Impacts of Improved Error Analysis on the Assimilation of Polar Satellite

Passive Microwave Precipitation Estimates into the NCEP Global Data

Assimilation SystemRobert J. Kuligowski

Office of Research and Applications, NOAA/NESDIS, Camp Springs, MD, USA

Russ TreadonEnvironmental Modeling Center, NOAA/NWS/NCEP, Camp Springs, MD, USA

Wanchun ChenCaelum Research Corporation, Silver Spring, MD, USA

Presented by Arnold GruberOffice of Research and Applications, NOAA/NESDIS, Camp Springs, MD, USA

1st International Precipitation Working Group Workshop, Madrid, Spain24 September 2002

Outline

• Background and Motivation

• Data Sets

• Error Analysis

• Assimilation Scheme

• Preliminary Results

• Future Work

Background: General

• Assimilation of precipitation observations has been shown to positively impact the initialization and forecast of NWP models via improved specification of water content and latent heat release.

• One approach to assimilate precipitation data makes use of an inverted model convective parameterization.

• Another approach makes use of variational techniques in which the model precipitation physics and their adjoints are used to minimize the difference between simulated and observed precipitation.

Background: GFS Assimilation

• The Global Data Assimilation System (GDAS) of the NCEP Global Forecast System (GFS) currently assimilates rain rate estimates from:– Special Sensor Microwave/Imager (SSM/I)— since February 2001

– Tropical Rainfall Measuring Mission (TRMM) Microwave Imager – since October 2001

• Impact of data assimilation was evaluated by comparing control runs to assimilation runs and runs with a new physics package.

Background: Impact StudyRuns compared:• “Control 00”—2000 physics; no precip assimilation• “Single-cloud”—2000 physics, adjustment made to coldest

cloud in Arakawa-Schubert ensemble• “Multi-cloud”—2000 physics, adjustment made to

randomly selected cloud in Arakawa-Schubert ensemble• “Control-01”—no precip assimilation, new physics:

– Prognostic cloud water/ice, plus:• Optical path and emissivity in radiation is calculated from the cloud

water/ice• Convective detrainment as a source of cloud water/ice

– Cumulus cloud induces momentum mixing– Cumulus cloud top chosen each time step from a range of values

bounded by the sounding profile

• Likewise, SSM/I and TRMM assimilation had little impact on performance when compared to either SSM/I or TRMM as “ground truth”, while physics change had significant impact

• 2001 change in physics has much greater impact than either single-cloud or multi-cloud assimilation for most model fields at initialization time

Impact of Rain Rate AssimilationGFS guess (06 hr forecast) vs. observations (15-18 August 1999)

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all q(17.5%)

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Forecast Impact of Rain Rate AssimilationGFS Geopotential Height Field Forecast Skill Scores (Time: 11-18 August 1999)

• Again, little impact for rain rate assimilation, especially compared to impact of 2001 physics change:

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Reasons for Limited Impact:

• Nonlinearities in forward model to map analysis state to rain rates. – Nonlinearities severely limit range of validity for tangent linear

and, therefore, adjoint model used in minimization

• Lack of detailed error analysis of SSM/I and TRMM rain rates:– Uncertainty in error characteristics leads to improper weighting of

observation within analysis system

• Response: Produce a detailed error analysis of SSM/I rain rates

Error Analysis: Data Sets

Time period: April-October 2001

• SSM/I rain rate estimates using the Ferraro (1997) algorithm, aggregated onto the GFS gaussian grid (triangular truncation at total wavenumber 126 ~ 100 km at the equator)

• Stage III radar/raingauge fields over the CONUS (Fulton et al. 1998), aggregated onto the GFS gaussian grid

Error Analysis: Methodology• Objective: obtain expressions of both error and error

uncertainty as a function of SSM/I rain rate• Error is expressed as the ratio of estimated to observed

amount• Since the precipitation distribution is highly skewed, the

analysis was done on a log(n+1) scale to obtain a more Gaussian distribution – n+1 used to avoid taking log(0)

• To obtain compatible error and uncertainty expressions:– Data were sorted according to SSM/I rain rate– Data were binned into groups of 50– Ratio mean and standard deviation were computed for each bin

• Separate analyses for each SSM/I algorithm type (e.g. land scattering, ocean emission, etc.)

