correcting land surface model predictions for the impact of …provide accurate accumulation...

960 VOLUME 4J O U R N A L O F H Y D R O M E T E O R O L O G Y

Correcting Land Surface Model Predictions for the Impact of Temporally SparseRainfall Rate Measurements Using an Ensemble Kalman Filter and Surface

Brightness Temperature Observations

WADE T. CROW

Hydrology and Remote Sensing Laboratory, USDA/ARS, Beltsville, Maryland

(Manuscript received 13 January 2003, in final form 25 April 2003)

ABSTRACT

Current attempts to measure short-term (,1 month) rainfall accumulations using spaceborne radiometers arecharacterized by large sampling errors associated with low observation frequencies for any single point on theglobe (from two to eight measurements per day). This degrades the value of spaceborne rainfall retrievals forthe monitoring of surface water and energy balance processes. Here a data assimilation system, based on theassimilation of surface L-band brightness temperature (TB) observations via the ensemble Kalman filter (EnKF),is introduced to correct for the impact of poorly sampled rainfall on land surface model predictions of root-zone soil moisture and surface energy fluxes. The system is evaluated during the period from 1 April 1997 to31 March 1998 over two sites within the U.S. Southern Great Plains. This evaluation includes both a dataassimilation experiment, based on synthetically generated TB measurements, and the assimilation of real TB

observations acquired during the 1997 Southern Great Plains Hydrology Experiment (SGP97). Results suggestthat the EnKF-based assimilation system is capable of correcting a substantial fraction (.50%) of model errorin root-zone (40 cm) soil moisture and latent heat flux predictions associated with the use of temporally sparserainfall measurements as forcing data. Comparable gains in accuracy are demonstrated when actual TB mea-surements made during the SGP97 experiment are assimilated.

1. Introduction

Over large portions of the globe, the accuracy ofrainfall data is a major source of error for efforts tomonitor and/or predict surface water and energy bal-ance processes. Rainfall rate measurements are basedprimarily on four observational techniques: ground-based radar, rain gauge observations, satellite-basedinfrared and visible observations, and satellite-basedradiometer observations. With the exception of theUnited States and Europe, land-based radar systemsare not well developed. Gauge-based networks aremore extensive but still lacking in many tropical andarid regions of the world (New et al. 2001). Infraredretrievals from geostationary satellites can provide fre-quent observations over continental-scale regions, butthe retrieval is based on the use of cloud height as asurrogate for rainfall rate. As such, rate retrievals areindirect and prone to error—especially over short tem-poral scales and at high latitudes (Huffman et al. 2001).Spaceborne radiometers offer perhaps the most attrac-tive option for global-scale coverage, but current

Corresponding author address: Dr. Wade T. Crow, Hydrology andRemote Sensing Laboratory, USDA/ARS, RM 104, Building 007,BARC-W, Beltsville, MD 20705-2350.E-mail: [email protected]

spaceborne systems [e.g., the Tropical Rainfall Mea-suring Mission (TRMM) and the Special Sensor Mi-crowave Imager (SSM/I)] make observations of a givenpoint at too infrequent a temporal rate (twice daily) toprovide accurate accumulation estimates at timescalesshorter than monthly. Providing sufficient temporalsampling to facilitate retrieval of accurate accumula-tions over finer timescales is a major objective of theproposed Global Precipitation Mission (GPM) satelliteconstellation scheduled to launch in 2007 (Flaming etal. 2001). As currently envisioned, the system will pro-vide approximately eight retrievals of rainfall rates perday for most areas of the globe within a relative ac-curacy of about 25% (Adams et al. 2002). Becauseoffline global land surface modeling efforts [see, e.g.,the Global Land Data Assimilation System (Rodell etal. 2003, manuscript submitted to Bull. Amer. Meteor.Soc.) and the United States Air Force Weather Agen-cy’s Agricultural Meteorological Model (AGRMET)project] rely heavily on satellite-based observations ofrainfall for forcing data, the improved sampling andaccuracy characteristics of the GPM constellationshould allow for enhanced global-scale monitoring ofsurface water and energy balance processes.

Given the long list of observation techniques, and theabsence of any currently viable method without at leastone shortcoming, it is natural that data-fusion strategies

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involving one or more observational technique have de-veloped. Examples within the United States include themerging of ground-based radar and rain gauge mea-surements in Stage-III precipitation products producedby regional National Oceanic and Atmospheric Admin-istration (NOAA) River Forecasting Centers and quiltedinto a national Stage-IV product by the National Centersfor Environmental Prediction (see information online athttp://www.emc.ncep.noaa.gov/mmb/stage4/). Over re-gions of the globe not covered by extensive ground-based radar or gauge networks, the best current sourceof rainfall measurements are obtained by merging high-frequency, but uncertain, infrared rainfall rate retrievalswith more direct, but temporally sparser, spaceborneradiometer observations (Todd et al. 2001). A merged18 lat 3 18 lon daily (1DD) product based on infraredretrievals from the Television Infrared Observation Sat-ellite (TIROS) Operational Vertical Sounder (TOVS)and the Geostationary Operational Environmental Sat-ellite (GOES) and passive microwave measurementsfrom SSM/I is currently being archived as part of theGlobal Precipitation Climatology Project (GPCP) (Huff-man et al. 2001).

