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Agricultural and Forest Meteorology 176 (2013) 38– 49

Contents lists available at SciVerse ScienceDirect

Agricultural and Forest Meteorology

jou rn al hom epage : www.elsev ier .com/ locate /agr formet

lobal evaluation of MTCLIM and related algorithms for forcing ofcological and hydrological models

heodore J. Bohna, Ben Livnehb, Jared W. Oylerc, Steve W. Runningc, Bart Nijssena,ennis P. Lettenmaiera,∗

Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USACooperative Institute for Research in Environmental Science (CIRES), University of Colorado, Boulder, 216 UCB, Boulder, CO, 80309, USANumerical Terradynamic Simulation Group, College of Forestry and Conservation, University of Montana, Missoula, MT, USA

r t i c l e i n f o

rticle history:eceived 30 August 2012eceived in revised form 20 February 2013ccepted 4 March 2013

eywords:olar radiationumidityongwave radiation

a b s t r a c t

We assessed the performance of the MTCLIM scheme for estimating downward shortwave (SWdown) radi-ation and surface humidity from daily temperature range (DTR), as well as several schemes for estimatingdownward longwave radiation (LWdown), at 50 Baseline Solar Radiation Network stations globally. All ofthe algorithms performed reasonably well under most climate conditions, with biases and mean abso-lute errors generally less than 3% and 20%, respectively, over more than 70% of the global land surface.However, estimated SWdown had a bias of −26% at coastal sites, due to the ocean’s moderating influenceon DTR, and in continental interiors, SWdown had an average bias of −15% in the presence of snow, whichwas reduced by MTCLIM 4.3’s snow correction if local topography was taken into account. Vapor pressure

ir temperaturelobal land surface modeling

(VP) and relative humidity (RH) had large negative biases (up to −50%) under the most arid conditions.At coastal sites, LWdown had positive biases of up to 10%, while biases at interior sites exhibited a weakdependence on DTR. The largest biases in both RH (negative) and LWdown (positive) were concentratedover the world’s deserts, while smaller positive humidity biases were found over tropical and borealforests. Evaluation of the diurnal cycle showed negative morning, and positive afternoon biases in vapor

wn re

pressure deficit and LWdo

. Introduction

Large-scale hydrological and ecological models require mete-rological forcings such as downward shortwave and longwaveadiation, humidity, and surface air temperature as inputs on dailynd sub-daily time scales. Because in situ observations of theseuantities are relatively sparse (especially at sub-daily time scales)nd because the spatial resolution required for these applica-ions often is higher than that provided by other sources (e.g., theCEP/NCAR Reanalysis, Kalnay et al., 1996; the ERA-40 Reanaly-

is, Uppala et al., 2005; or the North American Regional Reanalysis,esinger et al., 2006), algorithms for estimating these quantities

rom routinely observed variables such as the daily temperatureange are appealing. One such algorithm, the Mountain Microcli-

ate Simulation Model (MTCLIM; Hungerford et al., 1989; Kimball

t al., 1997; Thornton and Running, 1999; Thornton et al., 2000),as been widely used to estimate daily downward shortwave

∗ Corresponding author at: Department of Civil and Environmental Engineering,01 More Hall, PO Box 352700, University of Washington, Seattle, WA 98195-2700,SA. Tel.: +1 206 543 2532.

E-mail address: dennisl@u.washington.edu (D.P. Lettenmaier).

168-1923/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.agrformet.2013.03.003

lated to errors in the interpolation of the diurnal air temperature.© 2013 Elsevier B.V. All rights reserved.

radiation and vapor pressure, which are among the required forc-ings for off-line simulations of land surface models includingBiome-BGC (Thornton, 1998), the Variable Infiltration Capacitymodel (VIC; Liang et al., 1994) and the Distributed HydrologySoil Vegetation Model (DHSVM; Wigmosta et al., 1994), amongothers. Other algorithms have been commonly used by these mod-els to estimate downward longwave radiation (e.g., Prata, 1996).These models have subsequently used these estimated forcings,for instance, to assess drought over the continental U.S. (Andreadisand Lettenmaier, 2006; Wang et al., 2009); in downscaling of cli-mate change projections (e.g. Christensen and Lettenmaier, 2007;Hayhoe et al., 2007), and in seasonal hydrologic forecasting (Woodet al., 2002; Mo et al., 2012). These models have been applied atcontinental and global scales, across a wide range of climate condi-tions. It is important, therefore, to understand the accuracy of theMTCLIM and longwave algorithms over the range of the world’sclimates.

One complication in using algorithms like MTCLIM is that theytypically depend on other unobserved forcings. For example, the

MTCLIM algorithm for daily dew point temperature Tdew (Kimballet al., 1997; hereafter referred to as K97) depends on both thedaily temperature range (DTR) and downward shortwave radiation(SWdown), while the MTCLIM algorithm for daily SWdown (Thornton

Forest Meteorology 176 (2013) 38– 49 39

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Fig. 1. Schematic illustrating process flow for algorithms in simultaneous mode.DTR = daily temperature range; Precip = daily precipitation; Tair = instantaneous

T.J. Bohn et al. / Agricultural and

nd Running, 1999; hereafter referred to as TR99) depends on bothTR and vapor pressure (VP), which, in turn, must be estimated

rom Tdew. Similarly, most algorithms for estimating downwardlear-sky longwave radiation (e.g., Prata, 1996) depend on instan-aneous surface air temperature (Tair) and VP (Flerchinger et al.,009), while estimating full-sky longwave radiation (LWdown) addi-ionally requires cloud fraction (Deardorff, 1978; Crawford anduchon, 1999). Finally, estimating the diurnal cycles of all of these

erms (needed by many models) requires sequential or simulta-eous estimation due to cross-dependencies among the variablese.g., McVicar and Jupp, 1999).

Simultaneous estimation of all of these forcings (in which thelgorithms supply each other with simulated inputs), at daily andub-daily time scales, may be expected to lead to greater errorshan in stand-alone mode (wherein each algorithm uses observednputs). Despite the widespread use of these algorithms, errorsave not been globally quantified, particularly when they are cross-

inked. Several studies (e.g., TR99; Ball et al., 2004; Almeida andandsberg, 2003) reported negative biases in TR99 SWdown in theange of −5% to −20% at humid sites in the sub-tropical U.S. andrazil, leading to concern that TR99 may not perform well in theropics. Shi et al. (2010) evaluated TR99 SWdown estimates across therctic using observations from the Global Energy Balance Archive

GEBA) network (Ohmura et al., 1989; Gilgen et al., 1998) and foundtrong seasonal variation in biases, from −15% in spring to +10% inummer (although net annual biases were small). Both Kimball et al.1997) and Pierce et al. (2012) found that within the continental.S., K97 performed worse along the coasts and in arid regions thanlsewhere. Mo et al. (2012) found differences over the western U.S.etween short- and longwave radiation estimates from the Northmerican Regional Reanalysis (NARR; Mesinger et al., 2006) and

rom a combination of MTCLIM and the Tennessee Valley AuthorityTVA, 1972) algorithms. Yet, few studies have evaluated the effectsf simultaneous estimation of all of the variables of interest, usingnly observed DTR and precipitation, and none have evaluated theerformance of such a system over the complete range of globallimates.

