statistical downscaling of daily precipitation from observed and modelled atmospheric fields

HYDROLOGICAL PROCESSESHydrol. Process. 18, 1373–1394 (2004)Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.1418

Statistical downscaling of daily precipitation fromobserved and modelled atmospheric fields

Stephen P. Charles,1* Bryson C. Bates,1 Ian N. Smith2 and James P. Hughes3

1 CSIRO Land and Water, Wembley, Western Australia 6913, Australia2 CSIRO Atmospheric Research, Aspendale, Victoria 3195, Australia

3 Department of Biostatistics, University of Washington, Seattle, WA, USA

Abstract:

Statistical downscaling techniques have been developed to address the spatial scale disparity between the horizontalcomputational grids of general circulation models (GCMs), typically 300–500 km, and point-scale meteorologicalobservations. This has been driven, predominantly, by the need to determine how enhanced greenhouse projections offuture climate may impact at regional and local scales. As point-scale precipitation is a common input to hydrologicalmodels, there is a need for techniques that reproduce the characteristics of multi-site, daily gauge precipitation. Thispaper investigates the ability of the extended nonhomogeneous hidden Markov model (extended-NHMM) to reproduceobserved interannual and interdecadal precipitation variability when driven by observed and modelled atmosphericfields. Previous studies have shown that the extended-NHMM can successfully reproduce the at-site and intersitestatistics of daily gauge precipitation, such as the frequency characteristics of wet days, dry- and wet-spell lengthdistributions, amount distributions, and intersite correlations in occurrence and amounts. Here, the extended-NHMM,as fitted to 1978–92 observed ‘winter’ (May–October) daily precipitation and atmospheric data for 30 rain gaugesites in southwest Western Australia, is driven by atmospheric predictor sets extracted from National Centers forEnvironmental Prediction–National Center for Atmospheric Research reanalysis data for 1958–98 and an atmosphericGCM hindcast run forced by observed 1955–91 sea-surface temperatures (SSTs). Downscaling from the reanalysis-derived predictors reproduces the 1958–98 interannual and interdecadal variability of winter precipitation. Downscalingfrom the SST-forced GCM hindcast only reproduces the precipitation probabilities of the recent 1978–91 period, withpoor performance for earlier periods attributed to inadequacies in the forcing SST data. Copyright 2004 John Wiley& Sons, Ltd.

KEY WORDS statistical downscaling; precipitation modelling; climate models; climate variability

INTRODUCTION

Predicting the impacts of low-frequency climate variability and projected climate change on water resourcesis increasingly relevant to streamflow prediction (Burges, 1998). The need for predictions based on physicalmodels, rather than on purely statistical models, has led to the development of coupled atmosphere–oceangeneral circulation models (AOGCMs) and, nested at finer spatial scales, limited-area models (LAMs).Although these numerical climate models (NCMs) perform well at simulating large-scale atmospheric fields,they tend to overestimate the frequency and underestimate the intensity of daily precipitation when comparedwith historical records at local scales (Mearns et al., 1995; Bates et al., 1998). These limitations have led tothe development of statistical techniques to model local-scale precipitation as a function of NCM grid-scaleatmospheric fields (Xu, 1999). Bloschl and Sivapalan (1995) define scaling as ‘transferring information acrossscales’ and, similarly, ‘downscaling’ is defined as the ability to scale between the large-scale spatial fields ofNCMs and local-scale hydrologically relevant variables, such as daily rain gauge precipitation (Burger, 2002).

* Correspondence to: Stephen P. Charles, CSIRO Land and Water, Wembley, Western Australia 6913, Australia.E-mail: [email protected]

Received 15 July 2002Copyright 2004 John Wiley & Sons, Ltd. Accepted 7 February 2003

1374 S. P. CHARLES ET AL.

The intent of this paper is to investigate the ability of the extended nonhomogeneous hidden Markovmodel (extended-NHMM) to reproduce observed interannual and interdecadal precipitation variability whendriven by observed and modelled atmospheric fields. The paper begins with an overview of statisticaldownscaling techniques used to scale between large-scale atmospheric data and local-scale precipitation andissues associated with downscaling from NCM output. The investigations comprise three parts. Firstly, theability of the extended-NHMM to reproduce the observed interannual precipitation variability of the fittingperiod is assessed. Secondly, an out-of-sample validation assesses reproduction of the observed interannualprecipitation variability of a wetter period prior to the fitting period, and also the interdecadal variability acrossthe fitting and validation periods. Thirdly, driving the extended-NHMM with atmospheric predictors from anatmospheric general circulation model (AGCM) ‘hindcast’ forced with observed sea-surface temperatures(SSTs) aims to assess ‘potential predictability’—an indication of the forecasting skill potential of downscaledGCM forecasts. This is of relevance to hydrological models that require daily data from multiple gaugesto simulate the dynamics of hydrological response to precipitation variability, such as the integrated waterquantity and quality model (IQQM; Simons et al., 1996) and the large-scale catchment model (LASCAM;Sivapalan et al., 2002). Positive results from hindcast GCM downscaling would also add confidence todownscaled future climate-change projections.

The paper concludes with a summary of the relevance of statistical downscaling to hydrological research,potential applications of the extended-NHMM, and an outline of future research directions.