Additional opportunities for the fusion of various ob-servational sources are afforded by the development ofdata assimilation systems designed to update dynamicland surface models with remote observations. A par-ticularly powerful aspect of these systems is their abilityto integrate observations that are only indirectly relatedto rainfall. For instance, over lightly vegetated regionsof the globe, L-band surface brightness temperature (TB)observations can be inverted to produce estimates ofnear-surface (5 cm) soil moisture. Potential spacebornesources of high-frequency (1–3-day repeat time) globalL-band TB observations in the near future include theEuropean Space Agency’s (ESA) Soil Moisture andOcean Salinity Mission (SMOS) scheduled for launchin 2006 and the Hydrospheric States (HYDROS) mis-sion currently slated as a back-up mission in the Na-tional Aeronautics and Space Administration’s(NASA’s) Earth System Science Pathfinder (ESSP) pro-gram. Spaceborne TB observations provide an indirectmeasure of antecedent rainfall that, if properly inter-preted by the land data assimilation system, could cor-rect land surface model predictions for the impact ofrainfall inputs derived from the sparse sampling of anintermittent rainfall event. It is important to note thatsuch systems will not correct rainfall estimates them-selves. Rather, their aim would be to mitigate the impactof rainfall-forcing errors on a land surface model’s rep-resentation of surface state and flux variables.

The purpose of this analysis is to examine the po-tential of a data assimilation system designed aroundthe ensemble Kalman filter (EnKF) to combine tem-porally sparse rainfall rate measurements—ostensiblyfrom a spaceborne source–with TB observations drivenby near-surface soil moisture conditions. The applica-tion of the EnKF to the assimilation of TB observations

into a land surface model was first described in Reichleet al. (2002a). Recent work has successfully extendedthe application of the EnKF to cases involving real TB

observations acquired during the 1997 Southern GreatPlains Hydrology Experiment (SGP97) (Margulis et al.2002; Crow and Wood 2003). The approach used hereis based on the generation of a set of precipitation re-alizations (conditioned by both climatological expec-tations and temporally sparse rainfall observations) toforce an ensemble of land surface state forecasts. Theseforecasts are, in turn, updated using a remote obser-vation of L-band brightness temperature and the stan-dard Kalman filter update equation. Preliminary workin Crow and Wood (2003) describes an EnKF-based dataassimilation system where the model forecast ensembleis based solely on climatological expectations concern-ing precipitation. This implies that no observations ofantecedent rainfall are available at EnKF update times.Even for remote portions of the globe such an assump-tion is unrealistically restrictive. The development ofglobal spaceborne retrieval technologies virtually guar-antees that, however incomplete or temporally sparse,some type of rainfall observation will be available tocondition likelihood concerning recent rainfall accu-mulations beyond what is possible from purely clima-tological considerations. Consequently, this paper ex-pands on earlier work by presenting a data assimilationsystem capable of integrating both surface TB obser-vations and sparse rainfall accumulations derived fromthe temporal sampling of rainfall rates at frequenciesconsistent with expectations for current and next-gen-eration spaceborne radiometer systems (2–12 observa-tions per day). As a first approach for proof of concept,initial results are generated using an identical twin dataassimilation methodology where observations are syn-thetically generated by a model, perturbed with noise,and then assimilated back into the same model. Addi-tional results incorporating real TB observations madeduring SGP97 are also presented.

2. Data assimilation system

The data assimilation system examined here consistsof three parts: a land surface model to forecast landsurface model states, an observation model to predictsurface brightness temperatures (TB) based on land sur-face model state predictions, and an EnKF to updatestate forecasts with TB observations. The land surfaceand observation models are presented in sections 2a and2b. As described in section 2c, the EnKF is based onthe use of a model ensemble to temporally propagatethe error covariance information required by the stateupdate equation of the standard Kalman filter. For thisparticular application of the EnKF, the forecast ensembleis generated using a set of rainfall realizations consistentwith the likelihood of various daily rainfall accumula-tions given climatological considerations and the sparsesubsampling of actual rainfall at temporal frequencies


FIG. 1. (a) Times series of TOPLATS simulated 40-cm soil moistureresults and daily precipitation at the NOAA ATDD Little Washitasite between 1 Apr 1997 and 31 Mar 1998. (b) Same as (a), but forthe ARM CART EF site 13.

expected in next-generation spaceborne systems. Thestatistical procedure used to create these rainfall reali-zations is detailed in section 2d.

a. Land surface modeling and site descriptions

Numerical modeling of the land surface was basedon Topographically-based Land Atmosphere TransferScheme (TOPLATS) (Famiglietti and Wood 1994; Pe-ters-Lidard et al. 1997) simulations. The model has beensuccessfully applied to regions within the SouthernGreat Plains (SGP) by a number of studies (see, e.g.,Peters-Lidard et al. 2001; or Crow and Wood 2002).The top soil moisture layer in TOPLATS was set to adepth of 5 cm to reflect the expected vertical depth ofsensitivity for remote L-band TB observations. Simu-lations were run between 1 April 1997 and 31 March1998 on an hourly time step at the Department of En-ergy’s Atmospheric Radiation Measurement (ARM)Cloud and Radiation Testbed (CART) extended facilitysite 13 (EF13; 368369N, 978299W) near Lamont,Oklahoma, and the NOAA Atmospheric Turbulence andDiffusion Division (ATDD) Little Washita watershedsite (348589N, 978579W) near Chickasha, Oklahoma.Peak leaf area index (LAI) values during the growingseason were adjusted to fit local energy flux observa-tions. Simulated soil moisture time series are shown inFig. 1 and model validation results for both sites areshown in Figs. 2 and 3. Additional details on the ap-plication of TOPLATS to these sites can be found inCrow and Wood (2003). Despite their proximity, thetwo sites demonstrate substantially different root-zonesoil water dynamics during the 1997 growing season.The ARM CART EF13 site was usually wet due to theimpact of several large precipitation events in June andJuly. Conditions at the NOAA ATDD Little Washita siteare more typical of the region’s climatology, with an

absence of sustained precipitation during June and Julyleading to a strong dry down during the midsummermonths. In general, denser vegetation at the ARMCART EF13 site produces relatively more transpirationand faster root-zone dry-down dynamics.

