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Calibration and sensitivityanalysis of a spatially-distributed solar radiationmodelDANIEL W. MCKENNEYPublished online: 06 Aug 2010.

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int. j. geographical information science, 1999, vol. 13, no. 1, 49± 65

Research Article

Calibration and sensitivity analysis of a spatially-distributed solar

radiation model

DANIEL W. MCKENNEY² , BRENDAN G. MACKEY³ andBRIAN L. ZAVITZ²² Canadian Forest Service, P.O. Box 490, Sault Ste. Marie, Ontario, CanadaP6A 5M7 . e-mail: dmckenne@nrcan.gc.ca³ Department of Geography, The Australian National University, Canberra,Australia 2700

(Submitted 1 September 1 9 97 ; accepted 1 3 May 1 9 98 )

Abstract. SRAD, a spatially-distributed solar radiation model, was applied to aCanadian boreal forest environment in north-western Ontario. SRAD is gridbased, and factors in both topo- and meso-scaled processes using a digital eleva-tion model (DEM) and local monthly atmospheric parameters as inputs. SRADgenerates estimates of incident, outgoing, and net irradiance, as well as surfaceand air temperatures for each point in the DEM, over any time period rangingfrom one day to one year. Cloudiness and other atmospheric conditions are fac-tored into the shortwave irradiance estimates. From the DEM, the terrain e� ectsof slope angle, aspect, and topographic shading are calculated and used to modifythe estimates of shortwave irradiance. The SRAD-generated irradiance estimatesfor the study region were found to be consistent with irradiance data from othersources. Estimates of irradiance were most sensitive to the parameters of sunshinefraction and cloudiness. Radiation estimates were generated and compared usingboth a 20 m and a 100 m resolution DEM. Extremely low irradiance estimatesgenerated at the ® ne scale were absent at the coarser scale. However the meanvalue of irradiance at both scales was estimated to be the same at 12 .4 MJmÕ 2

day Õ 1 annually. Radiation estimates were also determined at the two scales for aseries of forest research plots. For 91% of the plots, the irradiance estimates duringthe growing season di� ered by less than 0 .5 MJmÕ 2 day Õ 1 between the two scales.Results presented here suggest that SRAD can provide useful input for predictivespatial models in boreal forest ecosystems.

1 . Introduction

The amount of radiation received at the Earth’s surface is a major forcing functionof forest ecology. The photosynthetically active component of radiation is one of themain determinants of biomass production. Radiation is the source for the latent heatof vaporisation, and therefore drives the rate at which water is evaporated from thelandscape to the atmosphere. This process, in turn, in¯ uences soil moisture statusand hence water availability for plants. Radiation levels also a� ect air, surface, andsoil temperatures. In boreal forest ecosystems these temperatures can a� ect the

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D. W. McKenney et al.50

timing of a plant’s active cycle following winter shut-down. It follows that the spatialand temporal distribution of surface radiation will exert a fundamental control onforest pattern. To some degree, therefore, spatial variation in the taxonomic composi-tion of forests, plant productivity, plant growth forms and forest structure shouldtrack the distribution of radiation.