STATISTICAL DOWNSCALING TECHNIQUES

Statistical downscaling involves developing quantitative relationships between large-scale atmospheric vari-ables (predictors) and local surface variables (predictands). In its most general form the downscaling model is

Rt D F�XT� for T � t �1�

where Rt represents the local-scale predictand at single or multiple sites at time t; XT is the predictor set (e.g.a collection of current and past values of large-scale atmospheric variables up to time t), and F representsthe technique used to quantify the relationship between the two disparate spatial scales. Most statisticaldownscaling work has focused on daily site (i.e. point-scale) precipitation as the predictand, because it isan important input variable for many natural systems models. Predictor sets can be derived from sea-levelpressure (SLP), geopotential height, absolute or relative humidity, and temperature variables. These variablesare available at the grid resolution of operational and research NCMs, with the horizontal resolution of aGCM typically 300–500 km an LAM typically 50–125 km. Driving a statistical downscaling model withNCM output requires interpolation of the NCM output to the grid resolution of the atmospheric predictor setused in fitting. Statistical downscaling techniques will be summarized here under the broad headings ‘weatherclassification’, ‘regression models’, and ‘weather generators’.

Weather classification schemes

Weather classification methods group days into a finite number of discrete weather types or ‘states’ accordingto their synoptic similarity. This can be represented formally by

Rt D FR�St� �2�

St D FS�XT� for T � t �3�

where St is the weather state at time t. Typically, weather state definition FS is achieved directly by applyingmethods such as cluster analysis to atmospheric fields (e.g. Corte-Real et al., 1999; Huth, 2000; Kidson, 2000)or using subjective circulation classification schemes (e.g. Bardossy and Caspary, 1990; Jones et al., 1993).

Copyright 2004 John Wiley & Sons, Ltd. Hydrol. Process. 18, 1373–1394 (2004)

DOWNSCALING OF DAILY PRECIPITATION 1375

The predictand is related to the weather states by resampling or regression functions FR (e.g. Hay et al.,1991; Corte-Real et al., 1999). These methods have had only limited success in reproducing the persistencecharacteristics of at-site wet and dry spells (e.g. Wilby, 1994). Recent approaches include the ability to generatemulti-site and multi-variate (e.g. precipitation and temperature) series (e.g. Bardossy and van Mierlo, 2000).

An alternative approach is to classify spatial rainfall occurrence patterns using hidden Markov models,then infer the corresponding synoptic weather patterns (Hughes and Guttorp, 1994; Hughes et al., 1999). Ahidden Markov model represents a doubly stochastic process, involving an underlying unobserved (hidden)stochastic process that can only be observed through another stochastic process that produces the sequence ofobserved outcomes (Rabiner and Juang, 1986). The observed process (precipitation occurrence at a networkof sites) is assumed to be conditionally, temporally independent given the hidden process. The hidden process(the weather state) is assumed to evolve according to a first-order Markov chain, with transition probabilitiesconditional on atmospheric predictors. It has been shown that these models can reproduce key characteristicsof at-site precipitation, such as the persistence characteristics of site wet and dry spells (Hughes and Guttorp,1994; Charles et al., 1999a; Hughes et al., 1999). Further details are presented below.

Regression models

Regression models are a conceptually simple means of representing linear or nonlinear relationships betweenR and X:

Rt D FY�XT; �� for T � t �4�

where � is the parameter set and FY is the linear or nonlinear regression function. The methods usedinclude multiple regression (Murphy, 1999), canonical correlation analysis (CCA; von Storch et al., 1993),and artificial neural networks, which are akin to nonlinear regression (Crane and Hewitson, 1998). Von Storch(1999) and Burger (2002) discuss the important issue of underprediction of variance often associated withregression approaches. Burger (2002) uses an approach termed ‘expanded downscaling’ to deal with thisproblem.

Weather generators

Weather generators can be conditioned on large-scale atmospheric predictors or weather states (Katz, 1996;Wilks and Wilby, 1999). This can be represented by

Rt D FW��jXT� for T � t

orRt D FW��jSt� �5�

where � is the parameter set of the weather generator represented by FW. Weather generators oftensimulate secondary variables (e.g. temperatures, solar radiation), conditional on precipitation occurrence. Wilks(1992) notes that parameter modification for future climate scenarios can affect the relationships betweenthe conditional variables. Moreover, weather generators often underestimate the temporal variability andpersistence of precipitation (Katz and Parlange, 1998).

Key issues

Key assumptions, common to all statistical downscaling techniques, apply when downscaling NCM outputfor current and projected climates (Hewitson and Crane, 1996):

ž Predictors relevant to the precipitation process are adequately reproduced in the NCM simulations.ž The relationship between the predictors and precipitation remains valid for periods outside the fitting period

(time invariance). This needs careful assessment for future climate projection.



ž The predictor set sufficiently incorporates the future climate-change ‘signal’. Some approaches, e.g. stepwiseregression, may exclude predictors based on current climate performance that could be important in futurechanged climates.

For current climate conditions, the validity of the first two assumptions can be assessed using observedrecords of sufficient length. Regarding climate-change investigations, Charles et al. (1999b) comparedCommonwealth Scientific & Industrial Research Organization (CSIRO) LAM 2 ð CO2 grid-scale dailyprecipitation occurrence probabilities with those obtained by driving an NHMM fitted to 1 ð CO2 LAMgrid-scale precipitation with 2 ð CO2 LAM atmospheric predictors (for a discussion of point versus grid-boxprecipitation, see Osborn and Hulme (1997)). The NHMM driven with 2 ð CO2 LAM atmospheric predictorsreproduced the 2 ð CO2 LAM grid-scale precipitation occurrence probabilities. As there was consistencybetween the predictor sets of the best performing LAM-fitted and site-fitted NHMMs, the site-fitted NHMMwas driven with the 2 ð CO2 LAM predictors to produce at-site 2 ð CO2 precipitation occurrence projections.Although not validation in the traditional sense, this approach adds confidence in the choice of predictors andthe assumption that the relationships derived during fitting remain legitimate for the changed climate. Busuiocet al. (1999) applied a similar method to a CCA of monthly precipitation data for sites in Romania.