b. Microwave emission modeling

Surface (5 cm) soil moisture and soil temperaturepredictions made by TOPLATS were processed throughthe Land Surface Microwave Emission Model(LSMEM) (Crow et al. 2001) to produce correspondingestimates of L-band surface brightness temperature (TB).Microwave radiative transfer parameters for both siteswere taken from Jackson et al. (1999). Brightness tem-perature validation results in Fig. 2 and 3 are based onairborne electronically scanning thinned array radiom-eter (ESTAR) measurements made during the SGP97experimental period (17 June to 16 July 1997). TheESTAR measurements have a pixel resolution of 800m. However, to account for georegistration uncertain-ties, ESTAR TB measurements used here were derivedfrom averaging observations within a 3 3 3 pixel win-dow centered on each site. It is worth noting that com-parisons between 5-cm soil moisture gravimetric soilmoisture samples in the immediate vicinity of the ARMCART EF13 site and TOPLATS predictions are quitegood. This suggests that the pronounced negative biasin LSMEM TB predictions shown in Fig. 3 is at leastpartially a scale effect reflecting the difference in sup-port between the plot-scale model simulation and thefield-scale ESTAR retrieval (Crow and Wood 2003).

c. The ensemble Kalman filter

The EnKF uses an ensemble-based Monte Carlo ap-proach to temporally propagate error covariance infor-mation required by the standard Kalman filter (KF) forupdating of model predictions with observations (Ev-enson 1994; Reichle et al. 2002a). Using notation pre-sented in Reichle et al. (2002a), this section describesthe state space representation of the EnKF. Take Y(t) tobe a vector of model state variables at time t. The po-tentially nonlinear prognostic equation f describing thetemporal evolution of these states can be represented as

dY5 f(Y, w). (1)

dt

The error term w originates from inadequacies in modelphysics, poor parameter selection, and/or errors in mod-el forcing data. Let the operator M represent the mea-surement operator that converts the state variables in Yinto a measurements taken at time tk:

Z 5 M[Y(t )] 1 v ,k k k (2)

where vk represents additive Gaussian measurementnoise with covariance Cyk. The EnKF is based on theMonte Carlo generation of an ensemble of Y predictions


FIG. 2. TOPLATS and LSMEM validation results for the ARM CART EF13 site near Lamont, OK.Plotted energy flux and surface temperature results are averaged values between 1000 and 1600 localtime. Observed brightness temperatures are taken from L-band ESTAR retrievals during SGP97.

via (1). This requires an a priori assumption concerningthe nature and structure of model error represented byw and the perturbation of individual model realizations(or forecasts) with an appropriate statistical represen-tation of this error. At each measurement time, statepredictions made by the ith model realization within theensemble are referred to as the forecast . If f is lineariY2

and all errors are additive, independent, and Gaussian,the optimal updating of by the actual measurementiY2

Zk is given byi i i iY 5 Y 1 K [Z 2 M (Y )], and (3)1 2 k k k 2

21K 5 [C (C 1 C ) ] , (4)k YM M y t5tk

where CM is the error covariance matrix of the measure-ment forecasts Mk( ), CYM is the cross-covariance ma-iY2

trix between the predicted measurements and state var-iables contained , and is the updated (or analysis)i iY Y2 1

state representation. For each ensemble realization, anadditive noise term consistent with vk must be synthet-ically generated and added to Zk to produce the perturbedobservation . This is required to ensure that the spreadiZk

of the updated state ensemble accurately reflects the truestate error covariance (Burgers et al. 1998). From theensemble, CM and CYM are statistically estimated by cal-culating covariances around the ensemble mean. Eachensemble replicate is updated using (3) and (4) and thenallowed to evolve via (1) until the next measurementtime. Filter predictions are typically derived from aver-aging model forecasts across the ensemble.

d. Conditioned rainfall likelihood distributions

A statistical representation of error in daily rainfallaccumulations associated with the sparse temporal sam-


FIG. 3. TOPLATS and LSMEM validation results for the NOAA ATDD Little Washita site nearChickasha, OK. Plotted energy flux and surface temperature results are averaged values between1000 and 1600 local time. Observed brightness temperatures are taken from L-band ESTARretrievals during SGP97.

pling of rainfall was constructed by applying a directsubsampling approach to 15-min rain gauge data col-lected at all Oklahoma Mesonet stations during the cal-endar years 1997 and 1999. For a daily sampling fre-quency of n, rainfall rates were assumed constant andequal to the observed 15-min gauge-derived rate for the24n21 h period centered on each observation. Rainfallrate estimates for the each of the 24n21 h periods in asingle day were then averaged and used to construct adaily rainfall accumulation estimate R̂. Each daily rain-fall estimate R̂ was paired with the corresponding truedaily accumulation rainfall value R derived from sum-ming all observations within a given day. This pairingwas repeated for every day at every Oklahoma Mesonetstation during 1997 and 1999. The resulting set of (R̂,R) pairs were then discretely binned according to bothR̂ and R and used to construct a series of conditional

likelihood distributions f n(R | R̂) for various discreteranges of R̂. This set of distributions included the caseof zero measured rainfall f n(R | R̂ 5 0) describing theprobability of falsely negative rainfall observations.

