J. Beringer Æ S. McIlwaine Æ A.H. Lynch

F.S. Chapin III Æ G.B. Bonan

The use of a reduced form model to assess the sensitivityof a land surface model to biotic surface parameters

Received: 1 October 2001 /Accepted: 30 January 2002 / Published online: 28 May 2002� Springer-Verlag 2002

Abstract Land surface models (LSM) are designed toprovide turbulent and radiative fluxes from the surfaceto the atmosphere that are in turn important in drivingatmospheric models. The fluxes in land surface modelsare controlled by the surface properties and hence thecorrect parameterization of these properties and theprocesses that define them is vital in obtaining realisticfluxes. We investigate the sensitivity of turbulent fluxespredicted by the NCAR LSM to biotic surface param-eters (roughness length, displacement height, leaf areaindex, rooting fraction with depth, albedo and minimumstomatal resistance). This is achieved using a multivari-ate reduced-form model that expresses the results ofmultiple realizations of the physical model as integrativeresponse metrics such as summer ground, sensible andlatent heat fluxes; average soil summer water content;and average soil temperature of the upper layer in eachseason. The sensitivity analysis shows that most re-sponse metrics were most sensitive to roughness lengthand displacement height. In summertime, leaf area indexwas important in determining summer ground heat flux,ground temperature and the timing of snow-free ground.This timing was also sensitive to albedo. Rooting frac-tion with depth was only important in determiningsummer soil water content. In general the NCAR LSMwas more sensitive to a range of climate driven pertur-

bations examined in a companion paper than to therange of biotic surface parameters chosen here.

1 Introduction

Models attempting to simulate processes at the landsurface are often integral components of larger regionalor global scale models and are vital in providing realisticfluxes of energy and water to the atmosphere. It is widelyagreed that these surface fluxes strongly influence theclimate and its variability (Chahine 1992) and are im-portant on larger scales. At these larger scales, the pa-rameterization of the surface in land surface models hasshown sensitivity to larger scale atmospheric circula-tions, for example, changes in land surface albedo affectthe thermally induced overturning circulations that flowbetween oceans and land (Lofgren 1995) and changes inland cover through deforestation resulted in changes influxes sufficient to influence tropical convective activity(Polcher 1995).

In land surface models, input drivers such as short-wave radiation, longwave radiation, precipitation, windspeed, air temperature and humidity are used to simulateoutput fluxes of heat and moisture as well as momen-tum, runoff and infiltration and the evolution of anumber of state variables (soil temperature and mois-ture) (Bastidas et al. 1999). The relationships betweenmodel driver and model response are determined byparameters that are conceptual representations ofphysical properties of the land surface (i.e. leaf area in-dex, roughness length, displacement height, soil mois-ture and texture, albedo, stomatal resistance and rootfraction) (Gupta et al. 1999). Hence the output fluxesdepend upon the magnitude and sensitivity of these landsurface properties in the model.

The validity of model predictions is quite dependenton representativeness of parameter values although ithas been shown that there is often no unique parameter

Climate Dynamics (2002) 19: 455–466DOI 10.1007/s00382-002-0237-9

J. Beringer (&)School of Geography and Environmental Science,Monash University, Clayton, 3800, AustraliaE-mail: Jason.beringer@arts.monash.edu.au

S. McIlwaine Æ A.H. LynchPAOS/CIRES, CB216, University of Colorado,Boulder, CO 80309-0216, USA

F.S. Chapin IIIInstitute of Arctic Biology, University of Alaska Fairbanks,Alaska, AK 99775-7000, USA

G.B. BonanNational Center for Atmospheric Research,Po Box 3000, Boulder, CO 80307, USA

set which will give the correct (validated by observa-tions) response from a land surface model (Verhoff et al.1999). The magnitude of land surface properties such asalbedo, vegetation cover and leaf area index can some-times be measured either at local or regional scales.However, other parameters are less easily measured atlarger scales, for example, hydraulic conductivity,stomatal resistance, and aerodynamic resistance (Guptaet al. 1999). In addition, measured parameters may notmatch those same parameters as defined in the model.Errors in the specification of these land surface param-eters can lead to unrealistic outputs from the model.

In attempting to make land surface simulations morerealistic, a problem arises in attempting to accuratelyrepresent surface/atmosphere exchanges because of themany complex interactions involved (Collins and Avissar1994). Land surface models have undergone a trend ofincreasing complexity in order to simulate physicalmechanisms and as a result the number of parametersrequired in these models has been increasing. For exam-ple large numbers of often poorly defined input variablesare required for the BATS 1e model (27 parameters)(Dickinson et al. 1993) and SIB2 (52 parameters) (Sellerset al. 1996). Hence there is a possibility of over parame-terization with more complex models (Franks et al. 1997)and a thorough sensitivity analysis may allow a reductionin the number of input parameters required.

Hence it is vital to understand which of the landsurface parameters induce the greatest sensitivity inmodel response and then an effort must be made toadequately parametrize these in land surface models. Ifmodel response is fairly insensitive to a given parameterthen this parameter may be estimated. However, if theresponse is very sensitive to small variations in param-eter specification then a better specification for the pa-rameter may be required and can give direction forfuture field research. In addition, a sensitive parametermay need to be calibrated to the model for optimal re-sults and that there may be multiple parameter states fora correctly calibrated model. Further, the relative sen-sitivity of fluxes to land surface parameters has abroader value for suggesting the relative importance ofthe physical processes represented in the model (Bastidaset al. 1999). Thus, further attention needs to be paid tothe accurate characterization of land surface propertiesand the sensitivity of land surface models to theseproperties (Chase et al. 1996).

A number of different studies and methods have beenused to assess the sensitivity of land surface models tosurface properties. The simplest approach is to vary asingle input parameter over a given parameter space(Wilson et al. 1987a, b; Jacquemin and Noilhan 1990;Pitman 1994; Xue et al. 1996). To obtain the sensitivityof model response for a given range of multiple inputparameters, several different techniques exist. The mostsimple of these techniques is the factorial approach thatuses high and low values of a number of input param-eters and model experiments are conducted for eachcombination (Bonan et al. 1990; Henderson-Sellers

1992, 1993; Franks et al. 1997; Hallgren and Pitman2000). This can be computationally prohibitive (i.e. 10parameter test requires 210 = 1024 experiments) and thesensitivity is not straightforward to analyze (Collins andAvissar 1994). The Monte Carlo method is also a com-monly used technique and is based on random samplingof the entire input parameter space but is very compu-tationally expensive. The Fourier Amplitude SensitivityTest (FAST) is another technique that uses continuousprobability distributions of model input parameters asdata, and determines the relative contribution of eachparameter to the variances in model outputs (Collinsand Avissar 1994). The FAST method is relatively effi-cient, with the number of sampling points equivalent tothe number of values chosen for each parameter. Lastly,Bastidas et al. (1999) described a multicriteria approachto evaluating parameter sensitivity by sorting possibleparameter sets via a ranking technique and by applyingbootstrapping and sequential sampling to ensure statis-tical robustness of the results. However this only allowsa relative sensitivity to be gained.