Intercomparison studies

Several recent studies have compared statistical downscaling methods or compared statistical downscalingwith dynamical (i.e. LAM-based) downscaling. Wilby and co-workers (Wilby and Wigley, 1997; Wilby et al.,1998) compared six statistical downscaling approaches (two neural nets, two weather generators, and twovorticity-based regression methods) for six US sites using observed and GCM data. The vorticity-basedregression methods were found to perform better. Performance criteria were root-mean-squared errors ofthe following diagnostics: wet day amount mean, median, standard deviation and 95th percentile; dry–dryand wet–wet day occurrence probabilities; wet day probabilities; wet and dry spell duration mean, standarddeviation, and 90th percentile; and standard deviation of monthly precipitation totals. Although the GCMprojected large changes in precipitation it projected only small changes in the circulation-based predictorsused—within the limits of modelled interannual variability. The various downscaling approaches gavesignificantly different 2 ð CO2 precipitation projections using common sets of GCM-derived predictors.Given this ambiguity, Wilby et al. (1998) suggested the need for additional atmospheric predictors, suchas moisture-based predictors, given that precipitation is a function of atmospheric saturation.

Zorita and von Storch (1999) compared an analogue method (Zorita et al., 1995) with: (i) a linear regressionmethod based on CCA applied to monthly site precipitation totals and SLP fields; (ii) a classification methodbased on classification and regression trees applied to daily precipitation occurrence and SLP fields; and(iii) a neural network, as an example of a nonlinear method, applied to daily precipitation amounts andSLP anomalies for the Iberian Peninsula (southwest Europe). In general, the analogue method performedcomparably, or better, at reproducing daily precipitation amount and frequency characteristics while beingtechnically simpler to implement.

Kidson and Thompson (1998) compared results from an LAM to a screening regression downscalingtechnique with indices of local and regional flow, using data from 1980 to 1994 for a network of 78 sitesacross New Zealand. The regression approach explained the daily variance in precipitation anomalies better.The poor relative performance of the LAM was attributed to its inability to resolve orography, a result ofthe 50 km grid spacing used. It was concluded that the (linear) regression relationships developed could beapplicable when the predictors extend a small amount beyond the range of the observed data used in fitting, butthat it was preferable to use dynamic models for significant climate change when factors such as atmosphericvapour content could influence storm intensity.

Mearns et al. (1999) compared a circulation classification approach (k-means clustering of the principalcomponents of 700 hPa geopotential height fields) with the National Center for Atmospheric Research (NCAR)



RegCM2 LAM nested within the CSIRO Mk 2 GCM of Watterson et al. (1997) for 5 years of 1 ð CO2 and2 ð CO2 runs. The LAM could often reproduce monthly or seasonal precipitation for the 12 sites in theeastern Nebraska study area quite well, due to compensating errors in the overestimation of the frequency(by a factor of 2 to 5) and underestimation of the intensity of precipitation events (by a factor of 2 to 14).The classification-based approach reproduced observed precipitation characteristics for the 12 sites; however,this is expected, as it was calibrated on observed data (1962–77) and then validated with observed data(1978–93). The climate-change projections obtained exemplify the problem of obtaining different results fromdifferent approaches, as the two approaches did not produce mean precipitation changes of the same directionfor 40% of months and locations investigated. The statistical downscaling results indicated predominantlyincreases in mean precipitation, whereas RegCM2 produced both increases and decreases for coherentsubregions. Results presented for January, April, July and October showed 12-site average changes in meandaily precipitation of 0Ð39 mm day�1, 0Ð72 mm day�1, 0Ð29 mm day�1 and 0Ð95 mm day�1 respectively forthe classification–based approach compared with �0Ð04 mm day�1, 0Ð07 mm day�1, 0Ð32 mm day�1 and0Ð38 mm day�1 respectively for the LAM. Although not able to discern the reasons for these differences,Mearns et al. (1999) conclude that it is at least partly due to the reliance of the statistical techniques on the700 hPa geopotential height fields only.

STUDY REGION AND DATA USED

Southwest Australia

For this study we define the southwest Australia (SWA) region as extending from approximately 115° to120° east and 30° to 35° south, bounded by the Indian Ocean to the west and the Southern Ocean to the south.The locations of 30 precipitation sites chosen for NHMM fitting are shown in Figure 1 and site details for sixrepresentative sites are presented in Table I. The six representative sites (sites 1, 4, 7, 9, 26 and 27) give agood geographical spread over SWA, encompassing north, central, and southern coastal and inland locations.

The SWA region has a flat, homogeneous topography with the exception of the Darling Scarp, a 300 mescarpment (arising from the coastal plain along the line of precipitation sites 5, 4, 12, 15, and 11 in Figure 1)producing a precipitation shadow to the east. The region experiences a Mediterranean-type climate, with winterprecipitation nearly double that of any similarly exposed locality in any other continent and intense summerdrought. Up to 80% of annual precipitation falls in the ‘winter’ half-year, from May to October. The majorityof winter precipitation is produced by midlatitude cyclonic frontal systems (Gentilli, 1972; Wright, 1974).A distinguishing feature of the frontal precipitation is the rapid northward spread and increase in intensitythroughout May, and the slower southward retreat and decrease during August to October. Over much ofSWA, winter rainfall has decreased substantially since the mid-20th century. Large areas of SWA experienceda sharp and sudden decrease in winter rainfall around the mid-1970s by up to 15–20%. It was not a gradualdecline, but more of a switching into an alternative rainfall regime. This has had serious implications for

Table I. SWA precipitation site details (six sites used to represent the region)

No. Bureauno.