Many factors and processes interact to determine the amount of solar radiationreceived at a given point on the Earth’s surface. These processes operate at a rangeof scales that can be conveniently identi® ed as global, meso, topo and micro. At theglobal scale, the amount of energy that strikes an area on the Earth is highlydependent on latitude and day of the year (day length). This energy, the extraterres-trial irradiance, is the daily power onto a unit area of the ground, if the atmospherewere absent. At the meso scale the presence of an atmosphere reduces the amountof energy that reaches the ground. Air, water vapour and particles in the atmospherere¯ ect a portion of energy back to space, absorb a portion to re-emit it in a lowerenergy form, and scatter a portion to alter the Earth-ward path of the beam. Di� useradiation is scattered out of the solar beam by gases and aerosols. All of this leadsto attenuation of the energy beam. The degree to which the beam will be attenuateddepends upon the volume of air the beam must travel through, which in turn isdetermined by the elevation above sea level, the Sun’s position in the sky, and localatmospheric conditions. The scattering of the energy beam by the atmosphere andclouds leads to some of the energy striking the ground from directions other thanthat of the direct beam of the sun. This is known as the di� use irradiance, and isproportionally increased on cloudy days. Di� use irradiance can be broken downfurther into isotropic (or sky-light) di� use irradiance, which comes from all directionsof the sky, and circumsolar di� use irradiance, which comes from within about ® vedegrees of the direct solar beam. The energy received from the direct beam of theSun is called the direct irradiance and makes up the high-energy sunshine that isevident on sunny days. Together, the di� use irradiance and the direct irradiancemake up the total (or global ) irradiance (see ® gure 1 , and Linacre 1992 ). Theirradiance commonly measured at solar radiation stations is the total amount of allthe Sun’s energy that strikes an unobscured horizontal surface on the ground (McKayand Morris 1985 ). On a completely cloudless day (i.e. the energy path is unobstructedand refraction of the sky is normal), the direct irradiance is at its maximum. Whenthis is the case, the total irradiance is known as the clear-sky irradiance, and can beconsidered the maximum potential irradiance for that location and day of the year.Topo-scaled processes include the terrain e� ects of slope angle, aspect, and topo-graphic shading in further modifying the actual irradiance received at a location.The incident radiation of a location may be reduced by shading from surroundingterrain, or increased by re¯ ection from surrounding terrain. The fraction of re¯ ectedirradiance is denoted by the albedo of the re¯ ecting surface. Finally, in a forestedenvironment, the forest canopy provides a micro-scaled ® lter that modulates theradiation regime experienced by understorey plants.

We have a long-term research goal of undertaking regional and landscape-wideanalyses of forest ecosystems in Canada (see McKenney et al. 1996 a). This demandsgenerating spatially distributed models of the key environmental processes thatdetermine the distribution and availability of heat, light, water and mineral nutrients(e.g. Mackey et al. 1995 , 1996 1995 ). These data are coupled to biological ® eld surveydata to empirically calibrate how forest characteristics vary as a function of theseprimary environmental regimes (e.g. Mackey and Sims 1993, McKenney et al. 1996 b).

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Applying SRAD in boreal forest ecosystems 51

Figure 1 . Components and parameters of the SRAD solar radiation model. Only thoseparameters relevant to incoming shortwave radiation are shown. Modi® ed fromMullen (1995 ).

As part of this ongoing research agenda, this paper examines the application ofSRAD, a spatially distributed radiation model, to a boreal environment, a majorforest biome in Canada.

Solar radiation models have been developed for a number of purposes at anumber of scales (for example, Swift 1976 , Hutchinson et al. 1982 , McKay andMorris 1985 , Bland and Clayton 1994 , Lourens et al. 1995 , Dubayah and Rich 1995 ,Cooter and Dhakhwa 1995 ). The di� culties in developing surface radiation modelsare pronounced in forested landscapes as they often have high relief or rugged

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D. W. McKenney et al.52

terrain, and are inevitably poorly sampled by the meteorological data collectionnetwork. The di� culty with factoring terrain e� ects can now be addressed throughthe development of modelling strategies that utilize digital elevation models basedon a regular grid data structure. In addition to addressing the terrain issue, SRADovercomes the problem of the lack of actual on-site meteorological measurementsby using general atmospheric information about the area of interest. SRAD is acomputer model developed by Ian Moore (1992 ) which calculates spatially distrib-uted estimates of a full radiation budget using as inputs: (1 ) a user-supplied parameter® le which calibrates the model for local meso-scaled atmospheric conditions, and(2 ) a digital elevation model (DEM) of the landscape. The approach used by SRADis to: (1 ) compute Sun position for each time step using latitude, date and time, (2 )determine ground-level clear sky direct and di� use irradiance components using thetransmittance and circumsolar coe� cient, (3 ) compile a set of values for the day(some including topographic e� ects and some not) and using cloudiness, sky view,and albedo, calculate the horizontal and inclined surface irradiance values, and (4 )compute temperatures and outgoing longwave irradiance using the radiation ratio.SRAD has been more fully documented by Wilson and Gallant (1997 ).