An alternative paradigm for model sensitivity analy-sis involves using a reduced form statistical model andthis technique (described in Sect. 3) has been applied inthis work to an implementation of the National Centerfor Atmospheric Research (NCAR) Land SurfaceModel (LSM) (Bonan 1996a) in the Alaskan Arctic. Thisstatistical model procedure provides a means of ad-dressing the interdependencies of the physical modelsensitivities over a likely range of values of various landsurface parameters that could be related to naturalecosystem variability or ecosystem changes expected totake place forced by anthropogenic climate changes. Inaddition, this approach allows a systematic evaluation ofimportant or unexpected model behavior and modelstability (Iman and Helton 1988).

The reduced form approach has been used to linkscience and policy models, to provide an integrated as-sessment of acid deposition effects and control strategies(Sinha et al. 1998). Chapman et al. (1994) used thistechnique to develop a parameter sensitivity evaluationstrategy for a dynamic-thermodynamic sea-ice model. Ina similar study, Persson and Hakanson (1996) developeda reduced form model based on rotated empirical or-thogonal functions to determine what characteristicswere most important for predicting the turnover of deepwater in Baltic coastal waters. In a new application, thereduced form statistical model has been applied in acompanion paper examining the sensitivity of theNCAR LSM to climatic driving variables expected tovary with anthropogenic climate change (Lynch et al.2001 hereafter referred to as L2001). In L2001, the fol-lowing input parameters were perturbed over a givenrange (air temperature (–5 to +10 K), precipitation (–25to +50%), relative humidity (–20 to +20%), windspeed (–50 to +50%), incoming shortwave radiation(–20 to +20%) and down welling longwave radiation(–20 to +20%)). The reduced form model showed thatthe land surface responses were most sensitive to

456 Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model

perturbations in atmospheric temperature and down-welling longwave radiation, although incoming short-wave radiation also played an important role.Realizations of NCAR LSM that were characterized bya warm and dry perturbation produced a larger relativeresponse than warm, moist realizations. The interactionsbetween surface fluxes and moisture were the mostnonlinear and showed the greatest propensity for strongfeedback processes (L2001).

In this application to the NCAR LSM, six land sur-face parameters expected to have an impact on theprocesses of interest were chosen: leaf area index (LAI),roughness length (Zo), displacement height (d), albedo(a), root fraction with depth (RF), and minimum stom-atal resistance (rs). A series of experiments were per-formed using the NCAR LSM in which these landsurface variables were perturbed simultaneously, and theresults used to create a multivariate reduced form modelwhich represents the statistical response of the physicalmodel to land surface parameter perturbations.

2 Land surface model description and simulations

The NCAR LSM (hereafter referred to as LSM), is a one-dimen-sional model of energy, momentum, water, and CO2 exchangebetween the atmosphere and land, and is described in detail byBonan (1996a). LSM is forced by incident solar and longwave ra-diation, convective and large-scale precipitation, temperature,wind, specific humidity, and pressure provided by an atmosphericmodel or specified from observations. LSM calculates surfacealbedos, upward longwave radiation, sensible heat flux, latent heatflux, and momentum flux, for return to a driving atmosphericmodel as well as simulating soil and vegetation temperatures,moisture content and phase. LSM accounts for ecological differ-ences among vegetation types, allowing multiple surface categories,including lakes and wetlands, within a grid cell, and for hydraulicand thermal differences among soil types. Vegetation effects areincluded by defining plant types that differ in leaf and stem areas,root profile, canopy height, leaf dimension, optical properties,stomatal physiology, roughness length, displacement height, andbiomass. In this study, the NCAR LSM calculates the roof profilefor each layer (i) based on Ri = 1 – RFz, where RF is the rootingfraction and z is the depth (cm) (Gale and Grigal 1987). RF isnormally constant for each vegetation type however we have cho-sen RF as a perturbation parameter to investigate LSM sensitivi-ties.

Soil differences are represented by allowing optical, thermal andhydraulic properties to vary. LSM has been used extensively instudies of global and regional terrestrial climate and has been usedto assess surface fluxes (Bonan 1995a; Bonan et al. 1997; Craig etal. 1998; Lynch et al. 1999), sensitivity to various land surfaceproperties (Bonan 1995b, 1996b; Kutzbach et al. 1996; Coe andBonan 1997; Beringer et al. 2000) as well as land atmosphereinteractions (Bonan 1997, 1999; Bonan and Stillwell-Soller 1998).

High latitude tundra regions are of particular interest becauseof the large changes in climate that are expected, because of thelarge biases seen in simulations of climate in the high latitudes, andbecause of the sensitivity of permafrost and snow regime to achanging climate. Insight into the role of land surface character-istics and processes are important in this region (Wilson et al.1987a) as are potential impact assessments of changes (Sud andMollod 1988). Hence, for this sensitivity study, the site chosen forthe simulations is located in the Imnavait Creek watershed ofnorthern Alaska (68�N 149�W). The watershed lies in an areaof continuous permafrost with an observed active layer depth oftypically 50 cm (Hinzman et al. 1991). This has been the site of

numerous other studies examining the role of the permafrost-dominated tundra biome in the regional climate system (Hinzmanand Kane 1992; McFadden et al. 1998; Lynch et al. 1999). TheNCAR LSM has been extensively validated for this region (Tilleyand Lynch 1998; Lynch et al. 1999; Wu and Lynch 2000).

For our sensitivity study all experiments using LSM were de-fined using a generic tundra vegetation type consisting of 70%arctic grass, 25% arctic deciduous shrub, and 5% bare ground.This generic tundra type is also used in global climate model ex-periments. An annual time series of atmospheric forcing data(1995) for our simulations was constructed using a composite ofobserved data, proxy data from nearby stations, and ECMWFoperational analyses (Tilley and Lynch 1998). For each realizationof LSM, a simulation was performed over three consecutive annualcycles, with the first two years designated for spin up and the thirdyear for analysis.

3 Reduced form model

In studies of land–atmosphere interactions, a land surface model isassumed to respond in a realistic way to changes in land surfaceproperties, despite the fact that the model may be validated only forspecific locations or surface types. However, model response ispotentially sensitive not only to changes in land surface properties,but also to interactions between them. Single realizations cannotaccount for the full range of parameter variations and interactionsand an analysis of such interdependencies can be computationallyprohibitive if the complete span of likely land surface is to beconsidered. Note that by doing this stand-alone we can reduce costbut cannot account for land–atmosphere feedbacks, only withinland model feedbacks. Our testing of the NCAR LSM multipleparameter sensitivity was performed in a multidimensional variablespace using a reduced form statistical model based on the meth-odology of Chapman et al. (1994) and Sacks et al. (1989a, b) andfollowing a companion study of the sensitivity of a land surfacemodel to climate perturbations (L2001). Details on the algorithmsused can be found in the appendix of Chapman et al. (1994).