Site name Latitude(S)

Longitude(E)

Elevation(m)

Mean winterprecipitation

(mm)

Winterprecipitation

(% of annual)

Wintermean wet–dayfrequency (%)

1 008039 Dalwallinu P.O. 30° 170 116° 390 335 261 73 314 009021 Belmont, Perth Airport MO 31° 560 115° 580 20 686 86 477 009131 Jurien 30° 180 115° 020 2 466 83 439 009518 Augusta, Cape Leeuwin 34° 220 115° 080 22 815 82 70

26 010612 Narembeen P.O. 32° 040 118° 230 276 232 70 2927 010622 Ongerup P.O. 33° 580 118° 290 286 261 68 38



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Figure 1. SWA study area showing the location of precipitation sites. Six representative sites are identified by heavier crossed dots. Plussigns denote grid points for atmospheric predictor data

water resources reliability in the region, as the 15–20% decrease in rainfall has translated to a 40% decreasein streamflow for SWA water supply catchments (IOCI, 2001).

Atmospheric data

National Centers for Environmental Prediction (NCEP)–NCAR reanalysis 1958–98. The NCEP–NCARreanalysis dataset (Kalnay et al., 1996) will be used to evaluate whether the extended-NHMM previouslyfitted to 1978 to 1992 data (Charles et al., 1999a) can reproduce the interannual and interdecadal variabilityof winter precipitation for the 1958 to 1998 period. The NCEP–NCAR reanalysis datatset is produced bystate-of-the-art assimilation of all available previously observed weather data into a global climate-forecastingmodel that produces interpolated grid output of many weather variables. A high level of quality control isapplied to the observed data. Most reanalysis output variables are generated for a 2Ð5° ð 2Ð5° latitude–longitudegrid (SLP, temperature and specific humidity at several levels, etc.). As the atmospheric predictors used byCharles et al. (1999a) were on a 2Ð5° ð 3Ð75° latitude–longitude grid, the reanalysis-derived predictors areinterpolated to this fitting grid resolution. Other investigations (not shown) have concluded that there are nospurious jumps or trends in the reanalysis-derived predictor series used.

GCM 1955–91. Atmospheric predictors from a GCM forced by observed monthly SSTs for 1955 to1991 were extracted. The GCM (CSIRO9 Mark 2) is an atmospheric GCM with nine vertical levels anda horizontal resolution of T63, approximately 1Ð875° ð 1Ð875°. The physical parameterizations used by thismodel include a modified Arakawa cumulus convection scheme, the Deardorff soil moisture scheme, theGFDL diurnally varying longwave and shortwave radiation scheme, a Monin–Obukhov similarity-theory-based stability-dependent boundary layer, a diagnostic cloud scheme, a gravity wave drag scheme and it is



fully flux corrected (McGregor et al., 1993; Watterson et al., 1997). The SST forcing was provided by theUK Meteorological Office’s GISST1.1 (global ice SST) monthly data set (Parker et al., 1995) interpolated toa daily time scale. It is acknowledged that high southern latitude SSTs and sea ice extents may not be reliableprior to the availability of satellite observations (Hurrell and Trenberth, 1999). The required atmosphericpredictors were extracted and interpolated to the grid used for NHMM fitting, as the T63 grid has a finerresolution than the data used for fitting.

EXTENDED NONHOMOGENEOUS HIDDEN MARKOV MODEL

The extended-NHMM uses the NHMM of Hughes et al. (1999) to downscale atmospheric predictors to multi-site daily precipitation occurrence and then uses conditional multiple linear regression to simulate multi-sitedaily precipitation amounts (Charles et al., 1999a). A summary of model formulation, fitting and selectionis presented here; however, for full details, the reader is referred to Hughes et al. (1999) and Charles et al.(1999a).

Precipitation occurrence

The NHMM models multi-site patterns of daily precipitation occurrence as a finite number of ‘hidden’ (i.e.unobserved) weather states. The temporal evolution of these daily states is modelled as a first-order Markovprocess with state-to-state transition probabilities conditioned on a small number of synoptic-scale atmosphericpredictors, such as SLP. By determining distinct multi-site daily precipitation occurrence patterns, rather thanatmospheric circulation patterns, the NHMM captures much of the spatial and temporal variability of dailymulti-site precipitation occurrence records (Hughes et al., 1999; Charles et al., 1999a).

The simplest formulation of the NHMM simulates precipitation occurrence at each site independently.The common weather state, however, induces significant spatial structure (e.g. see Hughes et al. (1999)). Amore complex ‘spatial’ NHMM may be used to model additional within-state dependence (such dependencemay result from important sub-grid-scale features such as topography). In this case, inter-site precipitationoccurrence is determined as a function of distance and direction between sites, as well as on a weather statebasis (Hughes et al., 1999).

Precipitation amounts

Charles et al. (1999a), furthermore, extended the NHMM of Hughes et al. (1999) to simulate multi-sitedaily precipitation amounts. For each weather state of a selected NHMM, precipitation amounts at each site aremodelled by regressions of transformed amounts on precipitation occurrence at key neighbouring sites. Thisapproach captures both the first- and second-order moments (i.e. means and variability) of the precipitationamounts data (Charles et al., 1999a).

Model fitting

Fitting the extended-NHMM follows the steps outlined in the left-hand panels of Figure 2. Model selectioninvolves the sequential fitting of a suite of NHMMs with an increasing number of weather states andatmospheric predictors. The model fit is evaluated in terms of the physical realism and distinctness of theidentified weather states, as well as the Bayes information criterion, as discussed in Hughes et al. (1999) andCharles et al. (1999a).