The conditioning of accumulation likelihoods de-pends on the frequency of sampling that supports theaccumulation estimate. Sets of conditional distributionswere constructed for rainfall sampling rates (n) of 2, 4,6, 8, and 12 day21. The special case of unconditionedrainfall intensities f 0(R) was also constructed to rep-resent daily rainfall likelihood in the absence of anyrainfall measurements (i.e., n 5 0). Figure 4 shows aset of f n(R | R̂) histograms for n 5 8 day21, constructedusing seasonally and geographically pooled observa-tions within the entire state of Oklahoma. No attemptwas made to parameterize or model the likelihood dis-tributions. Instead, individual rainfall realizations were


FIG. 4. Set of normalized conditional rainfall likelihood distributions for actual daily rainfallaccumulations given a rainfall estimate R̂ derived from the subsampling of eight observations aday. Results are derived from 15-min OK mesonet rain gauge measurements collected duringcalendar years 1997 and 1999.

randomly sampled from the exact set of observationsused to construct the likelihood distributions.

3. Methodology

Two separate methodologies were utilized to evaluatethe data assimilation system. The first approach wasbased on an identical twin data assimilation experimentdesign. In this approach, TOPLATS/LSMEM simula-tions forced by complete (i.e., not subsampled) localrain gauge observations were designated as truth. Thesesimulations, shown in Fig. 1 and validated in Figs. 2

and 3, will be referred to as ‘‘benchmark’’ simulations.LSMEM TB predictions from benchmark simulationswere perturbed with random error (Cy 5 9 K2) to forma set of daily synthetic observations Zk and reassimilatedback into TOPLATS via the EnKF. The second meth-odology utilized real ESTAR observations of TB ac-quired during SGP97. During the experiment (17 June1997 to 16 July 1997), ESTAR imaging was performedon 18, 19, 20, 25, 26, 27, 29, and 30 June, and on 1,2, 3, 11, 12, 13, 14, and 16 July.

For the 24-h period preceding 1600 UTC (the ap-proximate measurement time for ESTAR measurements


FIG. 5. (a) At the NOAA ATDD Little Washita site, time series of40-cm soil moisture results for: the benchmark TOPLATS simulation,TOPLATS simulations forced by eight-times-daily subsampling ofprecipitation, and EnKF results (eight-times-daily precipitation anddaily TB observations) during the 1997 growing season. (b) Same as(a), but for the ARM CART EF13 site.

during SGP97), daily estimated rainfall amounts (R̂)were derived at each site through the subsampling of n15-min rain gauge observations per day. This subsam-pled estimate was then used to select the proper f n(R | R̂)histogram (Fig. 4) from which to sample a set of dailyrainfall amounts. Sampled daily rainfall amounts weredistributed equally among 24cn21 consecutive hours ofrainfall randomly located within the 24-h period, wherec is the number of 15-min rainfall gauge measurementswhere rainfall was observed. This ensemble of hourlyrainfall time series was used to generate an ensembleof 25 TOPLATS state (Y) and LSMEM observation[M(Y)] forecasts from which forecast estimates of mod-el error (CYM and CM) could be obtained. Model ensem-bles were created for every 24-h period regardless ofwhether TB observations were available for assimilation.At times with observations, each ensemble member wasupdated using the TB observations (Zk) and the EnKFupdate equation given in (3). Four TOPLATS soil mois-ture states (0–5, 5–15, 15–40, and 40 cm to water table)and one soil temperature state (7.5 cm) were updatedin this way. These simulations will be referred to as‘‘EnKF’’ or ‘‘EnKF-based assimilation’’ results. Like-wise, simulations where rainfall ensembles were gen-erated but not updated with TB observations will bereferred to as ‘‘open loop’’ simulations.

Additional TOPLATS simulations were constructedthat relied directly on subsampled rainfall data to pro-vide hourly precipitation forcing. Like open loop results,these simulations did not assimilate TB observations.However, unlike open loop results, they did not employthe rainfall ensemble generation procedure described insection 2d. Instead, for a given daily sampling frequencyof n, hourly rainfall rates were assumed constant andequal to the observed 15-min gauge-derived rate for the24n21 h period centered on each observation. TOPLATSoutput for these simulations will be referred to as‘‘subsampled precipitation’’ results. The accuracy ofTOPLATS and LSMEM predictions derived from theassimilation of TB observations via the EnKF will beevaluated based on their ability to improve surface stateand flux predictions relative to subsampled precipitationsimulations that utilize neither TB observations nor theEnKF methodology.

4. Results: Identical twin experiment

Figure 5 shows root-zone soil moisture results derivedfrom the EnKF-based assimilation of L-band surfacebrightness temperature (TB) into TOPLATS simulationsforced using sparse observations of rainfall. The TB mea-surements assimilated to produce EnKF results in Fig.5 were synthetically generated every day at 1600 UTC(1000 CST) using the identical twin experiment meth-odology described in section 3. Rainfall observationswere taken from the subsampling of eight 15-min raingauge observations per day. This series of eight dailymeasurements were spaced evenly throughout the day

with the first measurement occurring at 0000 UTC. Alsoshown are TOPLATS results derived from the direct useof subsampled precipitation and benchmark TOPLATSpredictions based on all available rainfall data at bothsites. At the NOAA ATDD Little Washita site, the as-similation of TB observations allows for a more accuraterepresentation of a midsummer dry down by compen-sating for the consistently high bias of precipitation es-timates derived from sparse subsampling of rainfallevents. Conversely, at the ARM CART EF13 site, largeprecipitation events in late June and early July are un-derestimated by temporally sparse rainfall sampling,leading to anomalously dry conditions during the middleportion of the growing season. By interpreting surfaceL-band TB observations and accurately replenishingroot-zone soil water at deeper levels, the EnKF-basedassimilation of TB is able to compensate for error inrainfall forcing data. It should be noted that the root-zone depth assumed in Fig. 5 (40 cm) is considerablydeeper than the shallow vertical depth of sensitivity forTB observations (5 cm). Consequently, results do not


