21) compared to the radar observations from

Q2 (Fig. 7a) because of the systematic error in the level

2 PMW retrievals. The frequency for heavy precipitation

estimates generated by the original CMORPH drops sig-

nificantly over grid boxes where analysis is defined by

TABLE 2. Names and equatorial crossing times (ECT, local time) used in the synthetic experiments for CMORPH with different LEO

satellite configurations.

No. Satellite ECT One satellite Two satellites Four satellites Seven satellites Nine satellites

1 TRMM Precessing X X X

2 Aqua 1340 X X X X

3 NOAA-18 1345 X X

4 NOAA-19 1355 X X

5 NOAA-15 1645 X X

6 NOAA-16 1745 X X X X

7 DMSP-13* 1820 X X

8 NOAA-17 2125 X

9 MetOp 2135 X X X

* Defense Meteorological Satellite Program (DMSP).

FIG. 5. Correlation between the Q2 radar-estimated precipitation and IRFREQ (red), the

original CMORPH (black), and the prototype KF-CMORPH (green), plotted as a function of

local time (x axis). Comparisons are for 0.258 latitude–longitude 30-min precipitation rates over

the CONUS for July–August 2009. Results for CMORPH with (a) nine-, (b) seven-, (c) four-,

(d) two-, and (e) one-satellite configurations.



propagation of PMW over an extended period of time

(Fig. 7, black lines). The PDF for the KF-CMORPH,

meanwhile, is relatively stable for precipitation estimates

over grid boxes with different propagation times (Fig. 7,

green lines), thanks to the incorporation of IR-based es-

timates that retain the original PMW rainfall rate distri-

bution (Fig. 7, red lines).

Compared to the original CMORPH, the KF-CMORPH

described in this paper exhibits substantial improve-

ments and much more stable performance in integrating

high-resolution precipitation estimates with limited sam-

pling from the PMW observations. This shows clearly the

potential strength of the KF-CMORPH in constructing

high-resolution precipitation estimates for the entire

TRMM Global Precipitation Mission (GPM) era with

relatively stable performance.

4. Global implementation of KF-CMORPH

a. Development of a prototype system forgenerating global precipitation analyses

This conceptual KF-CMORPH developed using the

CONUS data is implemented for constructing the

precipitation estimates over the global domain from 608S

to 608N. Error statistics for PMW- and IR-based

precipitation estimates are defined for individual in-

struments as a function of region and season through

comparisons with the concurrent PMW estimates from

the TRMM TMI. Error functions for the TMI are taken

to be the same as those for the AMSR for Earth Ob-

serving System (EOS) (AMSR-E), based on an early

comparison against the stage-II radar observations over

CONUS. Over land, the error functions are computed

for each 108 latitude band using data collected over

a 308-wide latitude band centered on the target band. No

zonal differences in the error are considered because of the

limited sampling of the data. Over ocean, the error func-

tions are defined for each 208 3 208 latitude–longitude

box using data over a 408 3 408 latitude–longitude region

centered on the target box. Over both land and ocean, the

error functions are calculated for each month using data

over a five-month period centered on the target month to

account for the seasonal variations. The comparisons

against stage II were done once, while those against TMI

are updated monthly.

As shown in Fig. 8, evolution of estimation error, shown

as correlation with the TMI estimates for the Special Sen-

sor Microwave Imager (SSM/I) and AMSR-E estimates

over the propagation period, presents strong regional

variations because of differences in the time scales of

the target precipitation systems. In particular, error for

PMW estimates exhibit distinct contrasts over land and

ocean, implying the importance of defining the error

separately for land and ocean.

Utilizing the error statistics defined for the propagated

PMW and the IR-based precipitation estimates, a pro-

totype KF-based CMORPH algorithm system has been

developed at NOAA/CPC to produce high-resolution

precipitation analysis parallel with the original version of

CMORPH. Figure 9 illustrates the evolution of a rapid

developing precipitating system over CONUS as depicted

by the original CMORPH (left), the IR-based IRFREQ

(second from left), the KF-CMORPH (third from left)

and the stage-II radar estimates (right). PMW observa-

tions were scanned over the target region at the first and

last half-hourly time slots. The original CMORPH, in-

terpolating precipitation estimates from the two PMW

orbits, therefore missed the peak of the precipitation event

around 21:30 UTC (fifth row from top) as observed by

the radar and the IRFREQ. Incorporating IR-based pre-

cipitation estimates in 30-min intervals enables the KF-

CMORPH to capture the rapid development of the system,

improving the overall performance of the new technology.

b. Quantitative examination of the globalKF-CMORPH

The same synthetic tests are performed for the origi-

nal and KF-based CMORPH using PMW estimates from

FIG. 6. Correlation between the Q2 radar precipitation and

precipitation estimates derived from (top) the original CMORPH

and (bottom) the KF-CMORPH using input PMW observations

from various configurations of LEO satellites. Correlation is

computed for 0.258 latitude–longitude 30-min mean rain rates over

the CONUS for July–August 2009.



different LEO satellite configurations shown in Table 2.