Once the final (occurrence) NHMM is selected, the most probable weather state sequence is extracted usingthe Viterbi algorithm (Forney, 1978) to assign each day to its most probable weather state. Then, the amountsmodel is fitted to give the final extended-NHMM. This involves assessing the amounts-model performance fora range of neighbourhood radii (i.e. assessing the spatial extent of intersite relationships within the network).Further details can be found in Charles et al. (1999a).



MODEL FITTING

OCCURRENCE(NHMM)

AMOUNTS(REGRESSION)

Observedatmospheric andprecipitation data

Fittingdownscaling model (A)

Validation ofselected model (A)

(weather states & reproduction of precipitation occurrence

statistics)

CONDITIONAL SIMULATION

OCCURRENCE(NHMM)

AMOUNTS(REGRESSION)

Model (A) weather state sequence and

precipitation data

Fittingregression model (B)

Validation ofmodel (B)

(reproduction of precipitation amounts statistics)

Conditional simulationsof weather state

sequences and multi-site precipitationoccurrence [C]

Observed or NCMatmospheric

predictors

Selecteddownscaling model (A)

Selecteddownscaling model (A)

Weather state sequencesand multi-site

precipitation occurrence simulations [C]

Conditional simulationsof multi-site

precipitation amount

Fittedregression model (B)

Figure 2. Flowchart of the approach used to fit the extended-NHMM and produce conditional precipitation simulations

The results of fitting the extended-NHMM to 15 years (1978 to 1992) of observed SWA winter data forthe 30 sites were presented in Charles et al. (1999a). The selected model had six weather states and threeatmospheric predictors. The three predictors were the mean and the north–south gradient of SLP over theregion and the dew-point temperature depression, i.e. air temperature minus dew-point temperature, at the850 hPa level �DT850

d �. The six states were found to have a high degree of physical realism, successfully scalingbetween synoptic-scale atmospheric circulation and daily, multi-site precipitation occurrence patterns (seeCharles et al. (1999a: figure 2, table 2)). The model reproduced the observed daily precipitation probabilities,spatial correlations, and distributions of wet- and dry-spell lengths and precipitation amounts (Charles et al.,1999a). Split-sample validation of model performance is also described in detail in Charles (2002).

INTERANNUAL DIAGNOSTICS

The interannual performance of the extended-NHMM presented in Charles et al. (1999a) has not beenreported previously. Here, we assess this aspect of model performance. Figure 3 presents, for 1000 conditionalsimulations, the range in simulated winter wet-day frequencies for 1978 to 1992 for the six representative sites.A consistent pattern emerges—of good overall reproduction but poor performance in certain years (a resultis judged ‘poor’ when the observed wet-day frequency falls outside the interquartile range of the simulations,i.e. outside the ‘box’ of the box-plots). For example, a poor result was obtained for the 1982 winter for fiveof the six sites. Overall, wet-day frequency in 1982 was underestimated at 22 of the 30 sites, with a tendencyfor the sites in the northeast of the study area to have the largest discrepancy. The low simulated wet-dayfrequencies are consistent with the El Nino event (Trenberth, 1997) that occurred in 1982, as El Nino isassociated with below-average precipitation in SWA (Tapp, 1997) due to fewer frontal systems (Jones andSimmonds, 1993, 1994). However, the sites in the north and east of the study region often receive enhanced



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Figure 3. Observed versus downscaled 1978–92 winter wet-day frequencies for six representative sites. Solid line is observed and box-plotsdepict the range of 1000 simulation trials (the edges of the box represent the 25th percentile and the 75th percentile of the simulations). The

horizontal dashed line is the long-term observed mean

precipitation when fronts interact with cloud bands that sweep across Australia from the northwest (Tappand Barrell, 1984; Wright, 1997). Thus, it is postulated that the poor performance in 1982 could be becausethe atmospheric predictors of the selected model do not adequately account for this interaction. Research todetermine the extent and magnitude of such interactions on SWA winter rainfall is ongoing.

Figure 4 presents, for the 1000 conditional simulations used to produce Figure 3, the correspondingsimulated winter precipitation amount totals for 1978 to 1992. The postulated effect of frontal–cloud-bandinteractions is also evident, e.g. the 1982 winter precipitation totals are poorly simulated for the majorityof sites. It is also evident that the amounts model can perform poorly in years of extreme precipitation. Forexample, the 1983 winter for site 9 (Augusta, Cape Leeuwin) is well reproduced with regard to number of wetdays (Figure 3) but severely underestimated for precipitation amount (Figure 4). Improving the reproductionof periods of extreme precipitation is currently under investigation.

DOWNSCALING OF REANALYSIS ATMOSPHERIC FIELDS

There has been a decline in winter rainfall over SWA since about the middle of the 20th century (IOCI,1999; Tapp and Cramb, 2000). Since the mid 1970s, this decline has had important consequences for water



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Figure 4. Observed versus downscaled 1978–92 winter precipitation amounts for six representative sites. Solid line is observed and box-plotsdepict the range of 1000 simulation trials (the edges of the box represent the 25th percentile and the 75th percentile of the simulations). The

horizontal dashed line is the long-term observed mean

resources management in SWA (IOCI, 1999). Thus, it is important to assess whether the extended-NHMMcan reproduce the observed interdecadal winter precipitation variability. A positive result would give someconfidence that the selected model is able to account for the atmospheric conditions and resultant precipitationduring the earlier wetter period. Such robustness would add confidence when using it for seasonal predictionor even for climate-change projection.