FIG. 6. (a) At the NOAA ATDD Little Washita site, time series ofrms error in EnKF 40-cm soil moisture predictions. Errors are pooledvalues based on all possible start times for precipitation observations.Also shown are rms errors associated with the direct forcing ofTOPLATS using subsampled precipitation data. (b) Same as (a), butfor the ARM CART EF13 site.

FIG. 7. (a) At the NOAA ATDD Little Washita site, time series ofrms error in daily averaged (1000 to 1600 local time) EnKF latentheat flux predictions. Errors are pooled values based on all possiblestart times for precipitation observations. Also shown are rms errorsassociated with the direct forcing of TOPLAS using subsampled pre-cipitation data. To improve readability, all errors are temporallysmoothed within a 3-day moving average window. (b) Same as (a),but for the ARM CART EF13 site.

simply reflect the direct replacement of model-generatedsoil moistures with remote observations.

Results in Fig. 5 are based on the designation of justone of the 12 possible 15-min intervals between 0000and 0300 UTC as the start time for the cyclic sequenceof eight rainfall observations per day. Instead of plottingresults for all 12 possible start times, Figs. 6 and 7summarize them by plotting pooled root-mean-square(rms) differences between the benchmark TOPLATSsimulation and EnKF root-zone soil moisture results.Also plotted are pooled rms errors associated with thedirect use of eight-times-daily subsampled precipitationto force TOPLATS. EnKF root-zone soil moisture re-sults in Fig. 6 show substantial improvements versussubsampled precipitation results during the growing sea-son. Spikes in rms error, coinciding with large precip-itation events, suggest that the EnKF does not imme-diately incorporate the impact of intense precipitation;however, the assimilation of TB observations in the af-termath of rainfall events allows for a sharp correctionduring the early portion of dry-down events. Relative

to the growing season, less improvement is observedduring fall and winter months. Raising the observationalerror used to create synthetic TB observations from 3 to6 K increases rms error in EnKF predictions by about10% at both sites (not shown).

Analogous latent heat flux results are shown in Fig.7. Large errors in subsampled precipitation results aredue to the inability of sparse rainfall rate sampling toaccurately capture alternating periods of water- and en-ergy-limited evapotranspiration during the growing sea-son. For instance, subsampled precipitation results forthe NOAA ATDD Little Washita site in Fig. 7a showlarge errors during a dry period in July (see Fig. 5).Much of this error is due to instances where the sub-sampling of modest precipitation events in late June andearly July overestimates their intensity and underesti-mates the severity of the subsequent water-limitedevapotranspiration period. As seen in Fig. 5a, the EnKF-based assimilation of TB observations removes water


FIG. 8. (a) Pooled rms error for EnKF 40-cm soil moisture results over entire simulation period(1 Apr 1997 to 31 Mar 1998) for both study sites at a range of rainfall and TB sampling frequencies.Errors are calculated relative to benchmark TOPLATS simulations. (b) Same as (a), but only forthe growing season (1 May 1997 to 31 Sep 1997).

from the root-zone and compensates for the overesti-mation of antecedent rainfall amounts. This leads to animproved representation of soil water limitation onevapotranspiration at both sites. The absence of evapo-transpiration errors from October to May is due to thenear uniformity of energy-controlled evapotranspirationconditions at both sites during the winter and spring.

a. Impact of observation frequency

Figure 8a plots 40-cm soil moisture rms error resultsfor a range of rainfall and TB sampling frequencies dur-ing the entire simulation period (from 1 April 1997 to31 March 31 1998). Error statistics were derived frompooling soil moisture results at both study sites andusing all possible start times for daily rainfall obser-vations. Figure 8b is identical, except the values arederived from pooling results during the growing seasononly (from 1 May 1997 to 31 September 1997). Thelowest possible TB observation frequency (i.e., never)corresponds to an open loop case where individual rain-fall realizations are generated from rainfall likelihood

distributions but not updated via (3). Comparison be-tween open loop and subsampled precipitation casesprovides an important check that the rainfall ensembleprocedure described in section 2d is generating errorsconsistent with actual uncertainties associated with thedirect use of subsampled rainfall.