In this study, we evaluate the simultaneous estimation ofhort- and longwave radiation and vapor pressure through a com-ination of MTCLIM version 4.3, the Deardorff (1978) full-skyWdown scheme, and the Prata (1996) clear-sky longwave emissiv-ty scheme, and compare these estimates with observations at sitesrom the global Baseline Surface Radiation Network (BSRN; Ohmurat al., 1998), which span all of the world’s major climate regimes.e compare the performance of the simultaneous estimation algo-

ithm to that of the individual standalone algorithms at monthlyimescales, and identify the contributions of each individual algo-ithm to errors in the simultaneous estimates. We then estimate thelobal distributions of these errors. Finally, we examine the accu-acy of a common method of interpolating these quantities fromaily to hourly timescales.

. Background

.1. Shortwave radiation

For SWdown and VP, we evaluated MTCLIM version 4.3 (Thorntont al., 2000). In MTCLIM, daily SWdown is estimated via the TR99lgorithm, a schematic of which is shown in Fig. 1. In this algorithm,Wdown is estimated as the product:

W = Rpot × Tt,max × T (1)

down f,max

here Rpot is the theoretical incident top-of-atmosphere short-ave radiation (a function of location and day of year), Tt,max is

he total daily clear-sky transmittance, and Tf,max is the cloudy-sky

air temperature; SW = daily shortwave radiation; Fcloud = daily cloud fraction;Tdew = daily dewpoint temperature; RH = daily relative humidity; VP = daily vaporpressure; LW = instantaneous longwave radiation.

transmittance (i.e., the fraction of shortwave radiation not absorbedor scattered by clouds).

Clear-sky transmittance Tt,max has a weak dependence on VP asfollows:

Tt,max = Tt,dry + ˛VP (2)

where VP is in units of Pa, ̨ = −6.1 × 10−5 Pa−1; and Tt,dry is a func-tion of instantaneous clear-sky transmittance, day length, and thesite’s slope, aspect, and horizon. It is important to note that mostlarge-scale models that have used MTCLIM forcings assume a flatsurface topography. This practice can be expected to produce errorsin estimated Tt,dry. Because our focus was to assess the performanceof MTCLIM within the context of large-scale models, we suppliedvalues of 0 for slope, aspect, and horizon in our simulations (withthe exception of Section 5.1.1, where we test the effects of theseassumptions).

Cloudy-sky transmittance Tf,max is a function of DTR in MTCLIM,with a further reduction by 25% on days with precipitation. Thisis equivalent to the assumption that cloudiness is the main factorinfluencing DTR.

In MTCLIM 4.3, Thornton et al. (2000) added a correction to thediffuse component of SWdown in the presence of snow, to account forshortwave radiation that has been reflected from snow in the sur-rounding landscape and subsequently scattered by the atmosphereback down to the ground:

sc = 1.32 + 0.096 · SWE (3)

where sc is the correction to SWdown in MJ/m2 per day, dividedevenly over the day length (limited to 100 W/m2), and SWE isthe snow pack’s snow water equivalent in cm, as determined byMTCLIM 4.3’s degree-day snow model. This correction is added toSWdown after the product in equation (1) is computed and thus doesnot affect Tt,max or Tf,max.

2.2. Vapor pressure

Daily average VP in MTCLIM is computed as the saturation vaporpressure when air temperature equals Tdew. MTCLIM uses the K97algorithm (Fig. 1) to estimate daily dew point temperature Tdew

(based on a linear regression against EF and DTR):

Tdew = Tmin

(−0.127 + 1.121

(1.003 − 1.444EF + 12.312EF2

−32.766EF3)

+ 0.0006DTR)

(4)

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here Tmin is the daily minimum temperature in degrees Kelvinnd EF is a measure of aridity, defined as the ratio of daily totalotential evaporation Ep,day to annual precipitation Pann. Potentialvaporation Ep,day is computed via the formula of Priestley andaylor (1972). In the MTCLIM implementation of K97, Pann waseplaced with the effective annual precipitation estimated from a0-day window beginning on the current day, to allow for greaterensitivity to seasonal climate.

.3. Simultaneous estimation of shortwave radiation and vaporressure

As shown in equations (1–4), SWdown and VP estimates dependn each other: SWdown depends weakly on VP through Tt,max

equation (2)); VP depends strongly on SWdown through potentialvaporation. When observations are unavailable for either term,TCLIM estimates both, via a 2-pass iteration, depicted in Fig. 1.

P is first estimated by assuming Tdew = Tmin. This initial approx-mation is used in equation (2) to compute Tt,max. The resultingWdown is used to compute potential evaporation, which leads ton estimate of Tdew using equation (4). From this, a new VP esti-ate is made, which is subsequently used to update SWdown. InTCLIM 4.3, Thornton et al. (2000) modified this iteration to be

mplemented only at arid sites, defined as having annual averageF values greater than 2.5. For humid sites, the initial estimate ofdew = Tmin was retained.

.4. Longwave radiation

We evaluated several algorithms for clear-sky longwave emis-ivity and full-sky LWdown. Of the algorithms we examined, therata (1996) clear-sky algorithm, combined with the Deardorff1978) full-sky approach (also attributed to Crawford and Duchon,999), exhibited the smallest overall errors. For this reason, wesed the Deardorff/Prata combination for this study. Details of theWdown algorithm comparison are included in Appendix A.1.

The Deardorff full-sky approach divides LWdown into twoources, clear sky and clouds, and computes full-sky LWdown as theeighted average of the two terms based on an estimate of the sky’s

lear and cloudy fractions (fclear and fcloud, respectively). Longwaveadiation from both sources follows the form

Wdown = E�T4air (5)

here E is the source’s emissivity, � is the Stefan–Boltzmannonstant, and Tair is air temperature in degrees Kelvin, so that esti-ating the radiation from each source requires an algorithm for

redicting the source’s emissivity.In Deardorff-style schemes, cloud emissivity is typically

ssumed to be 1.0 (Flerchinger et al., 2009), as we do in this study.o compute clear-sky emissivity (Ea), we used the Prata (1996)lgorithm:

a = 1 − (1 + �)exp[−(1.2 + 3.0�)1/2

](6)

= 46.5(

VP

Tair

)(7)

here VP is vapor pressure in h Pa and Tair is air temperature inegrees Kelvin. The process flow for the Deardorff–Prata combina-ion is depicted in Fig. 1.

Unfortunately, we found few observations of clear-sky fraction

fclear) collocated with the other observations, so we followed thepproach of Crawford and Duchon (1999) and estimated fclear ashe ratio of actual (observed or simulated) SWdown to the theo-etical cloud-free SWdown predicted by MTCLIM (Rpot·Tt,max from

t Meteorology 176 (2013) 38– 49

equation (1)). In those cases when SWdown is simulated by MTCLIM,this definition of fclear is therefore equal to Tf,max.

2.5. Diurnal variation

We also evaluated a method commonly used in VIC modelstudies for estimating the diurnal cycles of these variables. Thismethod begins by estimating the diurnal cycle of Tair, using thehigh-frequency (30-s interval) time series of insolation computedby MTCLIM (as part of its calculation of Tt,max) to determine eachday’s times of sunrise (trise) and sunset (tset). tmin is assumed to occurat sunrise and maximum air temperature tmax is assumed to occurat time tmax:

tmax = trise + 0.67(tset − trise) (8)

At sites above the Arctic circle, times of sunrise and sunset areundefined in summer and winter. For these cases, trise and tset areassigned values of 2:00 and 14:00, respectively. Once the tmin andtmax are determined, hourly tmax values are computed using a splineof 3rd-order Hermite polynomials.