The reduced form statistical model allows for the efficienttesting of sensitivities in multidimensional parameter space. Themethod fits a statistical model to the output of a set of experimentsfrom the physical model. The response of the physical model isevaluated in terms of a set of integrated metrics (i.e. summer sen-sible heat flux) and can be viewed as dependant variables in thestatistical model. The model parameters that are perturbed aretreated as independent variables. In this study, six land surfaceproperties were perturbed simultaneously in each physical modelexperiment. These six parameters were leaf area index, roughnesslength, displacement height, albedo, root fraction, and stomatalresistance. A set of ten integrative response metrics were devised tocharacterize the response of the physical model in each realization.These ten metrics were chosen to highlight issues of importance toArctic ecosystem change and for congruence with the companionstudy of climate input parameter sensitivity (L2001). The tenmetrics chosen were: the date upon which the uppermost soil layerthaws; the date upon which the surface becomes snow free inspring; ground, sensible and latent heat fluxes averaged oversummer; average soil water content as a fraction of saturation insummer; and average soil temperature of the upper layer in each ofthe four seasons.

Two hundred experiments were performed using the NCARLSM (in a configuration outlined in Sect. 2) based on the experi-ence of Chapman et al. (1994) and L2001. The perturbations to beimposed in each LSM experiment were based upon the range ofphysically realistic values over which each variable was likely tovary within the tundra biome and in possible future climates(Table 1). The specification of each range is subjective and isachieved with some justification through physical argument andexperience (Franks et al. 1997). For each perturbation parameter,the range of perturbations was divided into 200 intervals andLatin hypercube sampling was used to determine the imposed

Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model 457

perturbations for a particular experiment. In this sampling method,the magnitude of the perturbation is chosen randomly from theequally spaced values for each perturbation parameter withoutrepeating previous values. Hence the number of model runs wasequivalent to the number of divisions for each value used once(Collins and Avissar 1994; Derwent 1987; McKay et al. 1979). Theresulting set of 200 perturbation combinations spanned the rangeof all possible land surface variations and distributed the combi-nations throughout the parameter space. Only two LSM experi-ments were unstable and hence 198 realizations could be used in theconstruction of the reduced form model.

The statistical model postulates that a response is a realizationof a stochastic process, however, the choice of the reduced statis-tical form of the physical model is not obvious and is compoundedwhen the response is complex (Sacks et al. 1989b). Employing the

assumption that the response metrics of the physical model, de-noted collectively by y, satisfy a normal distribution, a nonlinearreduced form model y can be specified by minimizing a chi-squared(v2) merit function. The model to be fitted is a sum of K Gaussians:

yyðx�Þ ¼

X6i¼1

XKk¼1

alik exp � xi � a2ika3ik

� �2" #

where the vector x�is the perturbation vector and the parameter a is

determined by a minimization procedure which uses the Marquardtmethod (Marquardt 1963). Several reduced form models weretested with varying values of K, but it was found that in all cases, avalue of K = 1 yielded a model with a sufficiently high level ofaccuracy. The outcome is that the statistical model represents acontinuous function of i parameters to which the sensitivities areevaluated, so the model is equivalent to an i-dimensional surface.The surface indicates the parameters and corresponding subrangesto which the model input is most sensitive (Chapman et al. 1994).

The adequacy of this reduced form model, due to the deter-ministic nature of the experiments, is determined solely by sys-tematic bias. Hence, a cross-validation method was used for testingthe accuracy of the reduced form model (Chapman et al. 1994). Inthis procedure, one realization is omitted from the suite of 200experiments, and the reduced form model is fitted to the remainingdata. The reduced form model is then used to predict the responseat the point that was omitted, and a comparison is made to theactual response. This process is repeated for each realization andthe results can be used as an overall measure of accuracy. Thereduced form model can then be used to predict the physical modelresponse to parameter combinations that have not been explicitlyused. Figure 1 and Table 2 show the results of the cross-validation

Table 1. The range of perturbations applied to land surface vari-ables used to drive the land surface model. The ‘control’ experimentused the default values for all fields. The default value representsthe standard value assigned for tundra in the model

Perturbation variable Minimum Default Maximum

Leaf Area Index 0.2 1.4 3.5Displacement height (m) 0.05 0.34 0.5Roughness length (m) 0.01 0.06 0.5Albedo (fraction change) 0.8 1.0 1.2Root fraction with depth 0.9 0.94 0.99Stomatal resistance(fraction change)

0.8 1.0 1.2

Fig. 1. Cross validation predicted versus ‘true’ values (simulated by the physical model) for four of the response metrics: a Julian day ofupper soil thaw; b Julian day that land surface becomes snow free; c average summer sensible heat flux and d average spring upper soiltemperature

458 Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model

process. The cross validation results illustrate that the reduced formmodel reproduces all metrics with a high degree of accuracy andvery few outliers are seen (Fig. 1a–d). Rank correlations were allover 0.9 except winter ground temperature and summer latent heatflux (Table 2). In contrast to the sea-ice model described inChapman et al. (1994), LSM is shown to be highly stable as alsofound by L2001. The response indicated in the reduced form modelcan be considered to be robust.

4 Results of sensitivity analysis

First, we consider the single perturbation sensitivity ofthe response metrics (Fig. 2a–h). These are obtained byintegrating y in the equation with respect to all but oneland surface parameter perturbation, then isolating theeffect of that one perturbation. Since this process resultsin a set of 60 single perturbation sensitivity analyses (sixperturbation parameters · 10 response metrics), only theparameters that explain the most variation (Table 2) orare ecologically interesting are shown for each responsemetric (Fig. 2).

It can be seen from these results that the date of snowfree and date of soil thaw ground vary only 1 and 2 daysrespectively over the range of perturbations (Table 1).The sensitivity of these response metrics to changes inbiotic land surface properties is much less than in thecompanion climate sensitivity study (L2001) where thedate of soil thaw and the date of snow-free ground canvary up to a month from one realization to another. Thissuggests that during these important ‘shoulder’ periods,for the ranges of perturbations we specified, the model isfarmore sensitive to climate than land surface parameters.This variation is of primary importance to issues such ascarbon fluxes (Oechel et al. 1995) and caribou migration(Brown and Theberge 1990; Danell et al. 1994). In thisstudy, the variance in the timing of snow free ground isexplained primarily by albedo and leaf area index. Higher

values of both parameters resulted in a linear delay in thetiming of snow-free ground (Fig. 2a). An increase inalbedo directly reduces absorbed radiation and results in adelay of snow-free ground (Lynch et al. 1998). Otherstudies have also found strong sensitivity to changes inalbedo (Charney 1975; Charney et al. 1977; Sud andFennessy 1982; Laval and Picon 1986), particularly in theinfluence of vegetation albedo in determining turbulentfluxes (Collins and Avissar 1994). Increases in leaf areaindex masks the snow underneath the canopy from solarradiation and hence delays snowmelt.