The SRAD model has previously been run for only a few locations in Australia(Moore et al. 1993 , Lougheed 1994 , Mullen 1995 ) and one mountainous region inthe western United States (Wilson and Gallant 1997 ). The purpose of this study wasto calibrate and test the robustness of SRAD in a boreal environment. There werea number of parts to this analysis: (1 ) calibration of the model parameter ® le inrelation to meso-scaled atmospheric conditions, (2 ) validation of the model bycomparing output with irradiance data estimated from other sources, (3 ) sensitivityanalysis to determine parameter e� ects on output values, and (4 ) an evaluation ofthe e� ect on the model output of varying the resolution of the DEM. The sensitivityanalysis was particularly important as some of the user-supplied atmospheric para-meters must be derived with varying degrees of di� culty from other climatic data.Also, the estimated errors of some of these parameters are potentially large, or atworst unknown. The sensitivity analysis is needed therefore to evaluate how muche� ort should be invested in estimating any given atmospheric parameter. It is di� cultto determine a priori the optimum resolution for the DEM. Intuitively, a smallerresolution would seem desirable and ® eld experience suggests that a 20 ± 40 m reso-lution should capture discernible terrain e� ects in these landscapes. However, digitaltopographic data and DEMs of this resolution are not generally available, while acoarser-scaled national DEM of approximately 100 m resolution is currently underconstruction (Sims et al. 1997 a). The e� ect of di� erently-scaled DEMs on spatialestimates of irradiance was therefore explored using both a 20 m and a 100 mresolution DEM.

2 . Methods

2 .1 . T he study region

The analyses were based on data from the Rinker Lake study region (approxi-mately 900 km2 in area) located at 49 .1 ß N latitude in north-western Ontario (® gure 2 ).Rinker Lake is the focus of a series of forest research studies including ForestEcosystem Classi® cation (FEC), hydrology, and tree productivity (see Sims et al.1997 b). The area has also been the target of various experimental spatial data basedevelopment exercises, hence the availability of the two di� erently-scaled DEMs.

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Applying SRAD in boreal forest ecosystems 53

Figure 2 . Location of the Rinker Lake study area in Canada.

2 .2 . Building the radiation surface

SRAD is driven by user-directives which ask for the number of time steps, theperiod of calculation, an input DEM, and a parameter ® le. The DEM is a regulargridded point ® le of elevation from which SRAD calculates the topographic e� ectsof slope, aspect, and shading on radiation. Two DEMs covering exactly the samearea have been generated for the Rinker Lake study region. One was a 20 m ® ne-scale DEM generated from nine digital Ontario Base Maps, the other was a 100 mmeso-scale DEM generated from a portion of the 52H National Topographic Seriesdigital mapsheet (Mackey et al. 1995 ). The elevation of the 20 m DEM ranged from371 to 544 m above sea level, and for the 100 m DEM, the elevation ranged from380 to 560 m above sea level. The 20 m DEM was a large ® le of 2 253 001 gridpoints and exceeded the processing capacity of SRAD. It therefore had to be splitinto four equal quarters that were processed separately for a total processing timeof 64 hours on a SPARC10 workstation. The 100 m DEM (90 601 grid points) wasonly 4% of the size of the 20 m DEM and could be processed by SRAD in one runof only four hours. Both DEMs were processed twice by SRAD, once to producedaily irradiance estimates averaged for the annual period, and once to produce dailyirradiance estimates averaged for the growing season period. The growing seasonwas de® ned as the period from 7 May to 21 October inclusive (see Mackey et al. 1996 ).

The parameter ® le is composed of a series of 15 local monthly radiation, temper-ature, and vegetation parameters which SRAD uses to calculate incident and out-going irradiance ¯ uxes, as well as surface and air temperatures for each point in theDEM. These parameters must be calibrated for each study region. The local monthlyparameters for Rinker Lake were derived from such sources as meteorological stationmeasurements, satellite images, modelled data, and published tables. The parameter® le can be created easily if the study region contains a station that collects therequired solar radiation and meteorological data. However, the Rinker Lake area is

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D. W. McKenney et al.54

typical for most boreal research environments in that solar radiation and meteorolo-gical data are not collected on site (mainly due to the prohibitive cost involved, andthe expertise required for the maintenance and calibration of the measurementequipment). In addition, Rinker Lake has only been an area of research interest for10 years, and it is desirable to have at least 20 to 50 years of data in order toadequately capture longer term climatic trends. In lieu of local measurements, thedata used to calculate the monthly radiation parameters were based on meteorolo-gical data from the three nearest available stations (from 580 ± 900 km!). Other inputparameters had to be calculated using published climatological relations (fromvarious sources) and satellite landcover images (Mackey et al. 1994 ). A listing of theparameter ® le used in this study can be obtained from the authors.