We evaluated two different methods of estimating hourly VP(following McVicar and Jupp, 1999): the first approach, tradition-ally used in VIC model studies, simply holds MTCLIM’s daily Tdew(and therefore VP) estimate constant over the course of the day,while the second approach assigns MTCLIM’s daily Tdew estimateto sunrise and interpolates hourly Tdew (and VP) linearly betweenthe sunrise of one day and the next. Hourly relative humidity (RH)and vapor pressure deficit (VPD) are then computed from hourlyTair and VP.

To compute hourly LWdown, clear-sky fraction fclear is assumedconstant throughout the day, and hourly clear-sky emissivity val-ues are computed from hourly Tair and VP. Hourly SWdown iscomputed as MTCLIM’s hourly fraction of insolation normalizedto sum to the daily total SWdown (which was either observed orestimated by MTCLIM).

3. Observations

We evaluated the estimates from the different forcing algo-rithms using observations from the global Baseline SurfaceRadiation Network (BSRN; BSRN, 2012; Ohmura et al., 1998). Animportant reason for choosing the BSRN is the global distributionof its stations (Fig. 3), spanning most of the world’s major climateregimes: arctic/boreal, dry-temperate, humid-temperate, Mediter-ranean, desert, sub-tropical, and tropical. Equally important forour study of simultaneous estimation of daily and hourly SWdown,LWdown, VP, and Tair are its collocated sub-daily observations ofthese variables, and consistent measurement protocols through-out the network. Table 1 presents a list of the stations used inthis study, along with information on their locations, elevations,annual average EF values, record length, and variables measured.Stations within 5 km of the ocean (18 of the 50 stations used inthis study) were set aside for special consideration (see Section5); these are listed as “coastal” in Table 1 and denoted in redin Fig. 2.

The MTCLIM algorithm requires daily precipitation and mini-mum and maximum temperature as inputs. Unfortunately, not allof the BSRN stations recorded air temperature and none of the sta-tions recorded precipitation. In most cases, precipitation was takenfrom the National Climatic Data Center (NCDC), Global HistoricalClimatic Network (GHCN) and Global Summary of the Day (GSOD)

archives (NCDC, 1998), using the meteorological station nearest tothe BSRN site. Where possible, daily minimum and maximum tem-peratures were taken from the BSRN site itself; otherwise thesewere also taken from the nearest GHCN or GSOD station. If the

T.J. Bohn

et al.

/ A

gricultural and

Forest M

eteorology 176 (2013) 38– 49

41Table 1Descriptions of BSRN stations used in this study.

Stn Lat (◦N) Lon (◦E) Elev (m) Coastal EFann T Met. Stationa % T Gaps P Met. Stationa % P Gaps RH? Startb Endb Nmoc AvgNdaysd NLt10e FracLt10f

Stn Dist(km)

Elev(m)

Stn Dist(km)

Elev(m)

ASP −23.7980 133.8880 547 7.80 ASN00015590 <1 546 0.1 ASN00015590 <1 546 0.7 No 1995 2008 167 29.04 1 0.01BAR 71.3230 −156.6114 11 Yes 2.87 USW00027516 <1 5 0.9 USW00027516 <1 5 9.4 No 2002 2010 55 17.66 13 0.24BER 32.3008 −64.7660 60 Yes 0.62 6.7 BDW00013601 11 4 0.7 1998 2010 118 27.42 2 0.02BIL 36.6050 −97.5160 317 1.33 USC00340755 10 305 12.6 USC00340755 10 305 0.7 No 1994 2009 155 12.53 61 0.39BON 40.0667 −88.3667 213 0.81 2.2 USW00054808 1.6 213 1.5 2002 2009 79 28.09 0 0.00BOS 40.1250 −105.2400 1689 3.09 US1COBO0076 7.1 1582 2.0 US1COBO0076 7.1 1582 12.3 No 2004 2009 61 25.74 1 0.02BOU 40.0500 −105.0070 1577 3.05 1.9 US1COWE0209 2.8 1549 13.0 2004 2010 69 25.45 1 0.01BRB −15.6010 −47.7130 1023 3.72 30.5 Grid 0.0 2006 2009 31 28.75 0 0.00CAB 51.9711 4.9267 0 0.88 3.1 063480/99999 <1 2 1.2 2005 2011 75 28.30 1 0.01CAM 50.2167 −5.3167 88 Yes 0.50 UK000003808 <1 88 0.0 UK000003808 <1 88 0.0 No 2001 2001 6 12.92 1 0.17CAR 44.0830 5.0590 100 4.55 FR000075860 <1 105 3.8 FR000075860 <1 105 2.2 1999 2011 134 25.97 2 0.01CLH 36.9050 −75.7130 37 Yes 0.71 8.2 Grid 0.0 2000 2010 139 25.7 4 0.03CNR 42.8160 −1.6010 471 1.59 1.3 080850/99999 6 453 0.0 2009 2012 35 30.04 0 0.00COC −12.1500 96.8333 0 Yes 11.39 1.3 CK000096996 4 4 32.7 No 2004 2008 44 16.41 7 0.16DAA −30.6667 23.993 1287 4.42 14.0 685380/99999 2 1287 1.3 2000 2004 48 29.12 0 0.00DAR −12.4250 130.8910 30 Yes 4.56 1.4 ASN00014015 5 30 0.2 2002 2007 62 28.92 1 0.02DOM −75.1000 123.3830 3233 1.75 898280/99999 2.3 3250 34.5 898280/99999 2.3 3250 34.2 No 2006 2010 45 17.41 10 0.22DRA 36.6260 −116.0180 1007 10.76 2.1 USC00262251 1 1009 0.7 1998 2010 154 28.87 1 0.01E13 36.6050 −97.4850 318 1.22 12.6 USC00340755 9 305 0.7 1994 2009 179 19.39 14 0.08FLO −27.5333 −48.5170 11 Yes 4.15 21.6 838990/99999 15 6 6.9 1994 2005 114 21.03 9 0.08FPE 48.3167 −105.1000 634 2.35 0.9 USW00094060 <1 636 3.0 2002 2010 106 27.38 2 0.02FUA 33.5817 130.3750 3 Yes 0.41 2.7 478070/99999 <1 15 0.0 2010 2012 24 26.96 2 0.08GCR 34.2500 −89.8700 98 0.77 USC00220488 12 67 3.9 USC00220488 12 67 1.6 No 1995 2007 154 29.84 1 0.01GVN −70.6500 −8.2500 42 Yes 5.01 1.3 890020/99999 1.9 50 43.4 1992 2012 237 14.98 26 0.11ILO 8.5333 4.5667 350 2.64 14.3 Grid 0.0 1995 2005 106 26.27 8 0.08IZA 28.3094 −16.4993 2373 Yes 11.31 3.1 SP000060010 <1 2371 29.3 2009 2012 24 27.88 0 0.00KWA 8.7200 167.7310 10 Yes 0.61 21.2 916660/04060 1.5 8 1.7 1999 2010 107 26.17 9 0.08LAU −45.0450 169.6890 350 2.45 Grid 0.0 Grid 0.0 No 1999 2011 99 29.35 0 0.00LER 60.1333 −1.1833 84 Yes 0.40 UK000003005 <1 84 0.1 UK000003005 <1 84 0.6 No 2001 2007 74 30.12 0 0.00LIN 52.2100 14.1220 125 1.01 2.2 010393/99999 <1 112 41.2 1994 2003 64 28.11 1 0.02MAN −2.0580 147.4250 6 Yes 0.87 4.9 920440/99999 1.3 6 22.2 1997 2009 150 21.57 14 0.09MNM 24.2883 153.9833 7 Yes 1.84 0.0 479910/99999 <1 8 0.0 2010 2012 24 30.08 0 0.00NAU −0.5210 166.9167 7 Yes 13.93 4.2 915310/99999 1.1 0 14.9 1998 2008 107 22.53 18 0.17NYA 78.9250 11.9500 11 Yes 1.84 2.2 070070/99999 <1 8 4.4 1997 2011 159 28.48 1 0.01PAL 48.7130 2.2080 156 1.10 14.6 CFR000007150 15 75 3.7 2003 2007 23 27.42 0 0.00PAY 46.8150 6.9440 491 0.82 4.3 066100/99999 <1 491 4.0 1994 2009 187 28.35 0 0.00PSU 40.7200 −77.9333 376 0.69 2.5 USC00368449 9.9 357 0.7 1998 2010 150 26.15 5 0.03REG 50.2050 −104.7130 578 3.28 1.8 CA004010811 <1 580 5.5 2001 2007 73 27.06 2 0.03SAP 43.0600 141.3283 17 Yes 0.59 0.4 JA000047412 <1 26 0.0 2010 2012 24 30.21 0 0.00SBO 30.9050 34.7820 500 8.62 3.0 Grid 0.0 2003 2007 58 27.49 0 0.00SMS −29.4428 −53.8231 489 0.52 37.3 Grid 0.0 2006 2008 12 5.33 8 0.67SOV 24.9100 46.4100 650 12.75 2.7 Grid 0.0 1998 2002 51 29.98 0 0.00SPO −89.9830 −24.7990 2800 1.31 65.3 890090/99999 1.9 2830 74.6 1992 2010 65 7.02 48 0.74SXF 43.7300 −96.6200 473 0.97 1.1 USW00004990 3.4 486 1.9 2003 2010 91 26.73 0 0.00SYO −69.0050 39.5890 18 Yes 6.11 0.2 895320/99999 <1 21 55.9 1994 2011 186 13.88 40 0.22TAM 22.7800 5.5100 1385 13.43 AG000060680 8 1364 0.8 AG000060680 8 1364 0.9 No 2000 2010 130 29.98 0 0.00TAT 36.0500 140.1333 25 0.48 0.4 Grid 0.0 1996 2012 177 14.92 21 0.12TIK 71.5862 128.9188 48 1.54 218240/99999 <1 7 0.0 218240/99999 <1 7 10.9 No 2010 2011 16 23.42 0 0.00TOR 58.2540 26.4620 70 0.94 EN000026242 16 68 0.1 EN000026242 16 68 1.1 No 1999 2011 145 29.79 1 0.01XIA 39.7540 116.9620 32 3.02 Grid 0.0 Grid 0.0 No 2005 2007 34 29.93 0 0.00