Leaf area also explains the majority of variance in thetiming of upper soil layer thaw, with a higher leaf areaindex being linearly related to later timing of thaw(Fig. 2b). Increased leaf area results in shading anddecreased soil heat flux producing a delay in soil thaw.Displacement height also explains a large amount ofvariance in the timing of soil thaw with an increase indisplacement height resulting in a linearly earlier thaw(Fig. 2b). Increasing the zero plane displacement formomentum, heat and water has the result of decreasingthe ability of turbulence to transport energy away fromthe ground surface. This results in increased energyretained at the surface and hence an earlier thaw.

When examining the summer energy balance (sensi-ble, latent and ground heat fluxes), sensible heat flux wasthe most sensitive to changes land surface properties(percentage changes up to 200% and absolute changesof 15 Wm–2) (Fig. 2c). Ground heat flux showed a verysmall response (percentage change 1% and absolutechanges of 1.1 Wm–2) (Fig. 2d). The companion climatesensitivity study (L2001) also showed a similarly largesensitivity in sensible heat flux (absolute change 80 Wm–2)compared to ground heat flux (absolute change4.25 Wm–2) indicating that responses to these pertur-bations are expressed through the same physical

Table 2. Summary of the reduced form model performance in-cluding the mean and standard deviation (SD) of the observed re-sponse metric from the model runs and the predicted responsemetric by the reduced form model. The results from the crossvalidation process are shown as the rank correlation between cross-

validation predictions and the physical model. Percentage of vari-ance in the response metric explained by each perturbation, whereLAI is leaf area index; d is displacement height; Zo is roughnesslength; and rs is the minimum stomatal resistance

Day ofsurfacesoil thaw(Julianday)

Day ofsnow freeground(Julianday)

SummergroundT (K)

WintergroundT (K)

SpringgroundT (K)

FallgroundT (K)

Summersoil watercontent

SummerH (Wm–2)

SummerLE(Wm–2)

SummerG(Wm–2)

Mean of observed responses 137.35 119.47 284.04 249.77 262.00 266.28 0.57 0.372 40.95 20.52Mean of predicted responses 137.36 119.61 284.03 249.69 262.00 266.28 0.57 0.211 38.2 20.52SD of observed responses 2.11 2.91 0.248 0.65 0.47 0.25 0.036 2.98 23.27 0.79SD of predicted responses 2.13 2.54 0.261 0.64 0.46 0.25 0.034 2.97 25.46 0.54Linear correlation coefficient 0.75 0.63 0.53 0.95 0.97 0.96 0.92 0.95 0.72 0.69Cross-validation rankcorrelation

0.984 0.917 0.955 0.523 0.999 0.933 0.996 0.912 0.833 0.964

Explained variance of LAI 34.3 4.8 49.4 2.5 1.7 0 0.8 0.6 2.3 6.1Explained variance of d 0 0 38.0 48.9 34.2 79.9 69.1 42.4 75.8 81.9Explained variance of Zo 17.4 0 0 48.6 44.7 15.9 12.3 49.3 16.2 0Explained variance of albedo 6.0 94.6 11.5 0 19.1 0.9 0 5.5 2.4 0Explained varianceof root fraction

0 0.6 0 0 0 0 17.8 2.2 0 0

Explained variance of rs 0 0 1.6 0 0.4 0 0 0.4 0 0

Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model 459

mechanisms but that the responses for the climate per-turbations are at least four times as strong as that for theland surface parameter perturbations. We recognize thatthe magnitude of change observed in the response met-rics does somewhat depend on the range of perturbationvalues chosen for each study but that these ranges rep-resent a subjective assessment of the range of expectedfuture changes in the Arctic.

Changes in surface roughness affect the turbulentexchanges with the atmosphere and can substantiallyimpact the fluxes of heat, moisture and momentum(Bounoua et al. 2000). In general, the response metrics

that we chose were highly sensitive to displacementheight and roughness length with five out of ten metricsbeing most sensitive to both these parameters and nineout of ten metrics being most sensitive to at least one ofthese parameters (Table 2). In simulations of tropicaldeforestation (Dickinson and Henderson-Sellers 1988)using the Biosphere Atmosphere Transfer Scheme(BATS) (Dickinson et al. 1986) the surface energy bud-get was also most sensitive to changes in roughnesslength using an individual factorial sensitivity analysis(Henderson-Sellers 1993). In contrast, several otherstudies have found relative insensitivity to roughness

Fig. 2a–h. Single perturbationsensitivities of the land surfacemodel, showing the responsemetric plotted against two landsurface perturbations. a Timingof snow free surface versusalbedo and leaf area index;b timing of the thawing of theupper soil layer versus dis-placement height and Leaf AreaIndex; c average summer sensi-ble heat flux versus displace-ment height and roughnesslength; d average summerground heat flux versus dis-placement height and Leaf AreaIndex; e average summer latentheat flux versus displacementheight and roughness length;f average winter ground tem-perature versus displacementheight and roughness length;g average summer ground tem-perature versus displacementheight and Leaf Area Index;h average summer soil watercontent as a fraction of satura-tion versus displacement heightand roughness length

460 Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model

length and displacement height, for example, Sun andBosilovich (1996) found that fluxes and planetaryboundary layer development were relatively insensitiveto roughness length. Franks et al. (1997) found that totalevapotranspiration in their Soil Vegetation AtmosphereTransfer (SVAT) model was insensitive to roughnesslength and displacement height. Sud et al. (1990) foundthat changes in vegetation cover produced significantchanges in roughness length but no change in surfacesensible and latent heat fluxes and Tilley et al. (1997)found that changes to tundra roughness length did notresult in significant changes to surface fluxes in Arcticsimulations using the Canadian Land Surface Scheme(CLASS). In this study, sensible and latent heat fluxeswere both highly sensitive to roughness length (Fig. 2cand 2e, respectively). Both turbulent fluxes decreased ina non-linear fashion with increasing roughness. This ismost likely as a result of the ln(z – d/Zo) term in theformulation of the surface temperature/moisture gradi-ent (where z is the reference height) in LSM (Bonan1996, pp 51). Interestingly, both turbulent fluxes werealso sensitive to displacement height, however, sensibleheat fluxes increased with increasing d (Fig. 2c) whilelatent heat fluxes decreased with increasing d (Fig. 2e).The sensitivity to displacement height is somewhat of anartifact as typically in natural environments Zo and dvary together, but in these experiments d is indepen-dently perturbed and the effect of perturbing d is thenisolated. The result is that LSM calculates sensible heatflux, for example, by using the temperature gradient andresistance to sensible heat transfer that are both depen-dant on the ln(z – d/Zo) term as described. In addition,wind speed at the top of the canopy and eddy diffusivitiesare calculated using a (ztop – d) term,where ztop is the top ofthe canopy (m). Hence we find a strong dependence ondisplacement height. Increases in displacement height dueto dense vegetation cover make physical sense and caneffectively make surface heat fluxes independent ofground surface conditions, particularly soil moisture(Zhang 1994). The sensitivity of latent heat fluxes todisplacement height found in our study is expected to varyin a converse manner to sensible heat flux.