While SRAD calculates a net irradiance (or f̀ull radiation budget’), our interestwas limited to incident radiation. Hence the model outputs that pertain to theoutgoing energy after it has already interacted with the landscape (such as longwaveradiation and air temperature) are not dealt with in this paper. Consequently, onlythose local input parameters which directly impact the estimation of incident radi-ation are outlined in detail. These ® ve parameters are the sunshine fraction, cloudi-ness, atmospheric transmittance, circumsolar coe� cient and albedo.

2 .2 .1 . Su nshine fraction

The sunshine fraction S is the daily proportion of bright sunshine. Data describingthis parameter were not directly available. Monthly average sunshine fraction forthe study region was determined using:

S = n /N (1 )

where n is actual number of hours of daily sunshine and N is potential number ofhours of daily sunshine (day length). The average daily number of sunshine hoursfor Rinker Lake were determined for each month by averaging 40 years of dailymeteorological measurements collected at Armstrong (latitude 50 .3 ß ) and ThunderBay (latitude 48 .4 ß ). Daylength may be determined for any latitude (Oke 1987 ) andday (Iqbal 1983 ) as:

N = (2/15 ) cos Õ 1 ((cos hz Õ sinw sind)/cosw cosd ) (2 )

where 2 and 15 are constants which relate the hour angle to daylength; hz is thesolar zenith angle in degrees; w is the geographical latitude in degrees; d is the solardeclination from the plane of the equator in degrees as given by:

d = 23.45 sin ((360/365 ) (dn+284 )) (3 )

23 .45 is the latitude of the Tropic in degrees; 360/365 is the daily fraction of theEarth’s annual rotation about the Sun; the expression (dn+284 ) is relative to21 March when day and night are of equal length and declination is zero; and dn isthe day number which varies from 1 on 1 January to 365 on 31 December(29 February is ignored).

Daylengths are usually calculated with the solar zenith angle set to 90 ß . However,common instruments which measure the number of sunshine hours cannot detectthe weak sunshine when the solar disc is within 5 ß of the horizon at sunrise andsunset (Linacre 1992 ). Consequently, the equation was resolved with wz set to 85 ß ,5 ß above the horizon, to calibrate day length to number of sunshine hours.

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Applying SRAD in boreal forest ecosystems 55

2 .2 .2 . Cloudiness

Cloudiness (b ) is the monthly average fraction of actual radiation to potentialradiation during cloudy periods Wilson and Gallant 1997 ):

b = (Qs/Qo Õ S)/(1 ± S ) (4 )

where Qs is total irradiance (actual radiation); and Qo is clear-sky total irradiance(potential radiation).

Of the 50 stations nation-wide in Canada that collect solar radiation data (McKayand Morris 1985 ), the closest stations to Rinker Lake are Moosonee ( latitude 51 .3 ß ),Toronto ( latitude 43 .7 ß ), and Winnipeg (latitude 49 .9 ß ), which roughly form a trianglewith Rinker Lake at the centre. These stations have recorded over 35 years of hourlytotal irradiance data, which were summed for each day, and then calculated asmonthly averages of daily power (total irradiance in MJmÕ 2 day Õ 1 ). The monthlytotal irradiances for each of the three locations were averaged to approximate12-monthly total irradiances at Rinker Lake in lieu of in situ measured data.

Daily data for total irradiance and sunshine hours exist for Moosonee, Torontoand Winnipeg, and daylengths at each location for each day of the year can becalculated (see equations (2 ) and (3 )). With this information, it is possible to deter-mine those days with 100% of possible sunshine (n/N= 1 , see equation (1 )), and usethe total irradiance values for those days as clear-sky values. However, it was foundthat many days with low amounts of possible total sunshine (n/N <1 , cloudy days)often had higher total irradiance values than days with 100% of possible sunshine.As an alternative method for determining the clear-sky irradiance, the maximumdaily total irradiance for each month from the 40 years’ worth of daily meteorologicalmeasurements was assumed to be from a completely cloudless day. In all cases, themaximum daily total irradiance for each month was also the day of the month withthe longest day length. The monthly maximum total irradiances were plotted againstJulian day, and a polynomial equation was derived from the curve (r2 >0 .99 for allthree locations). The clear-sky irradiance for each Julian day of the year was calcu-lated from the polynomial, and averaged for each month. The 12-monthly clear-sky irradiances at Moosonee, Toronto and Winnipeg were averaged to produce12-monthly clear-sky irradiances for Rinker Lake.