a Met. station codes beginning with two letters indicate GHCND stations; codes beginning with numerals indicate GSOD stations; and “Grid” refers to gridded forcings of Sheffield et al. (2006), Adam and Lettenmaier (2003)and Adam et al. (2006).

b Start/end years apply to the period of overlap among records of BSRN and any met stations or gridded forcings.c “Nmo” denotes the number of months contained in the record.d “AvgNdaysMo” denotes the average number of daily observations per month.e “NmoNdaysLt10” denotes the number of months with less than 10 daily observations.f “FracLt10” denotes the fraction of the total number of months with less than 10 daily observations.

42 T.J. Bohn et al. / Agricultural and Forest Meteorology 176 (2013) 38– 49

Fig. 2. Locations of BSRN sites used in this study. Labels “BOS/BOU” and “E13/BIL” refer to pairs of stations (BOS and BOU; E13 and BIL; respectively) located within 50 km ofe

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earest meteorological station having substantial temporal over-ap with the BSRN station was more than 20 km away, the griddedaily meteorology of Sheffield et al. (2006), with monthly precipi-ation rescaled via the methods of Adam and Lettenmaier (2003)nd Adam et al. (2006), was used instead. In all, 42 BSRN sta-ions either recorded temperature or were within 1 km (essentiallyollocated) of a meteorological station with usable temperatures;ix more were within 20 km of a meteorological station. For pre-ipitation, 18 sites were within 1 km of a meteorological station,nd 23 were between 1 and 20 km from a meteorological station.he sources of temperature and precipitation data for each site,long with the percentage of gaps in daily observations, are listedn Table 1.

Because MTCLIM requires continuous input time series, missingalues of daily precipitation, tmin, and tmax were filled by repeatinghe previous day’s values. Gap-filled records were flagged and datarom these days were discarded from our analysis. However, theap-filled precipitation values still might create errors in EF (andherefore VP), by their contribution to the annual precipitation esti-

ates. Nonetheless, as listed in Table 1, most (36) sites had missingalues in less than 5% of records (in some cases due to using grid-ed precipitation); and a further six had missing values in 5–20%f records.

Observations of hourly SWdown and LWdown were available atll BSRN sites. Most (36) BSRN sites also recorded hourly rela-ive humidity (RH), from which we computed hourly VP and vaporressure deficit (VPD) where hourly BSRN Tair was available (here-fter, “observed” VP refers to VP computed from observed RH andbserved Tair). Daily averages of all of these quantities were com-uted for all days in which all 24 hourly records were available.

Testing of MTCLIM 4.3’s correction to SWdown in the presence

f snow required observations of snow water equivalent. Due tohe low frequency of reliable snow data, both at BSRN sites and theearby GSOD stations, we used MTCLIM’s degree-day snow modelstimates as truth.

4. Methods

4.1. Evaluation of daily algorithms

To assess algorithm performance, we ran the MTCLIM andDeardorff–Prata algorithms at each BSRN station for all combi-nations of simulated and observed Tair, SWdown, and VP (withsimulated Tair being the daily average of the hourly spline-interpolated Tair values). In each case, for each BSRN station, wecomputed 12 average monthly errors of the variable in questionacross all days that had 24 h of valid observations. This strategyallowed us to investigate global relationships between algorithmperformance and the climate conditions captured by the monthlycomposites. We also computed a single mean (bias) and mean abso-lute error (MAE) of these average monthly errors across all stationsand months. In addition to the above three variables, LWdown, RH,and vapor pressure deficit (VPD) were computed at hourly inter-vals, keeping VP constant throughout the day at the simulated dailyvalue. These variables were subsequently aggregated to their dailyaverage.

4.2. Global distributions of monthly errors

While the BSRN network samples a wide range of globalclimates, the distribution of stations does not reflect the arealdistribution of these climates (e.g., coastal stations are over-represented). To properly assess the global distribution of errorsfrom the algorithms in this study, we used LOWESS piecewisecurves (Cleveland, 1979) to model the monthly errors as simplefunctions of DTR or EF. Then, using the global 0.5-degree grid-ded meteorology dataset of Sheffield et al. (2006), Adam and

Lettenmaier (2003), and Adam et al. (2006), described in Section3, we computed the monthly average DTR and EF for each land gridcell over the period 1991–2000. For each of the 12 months, we usedthe LOWESS curves to estimate biases in SWdown, LWdown, and RH

T.J. Bohn et al. / Agricultural and Forest Meteorology 176 (2013) 38– 49 43

F anels aa els e ar is figu

abs

4

fmtaustt

5

5

5

maTetw−attotga

TS

ig. 3. Monthly average errors in simulated (TR99) downward shortwave SWdown (pverage daily temperature range (DTR) and b, d) average air temperature (Tair). Panespectively, as a function of DTR.(For interpretation of the references to color in th

t each grid cell, as a function of monthly average DTR or EF. Theias in VP was computed as the product of monthly RH bias andaturation vapor pressure at monthly average temperature Tair.