‘‘Ground truth’’ for precipitation of high space–time res-

olution, such as the Q2 radar estimates, is not available

over most global regions for quantitative assessments of

the resulting CMORPH estimates. Therefore, we accu-

mulated the original and KF-based CMORPH to daily

precipitation averaged over a grid box of 0.258 latitude–

longitude and compared them with both the NOAA/CPC

unified global daily gauge analysis (Xie et al. 2010) over

land and the in situ measurements made by siphon gauges

installed on moored buoys of the Tropical Atmosphere

and Ocean (TAO) project (McPhaden et al. 1998) over

tropical oceans.

The CPC unified global daily gauge analysis is defined

by interpolating quality controlled gauge reports from

over 16 000 stations over the globe using the optimal

interpolation (OI) algorithm of Gandin (1965). Effects of

orographic influences to the precipitation are considered

in the definition of the gridded analysis (Xie et al. 2007).

The analysis is originally created on a 0.1258 latitude–

longitude grid and integrated to a 0.258 latitude–longitude

grid box mean for the verifications of CMORPH satellite

estimates in this study. The TAO buoy measurements of

daily rainfall used here are those observed at 40 moored

buoys over equatorial Pacific Ocean (http://www.pmel.

noaa.gov/tao/disdel/disdel.html). Since all of the TOA

buoys with in situ measurements are positioned at lo-

cations of even latitude–longitude (e.g., 88N, 1208E),

mean daily precipitation over four 0.258 latitude–longitude

grid boxes cornering at the buoy location is computed

for the CMORPH estimates and compared against the

buoy measurements. Although differences exist between

the area mean precipitation over a 0.58 latitude–longitude

grid box targeted by the satellite estimates and the ‘‘point’’

value measured at the buoy location, averaging over

a daily period reduces the discrepancies caused by the

differences in the spatial representativeness of the two

datasets. Same as in the CONUS experiments, exami-

nations are conducted for the two-month period from

1 July to 31 August 2009.

The KF-based CMORPH exhibits superior perfor-

mance over the original CMORPH in estimating pre-

cipitation over both land and ocean and for estimates

using PMW observations from all five LEO satellite

configurations (Table 3, Fig. 10). Pattern correlation

for the precipitation estimates over the global land

(equatorial Pacific) based on the original CMORPH

degrades sharply from 0.618 (0.596) when PMW ob-

servations from all nine satellites are included to 0.428

(0.437) when inputs are available from only one LEO

satellite. Performance of the KF-CMORPH, meanwhile,

is much more robust, with much smaller decreases in the

pattern correlation [0.556 (0.579) for only one LEO sat-

ellite] because of the inclusion of the IR precipitation

estimates. The two versions of the CMORPH present

biases of relatively close magnitude caused by the biases in

the PMW estimates used as primarily inputs to the in-

tegration algorithms.

To further examine the performance of the original

and KF-CMORPH, we analyzed the results from the

FIG. 7. Accumulated PDF for precipitation intensity derived from the Q2 radar (pink), the

IRFREQ (red), the original CMORPH (black), and the KF-CMORPH (green) using PMW

observations from four LEO satellites. The cumulated PDF is defined as the contribution to the

mean rainfall (mm day21, y axis) from all cases with instantaneous rain rates equal to or larger

than a selected intensity (mm h21, x axis). The PDF is derived from data over CONUS for July–

August 2009 from the synthetic satellite configuration experiments. Results are displayed

separately for PMW propagation time of a) 0, b) 30, and c) 240 min.



global synthetic experiment using four LEO satellites.

To this end, we compared the precipitation estimates

derived by the CMORPH algorithms from the four se-

lected LEO satellites with MWCOMB constructed from

the five withdrawn LEO satellites. Since the PMW es-

timates from the nine LEO satellites are all calibrated

against the same reference as described in section 2b,

comparisons against the MWCOMB based on the with-

drawn satellites’ estimates provide performance metrics

for the CMORPH integration algorithms, separating the

influence of the error (especially the bias) inherent in the

input PMW estimates to more clearly isolate the exami-

nation to the integration process performance.