2 .2 .3 . Atmospheric transmittance

The clear-sky atmospheric transmittance at sea level (t ) is the monthly fractionof solar radiation transmitted by the atmosphere (Wilson and Gallant 1997 ):

t = (Q0/Q0 ) Õ 0 .00008 z (5 )

where Qa is extraterrestrial irradiance, 8 Ö 10 Õ 5 is the typical lapse rate of atmospherictransmissivity in metresÕ 1 , and z is elevation above sea level of the study area inmetres. Monthly values of clear-sky atmospheric transmittance at sea level werecalculated by dividing the Rinker Lake monthly average clear-sky total irradianceby the monthly average extraterrestrial irradiance, and correcting at sea level for theelevation of Rinker Lake with the transmittance lapse rate (Wilson and Gallant 1997 ).

Monthly averages of the extraterrestrial irradiance at 10 ß intervals from Õ 60 ßto 60 ß latitude were taken from a table by Linacre (1992 ). The extraterrestrialirradiance values were plotted against latitude and a series of monthly polynomialequations were derived from the curve (r2 >0 .99 for all twelve months). The

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D. W. McKenney et al.56

polynomials were used to determine the average extraterrestrial irradiance for eachmonth at 49 .1 ß N latitude (the study region).

2 .2 .4 . Circumsolar coe� cient

The circumsolar coe� cient of di� use irradiance (Dc) is the monthly fraction ofdi� use irradiance originating near the solar disc, within about ® ve degrees of thedirect solar beam (Wilson and Gallant 1997 ).

Dc= D Qd/I o 24 (6 )

where D is di� use irradiance, Qd is direct irradiance, Io is the insolation (or solarconstant) and 24 is a constant.

The AES has created a suite of computer programs to model solar radiationacross the country. Using total irradiance and sunshine hour data from additionalmeteorological stations, the direct and di� use irradiance components of the totalirradiance were estimated and tabled for 129 sites across Canada (McKay andMorris 1985 ). Thunder Bay and Geraldton (latitude 49 .7 ß ) were the two locationsclosest to Rinker Lake with tabled estimates of component irradiance. The directand di� use component irradiances at Rinker Lake were determined by averagingthe values at these two locations.

2 .2 .5 . Albedo

The surface albedo (a) is the monthly fraction of incident radiation re¯ ected fromthe surrounding terrain

a= �i=1

n

(aI L I ) (7 )

where i is the landcover type, ai is the published albedo for landcover type I, and L i

is the proportion of landcover type i in the study region. The average monthlysurface albedo of the study region was determined from published albedo values ofcommon surfaces (Oke 1987 ) and satellite-derived landcover percentages (Mackeyet al. 1994 ). Although the albedo of snow may vary from 0 .40 to 0 .95 depending onits age (Oke 1987 ), an albedo of 0 .60 was used for the months during which snowis the predominant cover. For the months of December to April inclusive, thisincluded all landcover types except conifers, as they often shed snow. The albedo ofopen water was varied monthly to correspond with the sun’s average monthlyzenith angle.

2 .3 . Validation of SRAD radiation estimates

The purpose of the validation procedure was to compare the radiation estimatesgenerated by SRAD with radiation values as derived from other sources. Validationat a scale commensurate with the estimates produced by SRAD was obviously notpossible. For this reason, a single mean value of irradiance was determined for thestudy area from the SRAD output, at both the 20 m scale and the 100 m scale. As itis standard practice to model and collect radiation data for a horizontal surface,radiation estimated by SRAD for a horizontal surface was used in the validationexercise. For ease of calculation the annual period of irradiance was employed.Validation was by comparison with radiation as: (1 ) measured at nearby radiationstations, (2 ) estimated from interpolated radiation surfaces based on radiation and

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Applying SRAD in boreal forest ecosystems 57

sunshine hour data, and (3 ) estimated from a published map of national radiationisolines.