.3. Evaluation of simulated diurnal cycles

To assess the performance of simulated diurnal cycles separatelyrom the influence of errors in daily values, we removed the daily

ean from all hourly records (with the exception of SWdown). Wehen computed the RMSE, Pearson correlation coefficient (r), andmplitude ratio (the ratio between the standard deviations of sim-lated and observed data) of the simulated hourly anomaly timeeries at each station, and computed the averages of these statis-ics across all stations. For this part of the study, we considered onlyhe case of simultaneous simulation of all variables.

. Results

.1. Performance of daily algorithms

.1.1. Stand-alone shortwave radiationThe TR99 algorithm exhibited a striking difference in perfor-

ance between coastal sites (stations within 5 km of the ocean)nd sites further inland. Errors in SWdown are shown in Fig. 3 andable 2; data points for which observed SWdown < 50 W/m2 werexcluded to ensure that observation errors remained small rela-ive to true values. As shown in Fig. 3a and b, simulated SWdownas relatively unbiased at interior sites (blue dots), with a bias of0.7 W/m2 and mean absolute error (MAE) of 14.7 W/m2 (or −0.4%nd 8%, respectively, of the annual average shortwave flux acrosshe 32 interior stations). These statistics are roughly comparable tohose of Thornton and Running (1999), who found bias and MAE

f 4% and 15% of the annual average across 40 U.S. stations. Takinghese interior sites to be representative of the vast majority of thelobal land surface area, the TR99 algorithm appears to work wellcross all of the world’s climates.

able 2tatistics of monthly errors for the TR99 algorithm for SWdown , in stand-alone and simulta

Mode All (n = 50) C

Mean 178.63 M

Bias MAE B

Stand-alone −17.16 27.78 −Simultaneous −16.28 26.94 −

and b) and cloud transmissivity Tf,max (panels c and d), as a function of a, c) monthlynd f: quasi-observed (blue) and simulated (red) Tf,max at interior and coastal sites,

re legend, the reader is referred to the web version of the article.)

However, the algorithm exhibited a strong negative bias of−47.2 W/m2 (26% of the annual average) and MAE of 51.7 W/m2 atthe 18 coastal sites (red crosses in Fig. 3a and b). These errors rapidlybecame more negative (with a slope of approximately 32 W/m2/◦C)with decreasing monthly average DTR for DTR < 6 ◦C. Errors exceed-ing −50 W/m2 occurred at 10 of the 18 coastal stations, spanningmean monthly temperatures from −10 to 40 ◦C (Fig. 3b).

The cause of the bias appears to be the MTCLIM algorithm forcloud transmissivity Tf,max. Errors between MTCLIM’s Tf,max andquasi-observed fclear (computed as the ratio of observed SWdown toMTCLIM’s Rpot·Tt,max) followed essentially the same pattern as theerrors in SWdown (Fig. 3c and d). Interior sites also exhibited somedegree of negative bias at low-DTR values (<7 ◦C) but this did nottranslate to a large bias in SWdown because the low-DTR conditionsoccurred primarily in winter, when insolation is low. To summarizethe relationship between Tt,max bias and DTR, we fitted a LOWESScurve to the errors from all sites (solid curve in Fig. 3c). This curve,as well as the Tt,max values in Fig. 3e and f, show that the TR99 rela-tionship between cloudiness and DTR (Section 2.1) breaks down atthe lowest DTR values (<5 ◦C), which are found primarily at coastalsites.

Although errors in SWdown at interior sites were generallysmaller than those at coastal sites, positive biases averaging10.4 W/m2 were observed at interior sites on days when theMTCLIM snow model predicted that snow was present. Disablingthe MTCLIM 4.3 snow correction decreased simulated SWdown byan average of 18.2 W/m2, resulting in a smaller overall (negative)bias of −8.2 W/m2. Problems with the snow correction might bedue in part to our assumption of flat topography, as mentioned inSection 2.1. To test this hypothesis, we computed slope, aspect, andhorizon values at five U.S. stations (BON, BOU, DRA, E13, and PSU)using elevations from the Shuttle Radar and Topography Mission

(SRTM) 3-arc-second DEM (Farr and Kobrick, 2000), and comparedsimulations at these five stations using this local topographic infor-mation to simulations using the flat assumption. The results of thiscomparison indicated that the flat assumption caused a consistent

neous SW–VP modes. Units are W/m2.

oastal (n = 18) Interior (n = 32)

ean 180.14 Mean 177.77

ias MAE Bias MAE

47.22 51.67 −0.70 14.7145.90 50.60 −0.65 14.45

44 T.J. Bohn et al. / Agricultural and Forest Meteorology 176 (2013) 38– 49

F idity

u W–VPi

uilfrsmc

5

fu0aTi+acbow−swao

5

ft

TS

ig. 4. Panels a–d: monthly average errors in vapor pressure (VP) and relative humsing observed SWdown) and simultaneous (K97 and TR99 algorithms coupled with S

nterior (e) and coastal sites (f), as a function of EF, for simultaneous mode.

pward shift in SWdown of approximately 3.4 W/m2 (generally smalln comparison to typical wintertime SWdown values outside the highatitudes). Given that large-scale models do not in general accountor topography (not to mention the question of how best to rep-esent the effective slope, aspect, and horizon values of grid cellseveral kilometers in dimension), it may be advisable for large-scaleodel studies at high latitudes to disable the MTCLIM 4.3 snow

orrection.

.1.2. Stand-alone vapor pressure and relative humidityUnder all but the most arid conditions, the K97 algorithm per-

ormed well in estimating VP and RH. For the stand-alone case (i.e.,sing observed SWdown) VP had a global bias and MAE of −0.015 and.188 kPa, respectively (or −1.1% and 14%, respectively, of the aver-ge observed VP value across all stations). As shown in Fig. 4a andable 3, the largest errors were concentrated at arid sites (EFann > 2.5n Table 1), and humid coastal sites, with biases of −0.071 and0.171 kPa (−5.9% and +8.9%, respectively, of the correspondingverage observed values at those sites). These errors will be dis-ussed further in Section 5.1.3. Excluding these sites reduced theias and MAE to 0.019 and 0.059 kPa, or 1.7% and 5.1% of the averagebserved value, respectively. RH (Fig. 4c and Table 4) also performedell at humid (EFann < 2.5) interior sites, with bias and MAE of0.47% and 4.3% (0.6% and 5.6% of the average observed RH at those

ites, respectively). In contrast, while errors in VPD (not shown)ere the same size as those of VP, they comprised a larger percent-

ge (roughly 30%, in the case of MAE) of the average observed valuef VPD.

.1.3. Simultaneous shortwave and vapor pressure simulationsThe MTCLIM simultaneous SWdown–VP algorithm also per-

ormed reasonably well globally. In fact, for SWdown, results fromhe simultaneous simulations yielded slightly smaller biases and

able 3tatistics of monthly errors for the K97 algorithm for VP, in stand-alone and simultaneou

Mode All (n = 36) Humid coastal (n =

Mean 1.3484 Mean 1.9264

Bias MAE Bias M

Stand-alone −0.0151 0.1876 0.1710 0Simultaneous 4.2 −0.0635 0.2069 0.1522 0Simultaneous 4.3 −0.0146 0.2328 0.3247 0

(RH), from all stations, as a function of aridity (EF), for stand-alone (K97 algorithm iteration) modes. Panels e and f: observed and simulated monthly average RH from

virtually identical MAEs (Table 2). However, the basic pattern oflarge negative biases at coastal sites remained.