Examination of the ground temperature throughoutthe year indicated that winter soil temperatures weremost responsive to changes in land surface parametersthan any other season with winter temperatures varying3.7 �C over the range of perturbations (Fig. 2f). Thiscontrasts with the companion climate sensitivity study(L2001) where changes were greatest in spring and var-ied over a 13 �C range when soil thaw and snow meltprocesses are important. Ground temperatures weremore sensitive to climate perturbations rather than landsurface parameter perturbations over the range of per-turbations we chose. It is interesting to note that groundtemperature was sensitive to different land surfaceproperties in each of the four seasons. Winter, springand fall temperatures were most sensitive to roughnesslength and displacement height perturbations (Table 2).In summer however, the ground temperature was most

sensitive to leaf area index followed by displacementheight (Fig. 2g) and albedo (Table 2). Albedo alsoappeared to explain a moderate amount of variance inthe spring (Table 2). This suggests that parametersensitivities cannot be assessed on an annual basis orover one particular season but rather should be assessedon at least seasonal a basis.

Summer soil moisture was most sensitive to pertur-bations in displacement height and root fraction, fol-lowed by roughness length. The response of soilmoisture to roughness length was highly non-linear(Fig. 2h) and likely represents an inter-play betweenground evaporation and water uptake by plants. Of theresponse metrics we chose, only soil moisture was sen-sitive to changes in rooting fraction with depth and thisrelationship was linear (Fig. 2h). Some other studieshave also found some sensitivity to rooting depth (Acs1994; Pitman 1994). In contrast, tundra simulations us-ing the Community Climate Model (CCM), which iscoupled to NCAR LSM, showed that changes in thefraction of roots with depth had very little effect on thesimulation (Wilson et al. 1987a). The sensitivity to landsurface perturbations showed a range in soil moisturecontent of 0.12, which was comparable to the compan-ion climate sensitivity study (L2001) that showed a rangeof 0.16, suggesting that at least for soil moisture thesensitivity to land surface parameters is equivalent tothat for the climate perturbations.

Vegetation is a major pathway by which soil water istransferred to the atmosphere and therefore has thepotential to respond to and affect land surface process.Large-scale changes in vegetation have shown to havelarge impacts on modelled climate (Bonan et al. 1992;McGufie et al. 1995; Bounoua et al. 2000) and have beenshown to act as a triggering mechanism in generatingconvective clouds using a two-dimensional mesoscalemodel (Hong et al. 1995) and to influence the polarfronts and waves due to influences from the tropics(Chase et al. 1996). The amount of vegetation in LSM isparametrized using a leaf area index (LAI) and factionalcover for each of three vegetation types in a given gridcell. The total LAI for the grid cell is the weighted av-erage of the three vegetation specific LAIs and is timedependant. LAI is important in regulating the amount oftranspiration from the surface and thereby controllingthe partitioning of surface fluxes (Chase et al. 1996) aswell as influencing light extinction. However, the role ofLAI is complex in land surface models and somewhatambiguous in parameterizations of surface processes(Chase et al. 1996). Despite this many studies haveidentified a sensitivity of fluxes to vegetation cover.Arctic simulations have been found to be very sensitiveto vegetation cover as found using CCM coupled toNCAR LSM (Wilson et al. 1987a) and CLASS in astand-alone mode (Tilley et al. 1997). In a one-dimen-sional analysis of the model of Noilhan and Planton(1989), vegetation cover was most sensitive on a dailybasis over vegetated surfaces (Jacquemin and Noilhan1990). In contrast, Wetzel and Chang (1988) and Siebert

Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model 461

et al. (1992) noted greater sensitivity to soil water con-tent than to vegetation.

In this study, turbulent fluxes were relatively insen-sitive to perturbations of LAI but changes in LAI weresignificant in the shading effect on the ground. As a re-sult, summer ground heat flux and summer groundtemperature were both sensitive to increasing LAI(Fig. 2d and 2g). In addition, the timing of the snow freeand soil thaw were also sensitive to LAI (Fig. 2a and 2b)probably as a result of increased shading and lowerenergy absorption at the surface. The effect of pertur-bations on the turbulent fluxes resulted in a linear in-crease in latent heat flux with increasing LAI (Fig. 3). Inoffline sensitivity tests of the Simple biosphere (SiB)model (Xue et al. 1991) changes in latent heat flux withLAI were also found to be quite linear (Xue et al. 1996).Deardorff (1978) found that as the amount of vegetationcover increased, evapotranspiration could increase by afactor of two that in turn resulted in a correspondingdecrease in sensible heat flux. In this study, sensible heatflux also decreased in a non-linear fashion with in-creasing LAI (Fig. 3). Bonan et al. (1993) found astrongly non-linear relationship between LAI and sur-face fluxes too. This non-linear response is due to thefact that many of the effects of increasing leaf areaasymptote relatively quickly (Yang et al. 1999). Forexample, most of the influence of increasing LAI on lightextinction occurs at relatively small values of LAI lim-iting stomatal conductance (Collins and Avissar 1994).Vegetation also contributes to surface roughness,thereby increasing turbulence and acts as a sink ofatmospheric momentum. However, in this study changesin LAI do not affect the structural parameters of thesurface such as roughness and displacement height asthese are specified independently of LAI in the model.Therefore the sensitivity of the model to vegetation maybe expected to be greater than LAI alone if simultaneouschanges in roughness length, displacement height andalbedo were also to occur.

In this study, all response metrics were relativelyinsensitive to perturbations in minimum stomatal resis-tance. This is probably because simulated rs remainsmuch higher than the prescribed minimum value, whichwas the parameter perturbed in the sensitivity analysis.This contrasts with many other studies that have foundstomatal resistance is an important parameter (Wetzeland Chang 1988; Siebert et al. 1992; Acs 1994). Strongsensitivities are often reported because latent heat fluxdecreases with increasing resistance (Sun and Bosilovich1996), which is important because it can then feedbackto affect planetary boundary layer development. Using anumerical model, Avissar and Pielke (1989) concludedthat stomatal conductance determines most of the vari-ation of surface latent heat fluxes and that stomatalconductance and roughness length together account formost of the variation of the surface sensible heat flux.For bare soil, the soil wetness becomes important re-placing stomatal conductance (Collins and Avissar1994).

Although in this study only biotic land surface pa-rameters have been tested, surface fluxes are likely to besomewhat sensitive to soil moisture and soil texture asfound in many previous studies (Walker and Rowntree1977; Rind 1982; Shukla and Mintz 1982; Rowntree andBolton 1983; Mintz 1984; Yeh et al. 1984; Wilson et al.1987b; Sud and Mollod 1988; Gash et al. 1991;Mihailovic et al. 1992; Collins and Avissar 1994). Forexample, evapotranspiration has shown great sensitivityto initial root zone storage in a SVAT model (Frankset al. 1997) while energy partitioning over bare soil wassensitive to soil texture and initial soil moisture in a 1-Dsensitivity test of the model of Noilhan et al. (1989)(Jacquemin et al. 1990). Investigations into the sensi-tivity of three land surface models to soil water foundincreased sensitivity within the drier portion of the rangein soil moisture variability (Dirmeyer et al. 1999) as wasalso found in the companion climate sensitivity (L2001).For the NCAR LSM, Beringer et al. (2001) have

Fig. 3. Single sensitivities ofthe turbulent fluxes of sensibleheat and latent heat versusperturbations in Leaf AreaIndex

462 Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model

investigated the effect of adding additional soil texturetypes to the model and found significant differences insurface fluxes with the addition of organic soils andmosses. Investigations of the sensitivity to soil propertiesremains for further work.