An ensemble of 1000 downscaled simulations was generated from the 1958 to 1998 reanalysis-derivedatmospheric predictors. Figure 5 shows that the pre-fitting 1958 to 1977 period is well reproduced for sites1, 4, 9, and 26 (although missing observed data at site 26 makes comparison harder). For site 7, the observedrecords only started in 1970, and so the plot is truncated, but the predictions for 1970 to 1977 are satisfactory.For site 27, there is a consistent overestimation bias for the 1958 to 1977 period for the majority of winters.This problem is only seen in one other of the 30 sites (not shown). Post-fitting (1993 to 1998) results seemreasonable for sites 1, 4, 7, 26, and 27, with site 9 (Augusta, Cape Leeuwin, in the extreme southwest of thestudy region) exhibiting a consistent overestimation of wet days.

Figure 6 presents cumulative distribution plots of dry- and wet-spell lengths for the 1958 to 1977 validationperiod. The upper panels compare the observed dry-spell length distributions with the mean downscaleddistributions and the lower panels the wet-spell length distributions for the six representative sites. The



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Figure 5. Observed versus reanalysis-downscaled 1958–98 winter wet-day frequencies for six representative sites. Solid line is observedand box-plots depict the range of 1000 simulation trials (the edges of the box represent the 25th percentile and the 75th percentile of thesimulations). The horizontal dashed line is the long-term observed mean. The two vertical dashed lines delineate the start (1978) and finish

(1992) of the fitting period

downscaled distributions provide good approximations to the observed distributions, particularly for the short-duration spells that encompass up to approximately 99% of events. A slight bias in underestimating wet-spelllengths is evident, particularly for site 9. A tendency to underestimate the lengths of long spells can beattributed to uncertainty in their probability estimates due to the small sample sizes involved. This tendencyis exaggerated by the use of a log probability scale.

Regarding the interannual reproduction of 1958 to 1998 winter precipitation amounts, similar interpretationsto those made for wet-day totals apply, although an increased variability in simulated amounts is evident(Figure 7). Figure 8 presents, for the 1958 to 1977 validation period, the observed versus downscaled dailyprecipitation amount quantiles. There is good reproduction of the daily precipitation distributions at all sixsites. This is a particularly positive result, as it indicates that the precipitation amounts model fitted to the1978 to 1992 data adequately represents the distributions of the wetter 1958 to 1977 period. Site 26 is apartial exception, with underestimation of the upper tail evident, as some daily amounts in the 1958 to 1977period are higher that those in the 1978 to 1992 fitting period.



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Figure 6. Observed versus reanalysis-downscaled (1958–77) winter-spell lengths for six representative sites. Solid line is observed anddashed line is downscaled

Overall, given that the period 1958 to 1977 was wet relative to 1978 to 1992, these results suggest thatthe NHMM is robust against the effects of 1958 to 1998 climate shifts and trends in SWA precipitation. Inongoing work we are using the extended-NHMM as a ‘forensic’ tool to determine how atmospheric predictorproperties and weather state time series have changed between the 1958 to 1977 wet and 1978 to 1998dry climate regimes. This will aid our understanding of how changes in atmospheric circulation patterns areresponsible for regional interdecadal precipitation variability.

DOWNSCALING A GENERAL CIRCULATION MODEL HINDCAST

An ensemble of 1000 downscaled simulations was generated using the predictors from the hindcast GCMsimulation that had observed SST boundary forcing for 1955 to 1991. Initially, the atmospheric predictorsfrom the GCM are compared with those of the observed data for the 1978 to 1991 period (Figure 9). Poorperformance is evident when assessing the ability of the GCM to reproduce the interannual 1978 to 1991winter predictor series. As a gross measure of comparison, the corresponding winter’s positive and negativeanomalies of the median are tabulated (Table II). For SLP, only six of the 14 years show the same simulated



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anomaly (1979, 1982, 1983, 1986, 1988 and 1989 winters) and two show opposite anomalies (1978 and 1985winters). For north–south SLP gradient, a different set of six winters shows the same anomaly (1978, 1979,1982, 1983, 1990 and 1991) and four show opposite anomalies (1980, 1981, 1985 and 1987). DT850

d providesa more consistent picture, with 11 years giving the same anomaly (1978–1983, 1985, 1986, 1988 and 1989)and two giving opposite anomalies (1984 and 1990). In addition to these differences in the medians, predictorvariance differs between the GCM and observed data (Figure 9).

As downscaled reproduction of the 1955 to 1991 winter wet-day frequencies is a direct function of theGCM reproduction of the atmospheric predictors, poor downscaled precipitation simulations are inevitablewhenever there is a mismatch between the GCM simulated and historical predictors. This is evident whenexamining the hindcast downscaled simulations of wet-day frequencies for the full 1955 to 1991 period(Figure 10). Although there are some reasonable performances for the 1978 to 1991 NHMM-fitting period,there are consistent errors, such as the underestimation of 1984 wet-day frequencies. The GCM produceda positive SLP anomaly for 1984, and the simulation of low numbers of wet days are consistent with this.


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No such positive anomaly occurred in the observed 1984 data (Figure 9). For 1985, an overestimation ofwet-day frequencies is a result of the GCM’s negative SLP anomaly. In contrast, the observed 1985 datashow a positive SLP anomaly. Similar examples are evident for the north–south SLP data. The degradationin performance prior to 1978 occurs at all sites. The consistent underestimation of 1955 to 1977 winter wet-day frequencies is evident (with the partial exception of Ongerup, site 27). Given the poor reproduction ofwet-day frequencies, the simulation of downscaled amounts is deemed unnecessary.