Simultaneous simulations had a larger effect on the humidity-related terms, but still performed reasonably well at humid interiorsites, where VP and RH both had biases in the range −3% to −5%of average observed values for MTCLIM 4.2 (always performingSW–VP iteration) and 3–5% for MTCLIM 4.3 (only iterating if annualaverage EF > 2.5), as shown in Tables 3 and 4. However, as in thestand-alone case, simulated VP and RH (shown in Fig. 4b and d,respectively, for MTCLIM 4.2) exhibited conditional biases thatdepended strongly on EF, so that biases became large at humidcoasts and arid sites (illustrated by the LOWESS piecewise curvefit to RH errors in Fig. 4d). Switching from MTCLIM 4.2 to 4.3 hadno effect on errors at arid sites, by design; but it did improve per-formance at humid sites slightly (Tables 3 and 4).

For RH in particular, biases outside of humid interiors variedapproximately linearly with ln(EF), reaching up to +10% under wetconditions (monthly EF < 0.4), and down to −40% under the driestconditions (monthly EF > 20). At interior sites, these biases arosebecause simulated RH followed the lower bound of observed valuesas a function of EF (Fig. 4e). At coastal sites (Fig. 4f), where observedRH values exhibited little dependence on EF, biases were causedsolely by the dependence of simulated RH on EF.

5.1.4. Longwave radiationIn stand-alone mode, the combination of Deardorff (1978) full-

sky and Prata (1996) clear-sky schemes performed reasonably well,with a bias of −0.7 W/m2 and an MAE of 7.8 W/m2 (0.2% and 2.5%,respectively, of the average annual observed flux of 315 W/m2).

Monthly errors, plotted in Fig. 5 and listed in Table 5, displayed asmall dependence on DTR, with a slope of 1.20 W/m2/◦C (with 95%confidence limits of ±0.34 W/m2/◦C), as depicted by the solid linein Fig. 5a. Without observations of cloud fraction fcloud (=1 − fclear)

s SW–VP modes at stations that recorded RH. Units are kPa.

8) Humid interior (n = 13) Arid (n = 15)

Mean 1.1481 Mean 1.2127

AE Bias MAE Bias MAE

.2088 0.0193 0.0588 −0.0708 0.2853

.1868 −0.0386 0.0724 −0.1898 0.3235

.3247 0.0598 0.0716 −0.1898 0.3235

T.J. Bohn et al. / Agricultural and Forest Meteorology 176 (2013) 38– 49 45

Table 4Statistics of monthly errors for the K97 algorithm for RH, in stand-alone and simultaneous SW–VP modes, at stations that recorded RH. Units are %.

Mode All (n = 36) Humid coastal (n = 8) Humid interior (n = 13) Arid (n = 15)

Mean 69.38 Mean 75.33 Mean 72.92 Mean 63.25

Bias MAE Bias MAE Bias MAE Bias MAE

Stand-alone −0.9899 9.2785 6.6111 9.3555 −0.4731 4.2701 −5.4439 13.4780Simultaneous 4.2 −4.4891 10.3550 5.9493 8.2240 −3.8496 5.6897 −10.1597 15.1066Simultaneous 4.3 −0.4830 10.7421 12.7177 12.7177 2.5588 4.4903 −10.1597 15.1066

F ction

a by thL

ttfciflc3

lqeirTfst(

TSW

ig. 5. Panels a–d: monthly average errors in downward longwave (LWdown), as a funnd vapor pressure (VP). “All Sim” indicates that both fclear and VP were simulatedWdown at (e) interior and (f) coastal sites, from the “All Sim” case.

o compare with, it is uncertain whether this trend arose fromhe Prata clear-sky algorithm or from our method of estimatingclear based on the ratio of observed SWdown to MTCLIM’s theoreti-al potential radiation Rpot. Nevertheless, these conditional biasesn LWdown were smaller than ±10 W/m2 (±3% of annual averageuxes) over the range of observed DTR values. In a small number ofases, biases at coastal sites reached down to −50 W/m2 and up to0 W/m2 (−15–9% of annual average fluxes).

When we supplied the Deardorff–Prata algorithm with simu-ated fclear (via Tf,max) and VP from MTCLIM, the errors in theseuantities manifested themselves clearly in LWdown, although theirffects were relatively modest in comparison with the correspond-ng errors in SWdown and VP. As shown in Fig. 5b, when fclear waseplaced with MTCLIM’s Tf,max, MTCLIM’s strong negative bias inf,max at coastal sites resulted in strong positive biases in cloud

ractions, which in turn led to higher values of LWdown (a positivehift of 12.8 W/m2 relative to using quasi-observed fclear) due tohe high emissivity (1.0) of clouds. Impacts of VP errors on LWdownFig. 5c) consisted mainly of a general increase in scatter at both

able 5tatistics of monthly errors for the Deardorff–Prata scheme for LWdown , for various comb/m2.

Mode All (n = 36)

Mean 315.4

Bias MAE

Stand-alone −0.71 7.82

Sim Fclear, Obs VP 5.98 10.40

Obs Fclear, Sim VP −1.05 10.18

Simultaneous 4.87 11.59

of DTR, for various combinations of simulated and observed clear-sky fraction (fclear)e simultaneous SW–VP case. Panels e, f: monthly average simulated and observed

coastal and interior sites, with overall MAE increasing from 7.8to 10.2 W/m2. In the simultaneous SW–VP simulations (Fig. 5d),both the strong coastal bias in Tf,max and the general increase inscatter resulting from VP errors combined to yield overall bias andMAE of 4.9 and 11.6 W/m2, respectively (or 1.6% and 3.7% of theobserved mean flux, respectively). In all cases, the dependence oferrors on DTR remained at interior sites, with slopes of 1.28, 2.05,and 1.47 W/m2/◦C, for the cases of simulated fclear, simulated VP, andsimultaneous SW–VP simulations, respectively. Still, global perfor-mance remained quite good; as shown in Fig. 5e and f, monthlyerrors were much smaller than the variation of observed LWdownvalues across all stations. A LOWESS fit to errors at all stations as afunction of DTR is shown in Fig. 5d.

5.2. Global distribution of errors

To estimate the global distribution of biases from these algo-rithms, the LOWESS curves plotted in Figs. Fig. 33b, Fig. 44d andFig. 55d were applied to monthly DTR and EF computed from the

inations of observed and simulated inputs, at stations that recorded RH. Units are

Coastal (n = 14) Interior (n = 22)

Mean 333.0 Mean 304.8

Bias MAE Bias MAE

−2.51 9.25 0.64 6.7410.32 14.66 2.72 7.20−3.74 13.21 0.98 7.90

8.61 16.15 2.19 8.33

46 T.J. Bohn et al. / Agricultural and Forest Meteorology 176 (2013) 38– 49

F iases ia (d), c

0Gaa(tte6

Fs

ig. 6. Global maps of the number of months out of the year in which estimated bverage observed value. For panels (a) and (c), condition is >10%; for panels (b) and

.5-degree gridded meteorological fields described in Section 3.lobal maps of the number of months in which errors exceeded

threshold of 10% of the local monthly mean for a given variablere shown in Fig. 6. Monthly mean errors in SWdown were smallwithin 10% of the local average) year-round over most (80%) ofhe world’s land surface, including tropical interiors (Fig. 6a). Posi-

ive errors exceeding 10% did not occur anywhere. Negative errorsxceeding 10% in absolute value were confined to the coasts (about% of the land surface); the Jialing River basin in China; and to

ig. 7. Diurnal cycles of bias for the variables simulated in this study, for interiortations.

n simulated SWdown (a), LWdown , (b), and RH (c, d) exceed 10% of the local monthlyondition is <−10%.

winter months in northern Europe, northern Siberia, and the Cana-dian Archipelago, when low-DTR combined with low levels of dailyaverage insolation (<50 W/m2), allowing relatively small errors toexceed the 10% threshold. For LWdown (Fig. 6b), monthly errorsgreater than 10% of the local monthly average rarely occurred.