In summary, there are a number of differences in thesensitivity of the NCAR LSM to perturbed biotic pa-rameters and the results of previous studies on land sur-facemodel sensitivities. There are several reasons that thismay be the case. Firstly, the sensitivity of the physicalmodel (LSM) is very dependant on the range of pertur-bations chosen. For instance, if LAI was perturbed 200%from observed values but the other parameters only per-turbed 10% then we may expect LAI to appear mostsensitive. In our study, the range of perturbation valueswas chosen to reflect the expected changes to these pa-rameters under enhanced climate warming in the Arctic.Second, sensitivities are likely to be dependant on the typeof system that is simulated and it is likely that the Arcticsystem may respond differently to temperate or tropicalsystems. Third, all perturbation parameters were variedsimultaneously in our study and it is possible that certaincombinations of perturbations may result in the simula-

tion of unnatural systems. For instance, varying dis-placement height independently of roughness length canlead to sensitivities that have no physical meaning.

Many metrics show a response to forcing which is al-most linear, for example the response of summer groundtemperature to displacement height (Fig. 2g). Such a de-compositionof a response among individual parameters istypical of more limited sensitivity tests, but an extendedanalysis is possible in this case where joint sensitivities canbe analyzed. However, the sensitivity response space ofthe model must still be examined in a reduced number ofdimensions. In examining the joint sensitivities, severalresponse metrics illustrated a linear response to the bioticsurface perturbations such as sensible heat flux (Fig. 4a).In this case sensible heat fluxes responded linearly to bothd and Zo and the sensitivities to both were almost equal.Other response metrics illustrated highly non-linear re-sponses such as the timing of upper layer soil thaw(Fig. 4b). The timing of soil thaw was most sensitive toroughness length and was linear over most of the range ofZo values. However, leaf area index values between 0.5and 1.0 influenced the timing. At values less than 0.5, solarradiation easily penetrates to the surface and at LAI

Fig. 4a–d. Joint sensitivity analysis of the land surface modelshowing two parameters plotted against each other as a function ofthe response metric (contoured values). Relationships shown are: aaverage summer sensible heat flux versus displacement height androughness length; b timing of the thawing of the upper soil layer

versus Leaf Area Index and roughness length; c average summerground temperature versus Leaf Area Index and displacementheight; d average summer ground heat flux versus Leaf Area Indexand displacement height

Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model 463

values great than 1 the canopy is essentially fully shaded.Summer ground temperature and summer ground heatflux both showed sensitivities to leaf area index and dis-placement height and these relationships were also non-linear (Fig. 4c, d). Both temperature and ground heat fluxwere at a minimumwhen the leaf area index was around 1and declined with higher and lower leaf area indices(Fig. 4c, d). This relationship represents an interaction ofleaf area and physical processes of shading and longwaveradiation trapping by the canopy. Ground temperaturesand ground heat fluxes also increased with increasingdisplacement height but tended to saturate as the value ofdwas perturbed above the canopy height. Examination ofthese joint sensitivities is important and can be a usefultool to determine model behaviour and the physical in-terdependencies of the model.

5 Conclusions

The multivariate reduced form model is a useful tool inthe evaluation of the sensitivity of a land surface modelto changes in land surface parameters. The sensitivitiesof the land surface model are interdependent, and inseveral cases highly nonlinear, especially for joint sen-sitivities. The interdependencies between the responsesto different driving parameters are, however, physicallyplausible. The response metrics we chose were mostsensitive to roughness length and displacement heightand suggest that the efficiency of turbulent transportcontrols many of the land surface responses. Perturba-tions in leaf area index showed sensitivity in the summerground heat flux and ground temperature as a result ofshading. Albedo perturbations showed sensitivity in thetiming of snow-free ground. The response metrics weregenerally insensitive to parameters such as minimumstomatal resistance and root fraction.

In comparison to a companion climate sensitivitystudy (L2001), sensitivities of the NCAR LSM to per-turbations in land surface properties were much smallerthan perturbations in climatic inputs, over the range ofperturbations we have chosen. Sensitivities to climateare particularly greater in the spring during snow meltand suggest than changes in climate such as increasedanthropogenic warming are likely to be greater than theeffect of biotic land surface properties due to changes invegetation. The modeled summer energy balance, espe-cially sensible heat flux, was sensitive to perturbations inboth climate and land surface properties suggestingmodelled responses are driven by the same physicalmechanisms in the model. Soil moisture was as sensitiveto land surface perturbations as climate perturbations.

Acknowledgements We would like to thank S. Sorooshian and oneanonymous reviewer for their helpful comments on the manuscript.We would like to thank Andrew Slater for generating the Latinhypercube sampling algorithm used in this study. This research issupported through the Arctic System Science (ARCSS) program ofthe National Science Foundation (OPP-9732126 and OPP-9732461).

References

Acs F (1994) A coupled soil-vegetation scheme: Description,parameters, validation, and sensitivity studies. J Appl Meteorol33: 268–284

Avissar R, Pielke RA (1989) A parameterization of heterogeneousland surfaces for atmospheric numerical models. Mon WeatherRev 117: 2113–2136

Bastidas LA, Gupta HV, Sorooshian S, Shuttleworth WJ, Yang ZL(1999) Sensitivity analysis of a land surface scheme using mul-ticriteria methods. J Geophys Res 104(D16): 19481–19490

Beringer J, Lynch AH, Chapin III FS, Mack M, Bonan GB(2001) The representation of Arctic soils in the Land SurfaceModel (LSM): The importance of mosses. J Clim 14(15):3324–3335

Bonan GB (1995a) Land–atmosphere CO2 exchange simulated by aland surface process model coupled to an atmospheric generalcirculation model. J Geophys Res 100: 2817–2831

Bonan GB (1995b) Sensitivity of a GCM simulation to inclusion ofinland water surfaces. J Climate 8: 2691–2704

Bonan GB (1996a) A land surface model (LSM version 1.0) forecological, hydrological, and atmospheric studies: technicaldescription and user’s guide, Technical Note NCAR/TN-417+STR. National Center for Atmospheric Research, Boul-der, Colorado, pp 150

Bonan GB (1996b) Sensitivity of a GCM simulation to subgridinfiltration and surface runoff. Clim Dyn 12: 279–285

Bonan GB (1997) Effects of land use on the climate of the UnitedStates. Clim Change 37: 449–486

Bonan GB (1999) Frost followed the plow: impacts of deforestationon the climate of the United States. Ecol Appl 9: 1305–1315

Bonan GB, Stillwell-Soller LM (1998) Soil water and the persis-tance of floods and droughts in the mississippi River Basin.Water Resour Res 34: 2693–2701