Figure 11a presents NHMM reproduction of the mean 1978–1991 site precipitation probabilities whendriven by the atmospheric predictors used in fitting. In comparison, Figure 11b–d presents the results of driv-ing the NHMM with the GCM predictors for the three periods 1978–91, 1968–77 and 1955–67 respectively.The GCM-downscaled reproduction of the observed precipitation probabilities is only reasonable for the latestof these three periods (1978–91, Figure 11b) and then the performance degrades progressively the earlier thehindcast is assessed. It may appear contradictory to have reasonable reproduction of the 1978–91 precipita-tion probabilities (Figure 11b) and poor reproduction of the year-to-year variability (Figure 10). However, thissimply reflects the GCM’s ability to reproduce the gross statistics of the predictors for the 1978–91 periodas a whole.



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The inability of the GCM to reproduce the observed predictors during the earlier periods (1955 to 1977)is postulated to be due to limitations in the SST data used to force the simulation. There are limitations inthe GISST dataset, as the quality of SST data for large regions of the Southern Hemisphere is consideredparticularly poor prior to satellite data becoming available from 1980 onwards (Hurrell and Trenberth, 1999).As the GCM used here is forced by an earlier version of the GISST dataset (GISST 1Ð1; Parker et al., 1995),it is perhaps not surprising that performance of the GCM is poor at the scale of investigation.

To investigate this hypothesis, observed monthly (winter) SLP data for the grids used in NHMM fitting wereextracted from the quality-controlled global mean SLP (GMSLP) monthly database (GMSLP2Ð1f; Basnett andParker, 1997). A plot of GMSLP versus GCM monthly winter SLP is shown in Figure 12. The divergence forthe earlier period is striking, with the GCM giving positive SLP anomalies, particularly prior to 1970, consistentwith the underestimation of downscaled wet-day frequencies seen in Figure 10. Correlations between the twoseries for the sub-periods 1955 to 1967, 1968 to 1977, and 1978 to 1991 are 0Ð03, 0Ð18 and 0Ð13 respectively.The low 0Ð03 correlation of the 1955 to 1967 period supports the divergence seen in Figure 12.

This supports the hypothesis that poor GCM representation of the atmospheric predictors for this region, atthe scale required, leads to poor downscaling reproduction of precipitation occurrence. The expectation that a



Table II. Winter 1978–91 anomalies for observed and GCM atmospheric predictorsa

Year SLP N–S SLP DT850d

Obs. GCM Obs. GCM Obs. GCM

1978 � C � � � �1979 C C � � � �1980 0 � C � � �1981 � 0 C � � �1982 C C � � � �1983 C C 0 0 � �1984 0 C 0 � � C1985 C � � C � �1986 � � 0 C � �1987 C 0 � C 0 �1988 � � C 0 � �1989 � � 0 � � �1990 0 C � � � C1991 � 0 C C � �

a C: positive anomaly; �: negative anomaly; 0: no anomaly.

GCM will be able to reproduce specific predictors over a small part of the global domain (a few grid squaresover SWA) is quite a harsh test, and it is noted that only one GCM realization has been used. However,an ensemble of four runs from this GCM experiment was available (produced using slightly different initialconditions) and the remaining three runs produce SLP series with even less correspondence to the observeddata (not shown).

DISCUSSION

Here, we have assessed the ability of the extended-NHMM, as fitted to 1978–92 data in Charles et al. (1999a),to account for the predictor–predictand relationships of the 1958 to 1998 period. Such an assessment is crucialif the model is to be used, with any confidence, in forecasting applications such as interseasonal precipitationprediction or climate-change projection. Wilby (1998) states that statistical downscaling models conditionedon stationary atmospheric circulation pattern series cannot reproduce observed interannual and interdecadalprecipitation variability. However, statistical downscaling models do offer the prospect of capturing suchlow-frequency variability if the atmospheric predictors capture the low-frequency atmospheric periodicitiesand oscillations responsible for producing the precipitation variability.

The results presented (Figures 5 and 7) show that the extended-NHMM can reproduce the 1958 to 1977and 1993 to 1998 (i.e. 20 years prior to and 6 years after the fitting period) interannual and interdecadalvariability in winter precipitation occurrence and amounts reasonably well, although the performance variesbetween sites. As the 1958 to 1977 period was relatively wet compared with the fitting period, this showsthat the extended-NHMM is able to account for the predictor–predictand relationships across the range ofnatural climate variability experienced during the 1958 to 1998 period.

Given that the extended-NHMM successfully downscales the reanalysis data for the present-day climate,a GCM run operationally could drive it to provide seasonal forecasts of precipitation with confidence limitsobtained from multiple (e.g. 1000) downscaled simulations. This assumes the adequacy of the forecastatmospheric predictors. The hindcast experiment presented herein was undertaken to determine the potentialpredictability of the SWA region. The SST-forced AGCM simulation represents the ‘upper bound’ ofpredictability that could be expected from a coupled AOGCM used for forecasting. The poor performance of



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Figure 10. Observed versus GCM-downscaled 1955–91 winter wet-day frequencies for six representative sites. Solid line is observed andbox-plots depict the range of 1000 simulation trials (the edges of the box represent the 25th percentile and the 75th percentile of thesimulations). The horizontal dashed line is the long-term observed mean. The vertical dashed line is the start of the fitting period (1978)

the hindcast downscaling prior to 1978 (Figure 11) is hypothesized to be due to poor-quality SST forcing priorto the 1980s and not due to inadequacies in the GCM. Shah et al. (2000) also suggest that poor performanceof an atmospheric GCM hindcast in the Southern Hemisphere was due to errors in SSTs. However, even forthe 1978 to 1991 period, the reproduction of interannual variability is poor (Figure 10).