For RH (Fig. 6c and d), biases remained small (below the 10%threshold) for the majority of the year over most of the world’sland surface. However, negative monthly errors exceeding the 10%threshold occurred for 7 or more months out of the year over theworld’s deserts (27% of the global land surface), where RH valuesranged between 10% and 30%. Elsewhere, negative biases in RHexceeded the 10% threshold during dry months sub-tropical regionssuch as the Sahel and boreal North America and Asia. RH also hadupward biases exceeding +10% of the local monthly average overland north of the Arctic circle during summer months and alonghumid tropical and temperate coastlines. Biases in VP followed thesame pattern as RH.

5.3. Evaluation of simulated diurnal cycles

Performance statistics for the simulated diurnal cycles of allvariables are listed in Table 6. Quartiles of the distribution of biaseswere computed across all interior stations to avoid the effects ofcoastal biases on diurnal cycle amplitudes, averaged over eachquarter of the diurnal cycle (hours 1–6, 7–12, 13–18, and 19–24,

local time), plotted in Fig. 7.

The spline interpolation of Tair (Fig. 7a) performed well overall,yielding a mean hourly RMSE across all stations of 1.7 ◦C, a meancorrelation coefficient of 0.78, and a mean amplitude ratio of 1.08.

T.J. Bohn et al. / Agricultural and Forest Meteorology 176 (2013) 38– 49 47

Table 6Statistics of 6-h anomalies (with respect to daily mean) of simulated Tair , SWdown , LWdown , VP, RH, and VPD.

Obs S.D. RMSE Correlation Amplitude ratio

Subset (N) Variable VP Interp? Mean S.D. Mean S.D. Mean S.D.

All (50) Tair (◦C) n/a 2.92 1.66 0.69 0.78 0.24 1.08 0.20SWdown (W/m2) n/a 240.1 91.9 30.9 0.91 0.19 0.82 0.21VP (kPa) No 0.15 0.151 0.149 0.085 0.080 0.075 0.060

Yes 0.15 0.147 0.149 0.28 0.19 0.42 0.16RH (%) No 11.2 10.6 3.8 0.55 0.27 1.29 1.18

Yes 11.2 10.2 3.6 0.56 0.27 1.24 1.13VPD (kPa) No 0.42 0.24 0.14 0.74 0.25 1.14 0.39

0.218.818.7

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tifu2fbsb

Yes 0.42

LWdown (W/m2) No 19.1

Yes 19.1

owever, Fig. 7a reveals consistent negative biases of 0.6–0.9 ◦C inhe morning and positive biases of 0.7–0.8 ◦C in the afternoon. Sincehe daily extremes of simulated and observed Tair were identical,hese discrepancies indicate either incorrect timing of the extremesr too large a radius of curvature in the simulated cycle.

The diurnal cycles of simulated SWdown and VP (Fig. 7b and) were relatively unbiased throughout the day (in comparisonith their monthly MAEs of 14.5 W/m2 and 0.23 kPa, respectively).

Wdown additionally had a high correlation (0.92) with observa-ions, but VP (interpolated between consecutive sunrises) failedo capture the large hourly variability in the observations, leadingo negligible correlation with observations (0.08) and high RMSE0.150 kPa, equivalent to the standard deviation of the observed val-es over a typical day). In contrast, LWdown, RH, and VPD (Fig. 7c–f)ll exhibited diurnal bias patterns comparable in size to theironthly MAEs. LWdown and VPD were biased low in the morning

nd high in the afternoon, while RH exhibited an opposite pattern.hese bias patterns all are consistent with the diurnal bias patternf Tair, because VP, which exhibited no such pattern, is the onlyther diurnally varying term these three variables depend on.

The linear interpolation of VP between consecutive sunrisesielded improvements over holding VP constant (errors not shown),aising the correlation with observations from 0.08 to 0.28, andhe amplitude ratio from nearly 0 to 0.47. However, impacts of thenterpolation on other variables were very small.

. Discussion

Our findings indicate that simultaneous estimation of SWdown,P, and LWdown, via the coupled MTCLIM/Deardorff–Prata system,orked well over the majority of the world’s land surface. Theain exceptions were along coasts (6% of the land surface) and

n arid regions (27% of the land surface), where SWdown and VP,espectively, exhibited substantial negative biases. In addition, cou-ling the algorithms generally did not increase errors substantiallyelative to the algorithms’ results in stand-alone mode. The onlyxception was for humidity in arid regions, where performance waslready poor in stand-alone mode (although not shown here, wenvestigated replacing the 2-pass SWdown–VP iteration with itera-ion until values stabilized, and found that gains after the secondass were negligible).

The negative biases we found in SWdown and Tf,max were concen-rated along the coasts and occurred to a lesser degree in humidnteriors. This corroborates the findings of TR99, in which sitesrom coastal Florida produced outliers in their Fig. 5 that indicate annderprediction of Tf,max (Ball et al., 2004; Almeida and Landsberg,003). Our findings also resolve the question whether TR99 per-

orms well in tropical interiors: while TR99 may exhibit negativeiases in tropical interiors, these are generally small in compari-on with typical daily insolation values. One explanation for coastaliases in Tf,max could be the moderating influence of the ocean on

3 0.14 0.74 0.25 1.11 0.37 4.8 0.37 0.21 0.75 0.32

4.8 0.38 0.21 0.77 0.32

DTR, which could cause TR99 to erroneously assume the presenceof cloud cover. From the observations at coastal sites (Fig. 3f), itappears that a simple solution could be to implement a lower bound(e.g., 0.6) on Tf,max or to bias-correct Tf,max when daily DTR < 6 ◦C.

For humidity, our results corroborate the findings of K97 andPierce et al. (2012): performance was poorest in arid interiors (neg-atively biased) and along coasts (negatively or positively biasedat arid or humid coasts, respectively). The cause of these biasesmay be the K97 relation between humidity and local precipita-tion (equation (4)). Pierce et al. suggested that MTCLIM’s 90-dayprecipitation window for estimating aridity may be too short inMediterranean climates with long dry seasons. Similarly, alongcoasts, the ocean appears to provide a relatively constant moisturesource (RH between 65% and 85%) regardless of rainfall (Fig. 4f).

For LWdown, errors were generally small in comparison withtheir observed values. However, the dependence of errors on DTRresulted in positive biases of 10–20 W/m2 over regions with highDTR, such as the arid western U.S. This corroborates the findings ofMo et al. (2012), who found that coupling MTCLIM with the TVA(1972) LWdown algorithm yielded estimates of LWdown that were10–20 W/m2 higher than those of the NARR (Mesinger et al., 2006)over the western U.S. Use of observed cloud fractions as an input tothe full-sky scheme could help determine the cause of these errors.