In contrast to instantaneous measurements of precip-itation fluxes, TB observations measure a surface state—soil moisture—containing integrated information aboutpast rainfall events. Figures 8 and 9 demonstrate thepotential value of this memory for filtering errors as-sociated with sparsely subsampled and memoryless pre-cipitation flux retrievals. For instance, during the grow-ing season (Fig. 8b) the assimilation of daily surface TB

measurements reduces rms error in 40-cm soil moisturepredictions by about 50% for 12 rainfall samples perday and up to 65% for twice-daily sampling. Relativeto open loop results, the EnKF-based assimilation of TB

also reduces the sensitivity of root-zone soil moistureerrors to the frequency of rainfall observations. Thisloss of sensitivity is evident for TB measurement ratesas infrequent as once every 5 days. One consequence


FIG. 9. (a) Pooled rms error for daily averaged (1000 to 1600 local time) EnKF latent heat fluxresults over entire simulation period (1 Apr 1997 to 31 Mar 1998) for both study sites at a rangeof rainfall and TB sampling frequencies. Errors are calculated relative to benchmark TOPLATSsimulations. (b) Same as (a), but only for the growing season (1 May 1997 to 31 Sep 1997).

of this insensitivity is the relative superiority of a com-bination of sparse L-band TB observations and rainfallsampling rates versus much more frequent rainfall ob-servations in isolation. For instance, during the growingseason twice-daily rainfall sampling and one TB obser-vation every five days leads to errors that are compa-rable to 12 rainfall samples per day and no TB obser-vations. Likewise, results for twice-daily retrievals ofrainfall rate and daily TB observations are as accurateas those for any combination of more frequent rainfallobservations (up to 12 samples per day) and sparser TB

retrieval rates.Figure 9 is analogous to Fig. 8, except that it dem-

onstrates latent heat flux errors. One clear contrast be-tween Figs. 8 and 9 is the degree to which open loopand subsampled precipitation results differ. For latentheat flux, open loop TOPLATS results, where estimatedR̂ values are used to sample an ensemble of precipitationintensities from the appropriate f (R | R̂) likelihood dis-tribution, are more accurate than subsampled precipi-tation results based on the direct use of R̂. Sparse sub-sampling of precipitation tends to enhance precipitation

intermittency and strongly overpredict both the lengthand severity of soil-controlled evapotranspiration peri-ods. In contrast, using R̂ to generate a likelihood-basedensemble of precipitation events temporally smoothesprecipitation and moderates the severity of soil watercontent extremes. This keeps evapotranspiration ratesfor open loop results at or near potential evapotrans-piration levels. Because the 1997 growing season is rel-atively wet, a blanket assumption of potential evapo-transpiration is acceptable for many periods of time andopen loop latent heat flux predictions do not exhibitlarge errors. Nevertheless, daily assimilation of TB mea-surements allows for improved representation of soil-controlled periods and reduces rms errors in TOPLATSlatent heat flux predictions by up to 50% relative to theopen loop case.

b. Filter performance

EnKF results can also be evaluated based on theirconsistency with regards to the assumptions that un-derlie the optimality of the Kalman filter update equa-


FIG. 10. (a) Distribution of coefficient of skew results for soilmoisture ensemble forecasts at a range of depths. (b) Distribution ofnormalized filter innovations and a reference standard normal distri-bution.

tion. For instance, previous work has noted that uncer-tainty in rainfall does not necessarily lead to Gaussianerror forecasts for TB and surface soil moisture (Crowand Wood 2003). Figure 10a plots histograms for co-efficient of skew results calculated from pooled modelforecasts of soil moisture at both study sites. Surface(0–5 cm) soil moisture results are generally associatedwith large positive skew. Even when no rainfall is de-tected (i.e., R̂ 5 0) some positive rainfall realizationsare required for the rainfall ensemble to properly ac-count for falsely negative precipitation observations.Therefore, in contrast to the majority of ensemble re-alizations capturing a drying tendency, isolated ensem-ble members with positive rainfall forcing will becomesharply wetter. This leads to positively skewed forecastensembles for surface soil moisture and potentially non-optimal updating using (3). One influence on forecastskew is the frequency of rainfall observations. Increas-ing the frequency of rainfall rate observations from 2to 12 day21 reduces the average coefficient of skew in5-cm forecasts, but only slightly (from 1.87 to 1.58). Amuch stronger factor is the depth of the forecasted soilmoisture state. As demonstrated in Fig. 9a, forecastskew is progressively reduced within deeper soil layers.

The forecast skew observed in Fig. 10a can be re-

duced through ancillary measurements, which eliminatethe possibility of falsely negative rainfall observations.For instance, in cases where sparse rainfall radiometersubsampling detects no rainfall (i.e., R̂ 5 0), visible(VIS) and thermal infrared (IR) precipitation indicesfrom geostationary satellites could be used to make arain/no-rain determination for the entire day. Duringdays with no rain, a reliable no-rain determination elim-inates the need to generate the small number of positiverainfall realizations that tend to skew the entire forecastensemble. If the VIS–IR observation system detects rainand the sparse radiometer sampling does not, rainfallrates can be sampled from a conditioned likelihood dis-tribution reflecting positive rainfall, which is undetectedby sparse subsampling at a rate of n day21 {i.e., f n[R | (R. 0 and R̂ 5 0)]}. Incorporating this modification,EnKF results for eight rainfall observations per day anddaily TB measurements were repeated at the NOAAATDD site using a modified assimilation system thatassumed perfect rain/no-rain determinations were avail-able. Eliminating the possibility of falsely negative rain-fall observations reduces the coefficient of skew in sur-face (0–5 cm) soil moisture forecasts by 71% (1.71–0.50), yet improves model EnKF predictions of root-zone soil moisture by only 12% (0.0047–0.0041 m).Such a modest improvement in accuracy implies thatskew in model forecasts of TB and surface soil moistureis not a major source of overall error in results for theoriginal filter. One possible explanation for this is theconfinement of large skew to state forecasts within sur-face layers that constitute a minor fraction of overallroot-zone volume. Deeper, more substantial soil mois-ture states exhibit considerably less skew and are, there-fore, more amenable to updating using the EnKF. Thisresult is consistent with earlier work by Reichle et al.(2002b) who demonstrate the adequacy of the EnKF inupdating skewed forecast ensembles arising from non-linearites in land surface models.