Error Analysis: Sample Results

SSM/I estimates exhibit a dry bias for very low rates, then a wet bias that increases with SSM/I rain rate

Similar results for other algorithms

Assimilation Scheme• Intermittent assimilation system with a 6-hourly ingest cycle (00, 06, 12, 18

UTC) using observations within ±3 hours of the analysis time• Approximately 7600 SSM/I 1 superob rain rates are used in each analysis

cycle in the 60° S - 60° N latitude band• 3-D variational technique to minimize the cost function

2 J(xa) = (xb – xa)T B-1 (xb – xa) + (yobs – R(xa))

T O-1 (yobs – R(xa)) + (Jdiv + Jq)

where

xa the analysis

xb best estimate (background) of the current state of the atmosphere

yobs assimilated observations

R(xa) forward model - operator that transforms analysis state to type, location,

and time of observation. The forward model for rain rate is built around the GFS precipitation physics. The adjoint of the physics provides gradient information used by the minimization algorithm.

B error covariance matrix for the background stateO error covariance matrix for the observations and the forward model

Jdiv and Jq additional constraints placed on analysis state

O-1 and B-1 Errors

• “Observation” error, O– SSM/I error, Ossmi, from error analysis

– representativeness error, Orep, is set to constant, 0.1

– forward model error, Omod is estimated by comparing model rain rates computed from background at location of SSM/I observations.

– Total O = Orep + max[Ossmi , Ossmi + (1- )Omod], where =0.5

• “Background” error, B– statistics for analysis variables are computed from set of 24

and 48 hour GFS forecasts verifying at the same time

Preliminary Results• SSM/I assimilation reduces excessive precipitation both in

tropics and extratropics

• Less success in enhancing light rainfall rates. Most likely due to non-linearities in model physics.

Control

Assimilation-Control

SSM/I

Impact of Rain Rate AssimilationGFS guess (06 hr forecast) vs. observations (27 July - 05 August 2002)

-0.4%

-0.3%

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all ps (1.26hPa)

all T (1.3 K) all q (15.5%) all wind (3.88m/s)

sonde T(1.55 K)

sonde q(17.4%)

sonde wind(4.22 m/s)

SSM/I TPW(3.24 mm)

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all ps (0.4 hPa) all T (0.07K) all q (0.22%) sonde T (0.14 K) sonde q (-1.92%) SSM/I TPW (0.53 mm)

% d

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(observation-guess) bias

(observation-guess) rmsd

• Largest impact on moisture field; other impacts are slight

Forecast Impact of Rain Rate AssimilationGFS Geopotential Height Field Forecast Skill Scores (Time: 27 July -05 August 2002)

• Very slight positive impact in Northern (summer) Hemisphere• Neutral impact in Southern (winter) Hemisphere

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NH 1000 hPa SH 1000 hPa

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Summary of Results

• Even with improved error analysis, SSM/I assimilation has had only a slightly positive impact, mainly on moisture variables and in the longer-range performance of the model

• Most significant impact appears to be reduction of excessive moisture/ precipitation in summer hemisphere tropical regions

• Improvements in assimilation techniques may permit greater impact of assimilated precipitation in the future

Future Work• Error analysis of AMSU data has been performed over the

CONUS in preparation for AMSU-B assimilation experiments

• Results are similar to SSM/I, but apparently larger differences exist in the tropics—will need to be resolved.

SSM/I AMSU-B

Future Work

• Forward model development– minimize negative impact of non-linearities in GFS precipitation

physics (simplify physics to retain essential features) permits larger iterations in applying adjoints

– extend radiative transfer model (OPTRAN) used to assimilate radiances to include cloud and precipitation effects consider assimilation of radiances from cloudy/precipitating FOVS

• Analysis variable– current moisture analysis is univariate multivariate?– consideration of issues associated with analysis moisture variable:

• large dynamic range (several orders of magnitude from surface to TOA)

• phase changes—need to express errors as a function of phase instead of looking at total water