The biases in these algorithms could be expected to affect simu-lations of the land surface water and energy budgets, although theexact nature of the impacts would be location- and model-specific.In general, we could expect that negative radiation biases wouldyield lower surface temperatures along coasts, and negative humid-ity biases would lead to overestimation of evaporative demand inarid regions.

Our findings suggest potential improvements to the observ-ing strategy at the BSRN. Perhaps the most glaring omission atBSRN stations was the lack of collocated precipitation observations,needed by both TR99 and K97. Using records from the nearest mete-orological station often resulted in our having to discard up to 50%of the BSRN data record due to gaps in the precipitation observa-tions. Another useful variable to measure is clear-sky (or cloud)fraction, which could potentially help improve the performance offull-sky LWdown estimates. The lack of air temperature observationsat some stations should also be addressed. In terms of area, coastalclimates are over-represented within the network. More observa-tions of SWdown in tropical interiors could help further resolve thebehavior of low-DTR biases in TR99 Tf,max.

7. Conclusion

We conclude that

• Separate applications of the TR99 algorithm for SWdown and K97algorithm for VP performed reasonably well under climate con-ditions prevalent over most (73%) of the global land surface.

4 Fores

•

•

•

A

itwOo

Ar

LeisHes

TSu

8 T.J. Bohn et al. / Agricultural and

Systematic negative biases in the TR99 scheme were restrictedto two cases: large negative biases at coastal sites when dailytemperature range (DTR) fell below 6 ◦C; and smaller negativebiases in continental interiors in the presence of snow (remediedby the snow correction of MTCLIM 4.3 if topography is taken intoaccount).Simultaneous estimation of SWdown and VP had little impact onSWdown, but introduced large negative biases into VP and RH underthe most arid conditions. Globally, the largest negative humiditybiases were concentrated over the driest 27% of the global landsurface.Of the full-sky longwave algorithms tested, the Prata (1996) clear-sky algorithm, combined with the full-sky scheme of Deardorff(1978), performed best. However, using the cloud transmissivityestimated by TR99 as an estimate of clear-sky fraction (fclear) bothcreated a positive bias of LWdown at coastal sites and introduceda dependence of LWdown errors on DTR at interior sites. Globally,the LWdown biases were highest over deserts and mountains, butalmost never exceeded 10% of the local monthly average observedvalues of LWdown.Our method of interpolating the diurnal cycle of Tair yieldeda moderate RMSE (5–10% of DTR) and high correlation withobserved hourly values, but showed negative biases in the morn-ing and positive biases in the afternoon. These biases, in turn,caused corresponding negative (morning) and positive (after-noon) biases in VPD and LWdown, and biases in the oppositedirection for RH.

cknowledgments

We thank Gert König-Langlo of the World Radiation Monitor-ng Center (WRMC) for providing us with observational data fromhe Baseline Surface Radiation Network (BSRN). The work hereinas supported by grant no. NA08OAR4320899 from the Nationalceanographic and Atmospheric Administration to the Universityf Washington.

ppendix A. Comparison of full-and clear-sky longwaveadiation algorithms

Many previous studies (e.g., Wood et al., 2002; Andreadis andettenmaier, 2006; Christensen and Lettenmaier, 2007; Hayhoet al., 2007; Wang et al., 2009) that used MTCLIM 4.2 to providenputs to a longwave algorithm used the TVA (1972) full-sky

cheme. We initially used the TVA scheme for this study as well.owever, during our analysis, we noticed that monthly LWdownrrors exhibited a strong dependence on DTR, even when the TVAcheme was run in stand-alone mode, i.e., given observed Tair and

able A1tatistics of monthly errors of simulated full-sky longwave radiation, employing two diffsing observed Tair and VP as inputs.

Full-sky algorithm Clear-sky algorithm Bias (W/m2) Bias/Observed

TVA (1972) Anderson (1954) 3.2 0.010

TVA (1972) 4.4 0.014

Brutsaert (1975) −10.2 −0.032

Satterlund (1979) 3.9 0.012

Idso (1981) 16.4 0.052

Prata (1996) −1.6 −0.005

Deardorff (1978) Anderson (1954) 1.5 0.005

TVA (1972) 2.6 0.008

Brutsaert (1975) −9.1 −0.029

Satterlund (1979) 1.9 0.006

Idso (1981) 11.1 0.035

Prata (1996) −2.1 0.007

t Meteorology 176 (2013) 38– 49

VP, and quasi-observed fclear as inputs. To determine the source ofthese errors, we evaluated the performance of six different algo-rithms for clear-sky longwave emissivity (Anderson, 1954; TVA,1972; Brutsaert, 1975; Satterlund, 1979; Idso, 1981; Prata, 1996),and two full-sky LWdown schemes (TVA and Deardorff) in stand-alone mode.

The Deardorff (1978) full-sky scheme and the Prata (1996) clear-sky algorithm are described in Section 2.4. For descriptions of allother clear-sky algorithms except TVA, we refer the reader to theoriginal papers. The TVA (1972) algorithm is a full-sky scheme inwhich the contributions from cloud and clear-sky emissivities arenot explicitly separated:

LWdown = KEa�T4air (A1)

where K = 1 + 0.17N2 (unitless), cloud correction factor N =√(1 − It/Ic

)/0.65 (unitless), and It/Ic is the ratio of actual to clear-

sky SWdown.The TVA clear-sky emissivity is solely a function of VP:

Ea = 0.740 + 0.0049 VP (A2)

where VP is in h Pa.We then ran 12 sets of simulations, covering all combinations

of the two full-sky schemes (TVA and Deardorff) and six clear-skyemissivity algorithms. Statistics of monthly errors for all stations,for all 12 combinations of clear-sky and full-sky schemes, are listedin Table A1. All schemes performed reasonably well, with MAE val-ues less than 24 W/m2 or 8% of the average annual observed fluxof 315 W/m2. Across all clear-sky algorithms, the Deardorff full-skyscheme consistently outperformed the TVA scheme, with smallerbiases and MAE than TVA for each clear-sky algorithm. Amongclear-sky algorithms, the Prata algorithm, combined with the Dear-dorff full-sky scheme, exhibited the lowest MAE (12.2 W/m2, or3.9% of the average annual flux) and yielded the third lowestbias (−2.1 W/m2, or 0.7% of the average annual flux). This cor-roborates the findings of Flerchinger et al. (2009), Niemelä et al.(2001), and Staiger and Matzarakis (2010), all of whom found thatthe Deardorff–Prata (also referred to as Crawford–Prata) combi-nation was among the top-performers of all combinations tested.Therefore, we chose to use the Prata clear-sky algorithm and theDeardorff full-sky scheme for all subsequent analyses.

Another pattern evident across all combinations of full-sky andclear-sky schemes was a dependence of the errors on DTR. Theslopes of these relationships were between 1.0 and 2.6 W/m2/◦C

for all clear-sky schemes except that of Idso (1981). Here, too, theDeardorff–Prata combination outperformed most other schemes,with an error slope of 1.20 W/m2/◦C (95% confidence limits of±0.34 W/m2/◦C).

erent full-sky schemes and six different clear-sky longwave emissivity algorithms,

mean MAE (W/m2) MAE/Observed mean Error slope v. DTR(W/m2/◦C)

14.5 0.046 1.4614.3 0.045 1.0420.8 0.066 1.4418.4 0.058 2.5323.8 0.076 0.0614.4 0.046 0.97

13.0 0.041 1.6412.8 0.041 1.3016.3 0.052 1.5815.9 0.050 2.5618.1 0.057 0.5412.2 0.039 1.20

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