The statistical properties of the filter innovations pro-vide an additional diagnostic tool for assessing filterperformance. A filter’s innovations are defined as thesequence of differences between forecasted and actualobservations Zk 2 Mk( ). If the underlying assump-iY2

tions of the Kalman filter are fully met (i.e., linear mod-els and uncorrelated Gaussian errors), observed inno-vations should be temporally uncorrelated, mean zero,and Gaussian with a covariance equal to CM 1 Cy . Thedegree to which actual innovations depart from this idealgives a sense as to the applicability of the Kalman filterupdate equation to a particular filtering problem. Figure10b plots a histogram of normalized innovations—[Zk

2 Mk( )]/(CM 1 Cy )—observed at both study sitesiY2

during assimilation of daily TB observations and eight-times-daily subsampling of rainfall. A standard normaldistribution is also plotted for reference. The positiveshift of the normalized innovation distribution relativeto the standard normal reflects the continual readjust-ment of excessively wet (i.e., low TB) ensemble mem-


FIG. 11. Time series of TOPLATS LSMEM TB predictions derivedfrom both OK Mesonet rainfall gauge measurements and precipitationretrievals extracted from the GPCP 1DD dataset within the 18 lat 318 lon grid cell surrounding the ARM CART EF13 site (368 to 378Nand 2978 to 2988W). Also plotted are spatially averaged ESTAR TB

observations within the same degree box.

TABLE 1. Comparison between rms errors in EnKF 40-cm soil moisture (u40 cm) and latent heat flux (lE ) results utilizing both syntheticand actual ESTAR TB observations. Given rms errors are calculated by pooling results between 17 Jun and 16 Jul 1997. Results are shownfor rainfall rate subsampling frequencies (n) of both 2 and 8 day21.

Site n (day21) TB source u40 cm (m) lE (W m22)

NOAA ATDD Little Washita 222888

SyntheticESTARESTAR (bias corrected)SyntheticESTARESTAR (bias corrected)

0.00790.01140.00740.00610.01070.0061

26.563.221.721.458.619.6

ARM CART EF13 2288

SyntheticESTARSyntheticESTAR

0.01670.01880.01380.0154

24.429.727.328.0

bers produced to capture the possibility of falsely pos-itive rainfall observations. Frequent low TB forecastsrelative to actual measurements lead, in turn, to an ex-cessive amount of positive innovations. Likewise, thenon-Gaussian tail at large negative normalized inno-vations is due to the inability of the climatologicallybased ensembling procedure to capture large precipi-tation events during the modeling period. Because rain-fall ensembles are based on climatological likelihoods,large events are not well represented. In a Bayesiansense, this is because unusually intense rainfall obser-vations are more likely associated with large samplingerrors than an actual rare event. Consequently, for largeR̂, few, if any, rainfall realizations generated from thef (R | R̂) likelihood distribution will be greater than R̂(see Fig. 4). However, several large precipitation ob-

servations at the ARM CART EF13 site are, in fact,accurate representations of unusually intense precipi-tation events. The inability of the rainfall ensemble gen-eration procedure to reflect such extreme events leadsto the strong overprediction of TB and the non-Gaussiannegative tail on the innovation histogram shown in Fig.9.

5. Results: Real observations

Datasets collected during SGP97 provide an oppor-tunity to evaluate the proposed data assimilation systemusing real remote sensing observations of TB. Figure 11shows TB predictions for a TOPLATS LSMEM sim-ulation of the ARM CART EF13 site forced by bothrain gauge observations and rainfall data extractedfrom the satellite-derived GPCP 1DD dataset. Alsoplotted are L-band TB observations derived from air-borne ESTAR measurements during SGP97. To en-sure compatibility with the 18 resolution of the 1DDrainfall observations, ESTAR observations, LAI forc-ing for TOPLATS, and gauge-based precipitation ob-servations were averaged within the 18 lat 3 18 lon gridbox roughly centered on the ARM CART EF13 site.Due to apparent errors in the 1DD rainfall, the twosimulations diverge on 25 June, 29 June, and 15 July.While TOPLATS LSMEM TB predictions derived fromlocal rain gauge observations are quite accurate, resultswith spaceborne 1DD rainfall observations are clearlynot consistent with independent ESTAR TB observa-tions. It is this lack of consistency that forms the ob-servational basis for the detection, and eventual correc-tion, of land surface model errors associated with poorrainfall forcing.

While Fig. 11 demonstrates the basic detectabilityassumption at the heart of the data assimilation system,it does not validate the system itself. As a first steptoward this, Table 1 presents results for the assimilationof actual ESTAR TB measurements during the SGP97period (17 June to 16 July 1997). Results are shown forrainfall forcing consistent with both twice and eight-times-daily subsampling of rainfall rates. ‘‘ESTAR’’ re-sults are based on updating with real L-band TB obser-


vations at each of the 16 ESTAR observations times(see Fig. 11). Results for ‘‘synthetic TB’’ observationsare based on updating at the same 16 times, but withTB values synthetically generated by the identical twinexperiment. As in the identical twin experiment, errorsfor both are based on comparisons to the benchmarkTOPLATS simulation described in section 3. Conse-quently, comparisons in Table 1 give a sense as to thefeasibility of obtaining the accuracy improvements seenin Figs. 6, 7, 8, and 9 with real TB observations. At theARM CART EF13 site, real TB observations are nearlyas effective as synthetically generated observations.However, the assimilation of TB observations at theNOAA ATDD Little Washita site does not lead to com-parable accuracies until after the TB bias observed inFig. 3 is removed. In a truly operational setting, suchan adjustment would require the successful applicationof a bias detection and correction strategy (Dee andDaSilva 1998).