Bonan GB, Davis KJ, Baldocchi D, Fitzjarrald D, Neumann H(1997) Comparison of the NCAR LSM1 land surface modelwith BOREAS aspen and jack pine tower fluxes. J Geophys Res102: 29065–29075

Bonan GB, Pollard D, Thompson SL (1992) Effects of boreal forestvegetation on global climate. Nature 359: 716–718

Bonan GB, Pollard D, Thompson SL (1993) Influence of sub-gridscale heterogeneity in leaf area index, stomatal resistance, andsoil moisture on grid-scale land–atmosphere interactions. J Clim6: 1882–1897

Bonan GB, Shugart HH, Urban DL (1990) Sensitivity of somehigh-latitude boreal forests to climatic parameters. ClimChange 16: 9–29

Bounoua L, Collatz GJ, Los SO, Sellers PJ, Dazlich DA, TuckerCJ, Randall DA (2000) Sensitivity of climate to changes inNDVI. J Climate 13(3): 2277–2292

Brown WK, Theberge JB (1990) The effect of extreme snowcoveron feeding-site selection by woodland caribou. Journal WildlifeManage 54(1): 161–168

Chahine MT (1992) The hydrologic cycle and its influence on cli-mate. Nature 359: 373–380

Chapman WL, Welch WJ, Bowman KP, Sacks J, Walsh JE (1994)Arctic sea ice variability: model sensitivities and a multidecadalsimulation. J Geophys Res 99(C1): 919–935

Charney JG (1975) Dynamics of desert and drought in the Sahel. QJ R Meteorol Soc 101: 192–202

Charney JG, Quirk WJ, Chow S-H, Kornfeld J (1977) A com-paritive study on the effects of albedo change on drought insemi-arid regions. J Atmos Sci 34: 1366–1385

Chase TN, Pielke RA, Kittel TGF, Nemani R, Running SW (1996)Sensitivity of a general circulation model to changes in leaf areaindex. J Geophys Res 101(D3): 7393–7408

Coe MT, Bonan GB (1997) Feedbacks between climate and surfacewater in northern Africa during the middle Holocene. J Geo-phys Res 102: 11087–11101

Collins DC, Avissar R (1994) An evaluation with the Fourieramplitude sensitivity test (FAST) of which land-surface

464 Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model

parameters are of greatest importance in atmospheric modeling.J Clim 7: 681–703

Craig SG, Holmen KJ, Bonan GB, Rasch PJ (1998) AtmosphericCO2 simulated by the National Center for AtmosphericResearch Community Climate Model 1. Mean fields and sea-sonal cycles. J Geophys Res 103: 13213–13235

Danell K, Utsi PM, Palo RT, Erikson O (1994) Food plant selec-tion by reindeer during winter in relation to plant quality.Ecography 17: 153–158

Deardorff JW (1978) Efficient prediction of ground surface tem-perature and moisture, with inclusion of a layer of vegetation.J Geophys Res 83(C4): 1889–1903

Derwent RG (1987) Treating uncertainty in models of the atmo-spheric chemistry of nitrogen compounds. Atmos Environ 21:1445–1454

Dickinson RE, Henderson-Sellers A (1988) Modeling tropicaldeforestation: a study of GCM land-surface parameterizations.Q J R Meteorol Soc 114: 439–462

Dickinson RE, Henderson-Sellers A, Kennedy PJ, Wilson MF(1986) Biosphere-Atmosphere Transfer Scheme (BATS) for theNCAR Community climate model, NCAR Tech. Note NCAR/TN-275+STR. National Centre for Atmospheric Research,Boulder, CO, USA

Dickinson RE, Henderson-Sellers A, Kennedy PJ (1993) Bio-sphere-Atmosphere Transfer Scheme (BATS) version 1e ascoupled to the NCAR Community Climate Model, NCARTechnical note NCAR/TN-387+STR. National Center forAtmospheric Research, Boulder, CO, USA, pp 50

Dirmeyer PA, Zeng FJ, Ducharne A, Koster RD, Morrill JC (1999)Sensitivity of surface fluxes to soil water content in three landsurface schemes. In: 14th Conf Hydrology. American Meteoro-logical Society, American Meteorological Society, pp 225–227

Franks SW, Beven KJ, Quinn PF, Wright IR (1997) On the sen-sitivity of soil-vegetation-atmosphere transfer (SVAT) schemes:equifinality and the problem of robust calibration. Agr ForestMeteorol 86: 63–75

Gale MR, Grigal DF (1987) Vertical root distributions of noerth-ern tree species in relation to successional status. Can J For Res17: 829–834

Gash JHC, Wallace JS, Lloyd CR, Dolman AJ, Sivakumar MVK,Renard C (1991) Measurements of evaporation from fallowSahelian savannah at the start of the dry season. Q J R Mete-orol Soc 117: 749–760

Gupta HV, Bastidas LA, Sorooshian S, Shuttleworth WJ, Yang ZL(1999) Parameter estimation of a land surface scheme usingmulticriteria methods. J Geophys Res 104(D16): 19491–19503

Hallgren WS, Pitman AJ (2000) The uncertainty in simulations bya Global Biome Model (BIOME3) to alternative parametervalues. Glob Change Biol 6: 483–495

Henderson-Sellers A (1992) Assessing the sensitivity of a landsurface scheme to parameters used in tropical-deforestationexperiments. Q J R Meteorol Soc 118: 1101–1116

Henderson-Sellers A (1993) A factorial assessment of the sensitivityof the BATS land-surface parameterization scheme. J Clim 6:227–247

Hinzman LD, Kane DL (1992) Potential response of an arcticwatershed during a period of global warming. J Geophys Res97(D3): 2811–2820

Hinzman LD, Kane DL, Gieck RE, Everett KR (1991) Hydrologicand thermal properties in the active layer in the Alaskan Arctic.Cold Reg Sci Technol 19: 95–110

Hong X, Leach MJ, Raman S (1995) A sensitivity study of con-vective cloud formation by vegetation forcing with differentatmospheric conditions. J Appl Meteorol 34: 2008–2028

Iman RL, Helton JC (1988) An investigation of uncertainty andsensitivity analysis techniques for computer models. Risk Anal8: 71–90

Jacquemin B, Noilhan J (1990) Sensitivity study and validation of aland surface parameterization using the HAPEX-MOBILHYdata set. Bound a Layer Meteorol 52: 93–134

Kutzbach J, Bonan GB, Foley J, Harrison SP (1996) Vegetationand soil feedbacks on the response of the African monsoon to

orbital forcing in the early to middle Holocene. Nature 384:623–626

Laval K, Picon L (1986) Effect of change of the surface albedo onthe Sahel climate. J Atmos Sci 43: 2418–2429

Lofgren BM (1995) Sensitivity of land–ocean circulations, precip-itation, and soil moisture to peturbed land surface albedo.J Clim 8: 2521–2542

Lynch AH, McGinnis DL, Bailey DA (1998) Snow-Albedo feed-back and the spring transition in a regional climate systemmodel: influence of land surface model. J Geophys Res103(D22): 29037–29049