Hunt (1997) emphasizes the need for improved SST prediction ability, as well as improved atmosphericGCMs, if seasonal forecasts using forced GCMs are to become a reality; Saravanan et al. (2000) conclude thatmidlatitude atmospheric predictability using dynamical models, for seasonal to longer time scales, is limitedby the predominantly stochastic nature of atmospheric variability in the midlatitudes; and Grotzner et al.(1999) state that the signal-to-noise ratio of the midlatitude atmosphere is generally too low to gain relevantpredictive skill. Druyan et al. (2000) evaluated GCM fields, from five SST-forced GCM 1969–91 hindcasts,for regions including the midlatitude US Corn Belt. Comparing the hindcasts with NCEP–NCAR reanalysisdata, their GCM simulations did not consistently provide useful predictions of seasonal rainfall anomalies.

Thus, it remains to be seen whether GCM forecasts can provide suitable predictor sets for downscaling.GCM development is a vigorous field, however, and improved performance can be expected (Goddard et al.,



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2001). One alternative requiring further investigation is whether downscaling from an LAM nested in a GCMimproves forecast performance (Fennessy and Shukla, 2000). Miller et al. (1999) reported good qualitativeagreement between observed and simulated Northern Hemisphere winter (December–February) precipitationfor a nested-model dynamical downscaling study applied to the western USA. In their study, an LAM wasnested in the UCLA-GCM forced by SST forecast data produced by the NOAA Climate Prediction Center.

CONCLUSIONS AND FUTURE RESEARCH

Statistical downscaling models are potentially useful research tools for investigating the linkages betweenlarge-scale climatic processes and local-scale precipitation of relevance to hydrological processes. A wellimplemented and evaluated statistical downscaling model can provide multi-site daily precipitation sequencesreproducing observed statistics and interannual to interdecadal variability. This overcomes the ‘scale problem’of the coarse horizontal resolution of NCMs, thus providing precipitation data at the scale suitable for use inhydrological, agricultural, and ecosystem impacts models.



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The extended-NHMM performed reasonably well at reproducing interannual winter precipitation variabilitywhen downscaling from 1958–98 reanalysis-derived predictors. However, the performance could be improved,and one potential method could be to include a predictor that explicitly accounts for slowly evolving processesin the atmosphere, such as El Nino.

This investigation highlights the potential role that downscaling plays in the validation of NCM atmosphericfields (as suggested by von Storch (1995)). The extended-NHMM was fitted and validated for observedconditions and performed reasonably well in downscaling current-day (1978–91) hindcast GCM simulations,but it was not able to reproduce the precipitation occurrence statistics of the earlier period (1955–77). Thiswas determined to be a result of inadequacies in the GCM simulation of the SLP field over SWA for thisperiod, hypothesized to be due to deficiencies in the SST fields used to force the GCM.

There are ongoing challenges for the future development, assessment, and application of the extended-NHMM. These include:

ž Assessing the performance of coupling season-ahead NCM forecasts with the extended-NHMM. The aimwould be to produce a seasonal forecast tool useful for hydrological and agricultural prediction (e.g.probabilistic water supply or crop yield projections a season ahead). Our ongoing research is investigatingthe use of a global coupled atmosphere–ocean model (based on the CSIRO9 Mk 2 atmospheric GCM andthe Australian Community Ocean Model) to generate forecasts of the atmospheric predictors required by theNHMM. The coupled model is ‘spun-up’ using observed SST and surface wind stress data and then run inforecast mode for up to 12 months ahead. The aim is to produce a probabilistic forecast (i.e. with confidencelimits) of SWA winter-season precipitation with a lead time of up to 6 months. Although a 6 month lead timewould be more useful, particularly for water supply management, pragmatically, a forecast 1 to 3 monthsbefore the season starts appears to have more potential owing to the decrease in GCM skill with longer



lead times. Initial results using this approach to ‘forecast’ and downscale for the 1997 to 2002 winters havebeen encouraging, and this work will be published elsewhere.

ž Comparing palaeoclimatological records with results obtained from downscaling long-term (e.g. 1000 year)historically forced GCM runs. Assuming that a palaeoclimate record of sufficient quality and resolution wasavailable for a region of interest, this would provide a method of validating the climate variability seen insuch long GCM runs. Then, downscaling from this GCM run would provide precipitation series at scalessuitable for hydrologic modelling that incorporate high- and low-frequency climate variability.

ž Assessment and continued development of a version of the extended-NHMM that models other dailyvariables, such as temperatures, as well as precipitation.

ACKNOWLEDGEMENTS

Thanks to Eddy Campbell, CSIRO Mathematical and Information Sciences, for advice regarding some of theanalyses used herein. The NCEP–NCAR reanalysis data were obtained from http://www.cdc.noaa.gov/, withhelp from Wesley Ebisuzaki. Advice on reanalysis data extraction was gratefully received from Jack Katzfeyand Mark Collier, CSIRO Atmospheric Research. GMSLP data were provided by the UK MeteorologicalOffice. This research is part funded by the Australian Government’s National Greenhouse Research Program.

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Bloschl G, Sivapalan M. 1995. Scale issues in hydrological modelling: a review. Hydrological Processes 9: 251–290.Burger G. 2002. Selected precipitation scenarios across Europe. Journal of Hydrology 262: 99–110.Burges SJ. 1998. Streamflow prediction: capabilities, opportunities, and challenges. In Hydrologic Sciences: Taking Stock and Looking Ahead .

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