6. Summary and conclusions

Random sampling errors due to temporally sparse ob-servation frequencies (2–12 per day) are expected tocomprise a major fraction of retrieval error for currentand next generation radiometer systems designed to es-timate daily rainfall accumulations from space (e.g.,Bell et al. 1990, or Steiner 1996). The presence of ran-dom errors in precipitation forcing data for land surfacemodels can lead to large uncertainty in predictions ofroot-zone (40 cm) soil moisture and surface energy flux-es (Figs. 5 and 6). However, surface TB observationsappear to offer a viable observational basis to detectland surface model errors associated with poorly re-trieved rain rates (Fig. 11). This analysis exploits thispotential by developing an EnKF-based data assimila-tion system designed to update land surface model pre-dictions, made uncertain by the impact of random sam-pling error in rainfall observations, with surface TB ob-servations supported only by near-surface (0–5 cm) mi-crowave emission.

The EnKF-based land surface data assimilation sys-tem presented in section 2 is based on the use of tem-porally sparse rainfall observations—ostensibly from aspaceborne source—to condition expectations concern-ing daily rainfall accumulations. Using a Monte Carloapproach, rainfall realizations sampled from histogramsof conditional rainfall likelihoods are run through a landsurface and forward microwave emission model to cre-ate an ensemble of land surface state and surface mi-crowave brightness temperature (TB) predictions. Thisensemble provides the necessary error covariance in-formation to update individual members of the ensemblewith TB observations via Eq. (3). A synthetic identicaltwin experiment demonstrates that the approach is ca-pable of substantially reducing errors in both root-zonesoil moisture and surface energy flux predictions rel-ative to results derived from the direct use of sparsely

subsampled rainfall to force TOPLATS (Figs. 6, 7, 8,and 9). Preliminary results with real TB predictions ob-tained during SGP97 suggest that comparable levels ofcorrection are obtainable using actual L-band TB ob-servations (Table 1), although in some cases, reachingthis potential may require the application of an effectivebias detection strategy.

Results in Figs. 8 and 9 can also be used to gaugethe relative value of spaceborne brightness temperatureand rainfall rate observations for land surface modeling.A generalization emerging from the figures is the degreeto which a combination of relatively sparse rainfall rateand TB measurements leads to more accurate state andflux predictions than open loop (i.e., no TB assimilation)results driven by more frequent rainfall observations.Given twice-daily observations of rainfall, L-bandspaceborne retrievals of TB every 3 days are more valu-able for root-zone soil moisture and surface energy fluxprediction than an increase in the observational fre-quency of rainfall rate retrievals from 2 to 8 day21.There are also indications that adequate TB samplingmay preclude the need to improve the temporal samplingcharacteristics of spaceborne rainfall systems. Updatingwith daily observations TB and the EnKF substantiallyreduces the observed sensitivity of results to the fre-quency of rainfall observations.

A central issue in the design of any data assimilationsystem is the choice of a particular assimilation tech-nique. As a noted in Reichle et al. (2002a) the EnKFhas a number of attributes that make it well suited forthe assimilation of TB observations into a land surfacemodel. Of particular interest here is the EnKF’s flexi-bility with regard to model error type and ability totemporally propagate uncertainty associated with poorrainfall forcing. This flexibility distinguishes the EnKFfrom other variants of the Kalman filter—most notablythe extended Kalman filter (Reichle et al. 2002b). Onepotential downside for the EnKF is the presence of skewin ensemble model forecasts (Fig. 10), which will pre-vent optimal updating of ensembles via the Kalman fil-ter. Because alternative assimilation strategies, partic-ularly the fully nonlinear Monte Carlo Bayesian filterpresented by Anderson and Anderson (1999) and thevariational smoother incorporating model error pre-sented by Reichle et al. (2001), are better suited fordealing with non-Gaussian errors than the EnKF, mea-suring the impact of this forecast skew on eventualEnKF update accuracy is critical for assessing the rel-ative suitability of the EnKF versus other assimilationtechniques. Section 4b demonstrates that assuming theavailability of accurate rain/no-rain determinationseliminates a majority of the forecast skew. Crucially,this sharp reduction is not associated with substantialimprovements in assimilation results. This implies thatforecast skew was not a major source of error in theoriginal EnKF-updated state predictions, which, in turn,supports the EnKf’s overall suitability for this appli-cation.


Several caveats should be noted concerning overallresults presented here. First, the U.S. SGP region iswidely regarded as nearly optimal for soil moisture re-mote sensing. The value of L-band TB observations forthe inference of surface state conditions will almost cer-tainly be reduced for more densely vegetated regions.Finally, a more thorough analysis would include addi-tional causes of uncertainty in spaceborne rainfall rateretrievals (e.g., ambiguities surrounding the selection ofan appropriate rain rate–reflectivity relationship andbeam-filling problems for spaceborne radiometers) aswell as a realistic spatial resolution for spaceborne TB

observations.

Acknowledgments. Data support from the DOE’s At-mosphere Radiation Measurement Program, TildenMeyers (NOAA ATDD), Thomas Jackson (USDAARS), the Oklahoma Mesonet, and the Global Precip-itation Climatology Project is gratefully acknowledged.

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