Lynch AH, Bonan GB, Chapin III FS, Wu W (1999) The impact oftundra ecosystems on the surface energy budget and climate ofAlaska. J Geophys Res 104(D6): 6647–6660

Lynch AH, McIlwaine S, Beringer J, Bonan GB (2001) An inves-tigation of the sensitivity of a land surface model to climatechange using a reduced form model. Clim Dyn 17: 643–652

Marquardt DW (1963) An algorithm for least-squares estimationof non-linear parameters. J Soc Indus Appl Math 11: 431–441

McFadden JP, Chapin III FS, Hollinger DY (1998) Subgrid-scalevariability in the surface energy balance of arctic tundra.J Geophys Res 103(D22): 28,947–28,961

McGufie K, Henderson-Sellers A, Zhang H, Durbidge TB, PitmanAJ (1995) Global climate sensitivity to tropical deforestation.Global Planet Change 10: 97–128

McKay MD, Beckman RJ, Conover WJ (1979) A comparison ofthree methods for selecting values of input variables in the anal-ysis of output from a computer code. Technometrics 21: 239–245

Mihailovic DT, De Bruin HAR, Jeftic M, van Dijken A (1992) Astudy of the sensitivity of land surface parameterizations to theinclusion of different fractional covers and soil textures. J ApplMeteorol 31: 1477–1487

Mintz Y (1984) The sensitivity of numerically simulated climates toland-surface conditions. In: Houghton J (ed) The Global Cli-mate. Cambridge University Press, Cambridge UK, pp 79–105

Noilhan J, Planton S (1989) A simple parameterization of landsurface processes for meteorological models. Mon Weather Rev117: 536–549

Oechel WC, Vourlitis GL, Hastings SJ, Bochkarev SA (1995)Change in Arctic CO2 flux over two decades: effects of climatechange at Barrow, Alaska. Ecol Appl 5(3): 846–855

Persson J, Hakanson L (1996) A simple empirical model to predictdeepwater turnover time in coastal waters. Can J Fish AquatSci 53: 1236–1245

Pitman AJ (1994) Assessing the sensitivity of a land-surface schemeto the parameter values using a single column model. J Clim7(12): 1856–1869

Polcher J (1995) Sensitivity of tropical convection to land surfaceprocesses. J Atmos Sci 52(17): 3143–3161

Rind D (1982) The influence of ground moisture conditions NorthAmerica on summer climate as modeled in the GISS GCM.Mon Weather Rev 110: 1487–1494

Rowntree PR, Bolton JA (1983) Simulation of the atmosphericresponse to soil moisture anomalies over Europe. Q J R Me-teorol Soc 109: 501–526

Sacks J, Schiller SB, Welch WJ (1989a) Designs for computerexperiments. Technometrics 31: 41–47

Sacks J, Welch WJ, Michell TJ, Wynn HP (1989b) Design andanalysis of computer experiments. Stat Sci 4(4): 409–935

Sellers PJ, Randall DA, Collatz GJ, Berry JA, Field CB, DazlichDA, Zhang C, Collelo GD, Bounoua L (1996) A revised landsurface parameterization (SiB2) for atmospheric GCMs. Part I:model formulation. J Clim 9(4): 676–705

Shukla J, Mintz Y (1982) Influence of land surface evapotranspi-ration on the Earth’s climate. Science 125: 1498–1501

Siebert J, Sievers U, Zdunkowski W (1992) A one-dimensionalsimulation of the interaction between land surface processesand the atmosphere. Boundary Layer Meteorol 59: 1–34

Sinha R, Small MJ, Ryan PF, Sullivan TJ, Cosby BJ (1998)Reduced form modelling of surface water and soil chemistry forthe tracking and analysis framework. Water, Air Soil Poll 105:617–642

Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model 465

Sud YC, Fennessy MJ (1982) A study of the influence of surfacealbedo on July circulation n semi-arid regions using the GIASGCM. J Climatol 2: 105–125

Sud YC, Mollod A (1988) A GCM simulation study of the influ-ence of Sahara evapotranspiration and surface-albedoanoma-lies on July circulation and rainfall. Mon Weather Rev 116:2388–2400

Sud YC, Sellers PJ, Mintz Y, Chou MD, Walker GK, Smith WE(1990) Influence of the biosphere on the global circulation andhydrological cycle – A CGM simulation experiment. Agr ForestMeteorol 52: 133–180

Sun W-Y, Bosilovich G (1996) Planetary boundary layer and sur-face layer sensitivity to land surface parameters. BoundaryLayer Meteorol 77: 353–378

Tilley JS, Lynch AH (1998) On the applicability of current landsurface schemes for arctic tundra: an intercomparison study.J Geophys Res 103: 29051–29063

Tilley JS, Chapman WL, Wanli W (1997) Sensitivity tests of theCanadian Land Surface Scheme (CLASS) for Arctic tundra.Ann Glaciol 25: 46–50

Verhoff A, Allen SJ, Lloyd CR (1999) Seasonal variation of surfaceenergy balance over two sahellian surfaces. Int J Climatol 19:1267–1277

Walker J, Rountree PR (1977) The effect of soil moisture on cir-culation and rainfall in a tropical model. Q J R Meteorol Soc103: 29–46

Wetzel PJ, Chang JT (1988) Evapotranspiration from a nonuni-form surface: a first approach for short term numerical weatherprediction. Mon Weather Rev 116: 600–621

Wilson MF, Henderson-Sellers A, Dickinson RE, Kennedy PJ(1987a) Investigation of the sensitivity of the land-surfaceparameterization of the NCAR community climate model inregions of tundra vegetation. J Climatol 7: 319–343

Wilson MF, Henderson-Sellers A, Dickinson RE, Kennedy PJ(1987b) Sensitivity of the biosphere-atmosphere transfer scheme(BATS) to the inclusion of variable soil characteristics. J ClimAppl Meteorol 26: 341–362

WuW, Lynch AH (2000) The response of the seasonal carbon cyclein high latitudes to climate anomalies. J Geophys Res 105:22897–22908

Xue Y, Bastable HG, Dirmeyer HG, Sellers PJ (1996) Sensitivity ofsimulated surface fluxes to changes in land surface parameter-izations – A study using ABRACOS data. J Appl Meteorol 35:386–401

Xue Y, Sellers PJ, Kinter III JL, Shukla J (1991) A simplifiedbiosphere model for global climate studies. J Clim 4: 345–364

Yang Z-L, Dai Y, Dickinson RE, Shuttleworth WJ (1999) Sensi-tivity of ground heat flux to vegetation cover fraction and leafarea index. J Geophys Res 104(D16): 19505–19514

Yeh TC, Wetherland RT, Manabe S (1984) The effect of soilmoisture on the short-term climate and hydrology change – anumerical experiment. Mon Weather Rev 112: 474–490

Zhang T (1994) Sensitivity properties of a biosphere model basedon BATS and a statistical–dynamical climate model. J Clim 7:890–913

466 Beringer et al.: The use of a reduced form model to assess the sensitivity of a land surface model