As expected, the KF-CMORPH shows consistently

superior performance compared to the original CMORPH

(Figs. 11 and 12). Pattern correlation for precipitation

estimates constructed by the original CMORPH decreases

linearly with the propagation time for the PMW observa-

tions. Correlation for estimates of 30-min mean pre-

cipitation at a grid box of 0.258 latitude–longitude is as high

as ;0.8 when the PMW observations are available within

the 30-min window. It degrades down to less than 0.3 when

FIG. 8. Correlation between instantaneous rain rates derived from TRMM TMI and esti-

mates defined by propagating SSM/I and AMSR-E observations (left) forward and (right)

backward over various lengths of time, from (top) 0 to (bottom) 120. Correlation is computed

for the month of September 2009, using data over a five-month period from July to November

2009.



FIG. 9. Evolution of a precipitating system over central United States depicted in 30-min intervals, from (top) 19:30 to (bottom)

23:30 UTC on 16 Jul 2009. (left to right) Precipitation distribution observed by the original CMORPH, IRFREQ, KF-CMORPH, and the

radar estimates.



defined by propagating an instantaneous PMW observa-

tion 5 h apart using the original CMORPH algorithm.

With the KF-CMORPH, the pattern correlation decreases

only slightly for the same propagation length, from ;0.8 to

;0.65, thanks to the integration of IR-based precipitation

estimates.

The KF-CMORPH also exhibits stronger capability in

generating precipitation estimates with much better fi-

delity in the PDF of precipitation intensity compared to

the original CMORPH (Fig. 12). PDF is identical for

precipitation estimates derived from the two versions of

CMORPH algorithms with propagation time less than

45 min, a reflection that no IR-based estimates are in-

cluded in the KF-CMORPH when PMW observations

are available nearby. The PDF for the CMORPH esti-

mates with propagation time of 0 min (PMW observa-

tions available within the 30-min target analysis window)

is very close to that for the withdrawn MWCOMB (Fig.

12a). The small differences in the PDF at low rain rates

are attributable to the fact that four of the five withdrawn

LEO satellites in this synthetic experiment carry sounder-

based PMW instruments that are relatively poor at de-

tecting weak precipitation, especially over midlatitude

oceans. Morphing the propagated PMW estimates re-

duces(increases) the PDF for heavy (light) precipitation,

even when the propagation is less than 30 min (Fig. 12b).

The PDF aliases degrade quickly with the propagation

time for precipitation estimates defined with the original

CMORPH. The KF-CMORPH, however, generates pre-

cipitation analysis with PDF close to that for the withdrawn

MWCOMB estimates for propagation time of various

lengths (Fig. 12c).

Degree of agreements in precipitation patterns ex-

amined in sections 3 and 4 is measured mainly using

pattern correlation as defined in Eq. (5). We did not

perform a significance test for each of the correlation

coefficients and the correlation differences shown in the

tables and figures. However, a brief estimation using the

methods described in the appendix of Xie and Arkin

(1995) revealed that most correlation coefficients shown

there and any correlation difference of 0.01 or larger is

statistically significant at a level of 95% or higher because

of the massive number of cases involved in the calcula-

tions (e.g., .600 000 cases in calculating each statistic

in Table 1). Taking together the statistical significance

of the correlation and the consistent trends of variation

patterns in the statistics, it is clear that all conclusions we

made are based on a solid physical foundation.

5. Summary

A new algorithm has been developed for CMORPH.

The Kalman filter technique is adopted to integrate the

TABLE 3. (top) Correlation and (bottom) bias (%) between the CMORPH daily 0.258 precipitation estimates and gauge observations for

July and August 2009.

a) Results over land

CMORPH version One satellite Two satellites Three satellites Seven satellites Nine satellites

Original CMORPH 0.428 0.496 0.580 0.587 0.618

9.7 82 8.7 8.6 7.3

KF-CMORPH 0.556 0.571 0.599 0.601 0.621

6.0 10.6 7.7 6.6 8.0

b) Results over equatorial Pacific

CMORPH version One satellite Two satellites Three satellites Seven satellites Nine satellites

Original CMORPH 0.437 0.498 0.573 0.581 0.596

31.3 32.6 32.9 34.0 31.0

KF-CMORPH 0.579 0.582 0.608 0.609 0.611

21.4 22.1 24.6 26.4 28.6

FIG. 10. Time series of pattern correlation between the

CMORPH daily precipitation estimates and the CPC unified

global daily 0.258 latitude–longitude precipitation analysis over the

global land. Only data over grid boxes with at least one reporting

gauge are included in the calculation. Results for (top) the original

and (bottom) Kalman filter–based CMORPH, with correlation for

CMORPH derived from different LEO–PMW satellite configu-

rations plotted in different colors.



PMW precipitation estimates from LEO satellites and

IR observations from GEO platforms.

The KF-CMORPH derives the precipitation analysis

at a grid box of 8 3 8 km2 in three steps. First, PMW

estimates of instantaneous rain rates closest to the target

analysis time in both the forward and backward direc-

tions are propagated from their observation times to the

analysis time using the CSAVs computed from the GEO–

IR images. The forecast of the precipitation analysis is

then defined by averaging the forward- and backward-

propagated PMW estimates with weights inversely pro-

portional to their error variance. The IR-based precipitation

estimates are incorporated if the gap between the two

PMW observations is longer than 90 min.

The CSAVs used to propagate the PMW estimates

are calculated by computing the pattern correlation

between spatially lagged GEO–IRTb arrays from two

consecutive images. The spatial displacement with the

highest correlation is used to define the CSAVs. The IR-

based precipitation estimates used in this study are de-

fined by matching the PDF of GEO–IRTb with that of

the instantaneous PMW estimates.

Major differences between the KF-CMORPH and the

original CMORPH include i) the inclusion of the IR-based

precipitation estimates to fill in the gaps when PMW ob-

servations are not available nearby and ii) the improved

error definition for the PMW and IR precipitation esti-

mates as a function of instrument type, surface type, and

length of and temporal direction of propagation time, re-

gion, and season.

Validation tests showed substantial improvements of

the KF-CMORPH against the original version in both the

pattern correlation and fidelity of the precipitation intensity

PDF. In general, performance of the original CMORPH

FIG. 11. Correlation between the MWCOMB constructed from

withdrawn independent LEO satellites and precipitation estimates

derived from the IRFREQ (red), the original CMORPH (black),

and the KF-CMORPH (green) using PMW observations from four

LEO satellites. The MWCOMB is defined using the PMW esti-

mates from the five LEO satellites not included in the creation of

CMORPH analysis. Correlation is computed for 30-min mean rain

rates over 0.258 latitude–longitude grid boxes over the globe for

July–August 2009.

FIG. 12. Accumulated PDF of precipitation intensity derived from the MWCOMB based on

the withdrawn LEO satellites (purple), IRFREQ (red), the original CMORPH (black), and the

KF-CMORPH (green) using PMW observations from four LEO satellites. The cumulated PDF

is defined as the contribution to the mean rainfall (mm day21, y axis) from all cases with in-

stantaneous rain rates equal to or larger than a selected intensity (mm h21, x axis). The PDF is

derived from data from the synthetic experiments using four LEO satellites. Results are dis-

played separately for PMW propagation time of a) 0, b) 30, and c) 240 min.



degrades sharply with poor pattern correlation and sub-

stantially elevated (damped) frequency for light (strong)

precipitation when PMW precipitation estimates are

available from fewer LEO satellites. The KF-CMORPH is

capable of producing high-resolution precipitation analysis

with much more stable performance with various levels of

availability for the PMW observations.

Further improvements and enhancements are desir-

able for the KF-based CMORPH described in this pa-

per. In particular, error for the individual input PMW

and IR precipitation estimates and the propagation of

the error along the model integration process need to be

accurately quantified. This requires a comprehensive

examination of the error in the level 2 PMW precipita-

tion retrievals as well as that generated in the process

of propagating precipitating systems. The results of this

error analysis will not only lead to improved error def-

inition and thereby the final precipitation analysis, it will

also provide insights to how the integration algorithm

should be refined to reduce the generation and propa-

gation of errors. While this paper describes an algorithm

to construct high-resolution precipitation estimates through

the integration of information from individual sources,

success of such integration techniques is built upon the

production of the input level 2 PMW and IR precipi-

tation estimates with improved quality and refined error

quantification.

A prototype system has been developed at NOAA/

CPC to construct 30-min precipitation estimates on an

8 3 8 km2 grid over the globe from 608S to 608N by in-

tegrating PMW estimates from LEO satellites and IR

observations from GEO platforms through the KF-

CMORPH algorithm described in this paper. Further

work is under way to extend the analysis domain to

cover the entire globe from pole to pole and to remove

the bias in the integrated satellite estimates through

comparison against gauge observations.

Acknowledgments. The authors thank S.-H. Yoo and

Y. Yarosh for their technical support to part of the study

described in this paper. They are grateful to M. Sapiano

who kindly provided the SSM/I-based level 2 data used

in the synthetic experiments for July–August 2009.

Comments from P. A. Arkin, J. Janowiak, R. Ferraro,

G. Huffman, W. Shi, M. Chen, and anonymous reviewers

were invaluable for improvements to the manuscript. This

work is supported by NOAA/Climate Prediction Center

(CPC), NOAA/Climate Program Office (CPO), NOAA/

National Climatic Data Center (NCDC), and NOAA/

USWRP Hydrometeorology Testbed (HMT) as part of

NOAA’s contribution to the NASA Precipitation Mea-

surement Mission (PMM) and GEWEX Global Precipi-

tation Climatology Project (GPCP).

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