Average daily irradiance for the annual period was calculated from more than35 years of hourly horizontal surface measurements at the three radiation stationsnearest Rinker Lake. The Moosonee irradiance was 11 .5 MJ mÕ 2 day Õ 1 , Torontowas 13 .0 MJmÕ 2 day Õ 1 , and Winnipeg was 13 .5 MJ mÕ 2 day Õ 1 . These three valueswere averaged to approximate irradiance at Rinker Lake. A computer-generatedradiation model was developed for Ontario based on mathematical interpolation of20 years of sunshine hour data from over 80 meteorological stations, using themethod of Hutchinson and documented for an Ontario application by Mackey et al.(1996 ). From this Ontario radiation surface, radiation for the centre of the RinkerLake study region was interpolated. Finally, with data collected from 50 radiationstations across the country, radiation values were modelled for an additional 129meteorological stations using their sunshine hour measurements. The daily irradiancefor the annual period was tabled for two meteorological stations close to RinkerLake. The Thunder Bay irradiance was 13 .1 MJmÕ 2 day Õ 1 , and Geraldton was11 .5 MJ mÕ 2 day Õ 1 . These two irradiance values were averaged to approximate avalue for Rinker Lake. In addition, the AES produced a series of ® gures showingnational irradiance isolines for monthly as well as annual periods. The irradiancefor Rinker Lake was also inferred from the isolines on the annual period ® gure.

2 .4 . Parameter sensitivity

The purpose of the parameter sensitivity exercise was to identify the parameterswhich have the greatest in¯ uence in determining the model output. The analysis wasperformed by running SRAD with varied parameter values, and comparing theradiation estimates produced using the baseline parameter values. Only one para-meter was varied at a time for each run through SRAD in order to isolate the e� ectsof that parameter. In varying a parameter, all monthly values were set to one value.Each parameter was varied twice; once to a high, and once to a low value. Reasonable,though highly unlikely values were chosen for these extremes. The target set ofparameters were the sunshine fraction, cloudiness, atmospheric transmittance, andthe circumsolar coe� cient, for a total of eight runs varying four parameters twice.Only one quarter of the 20-m resolution Rinker Lake DEM (563 250 grid points)was analysed in these cases for ease of processing. The elevation for this quarter ofthe DEM ranged from 371 to 536 m above sea level, and the radiation estimateswere determined for an inclined surface and the growing season period.

2 .5 . Scale sensitivity

The purpose of the scale sensitivity analysis was to compare radiation estimatesproduced by SRAD using two di� erently-scaled DEMs of the same area. For thisanalysis, radiation as estimated for an inclined surface and the growing season periodwas employed. There are 90 601 grid points in the 20 m DEM with the same X andY co-ordinates as the 100 m DEM. The e� ect of scale on the radiation estimates wasexamined by plotting the 90 601 radiation estimates generated with the 20 m DEM,against the 90 601 radiation estimates generated with the 100 m DEM. Due to theinability to calculate an actual error term for the radiation estimates, a value of0 .5 MJ mÕ 2 day Õ 1 was used as a r̀eference value of di� erence’ between the radiationestimates of the two DEMs. Any value less than this is probably inferring aninappropriate level of accuracy.

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D. W. McKenney et al.58

The e� ect of scale when applied in a forest-related context was also examined,in order to test a forest ecology application of the model. Radiation was estimatedfrom the 20 m and 100 m DEMs for a network of forest survey plots within theRinker Lake study region. Each plot consisted of a 10 m by 10 m quadrat withinwhich detailed vegetation and soil data were collected. The plots were surveyed tohelp generate a Forest Ecosystem Classi® cation, and are consequently known asFEC data. FEC data are not randomly distributed throughout the landscape, as ane� ort was made to ensure that FEC plot locations sampled the full range of topo-graphic features (slope, aspect, slope position, landform, etc.) and landcover classes(forested, wetland, bedrock, etc.) within an undisturbed and mature forest framework(see Sims et al. 1989 , Sims and Uhlig 1992 , and McKenney et al. 1995 , for furtherdetails).

3 . Results and discussion

3 .1 . Validation of SRAD radiation estimates

The average daily shortwave irradiance (calculated for a horizontal surface andthe annual period) of the Rinker Lake study area was determined by SRAD as12 .5 MJ m Õ 2 day Õ 1 , at both the 20 m scale and the 100 m scale. This value is similarto irradiance values: (1 ) measured at three locations and averaged to approximatea value for Rinker Lake (12 .7 MJmÕ 2 day Õ 1 ), (2 ) estimated from an interpolatedradiation surface based on available radiation data supplemented by sunshine hourdata (12 .5 MJ mÕ 2 day Õ 1 ), (3 ) calculated from nation-wide radiation data modelledfrom sunshine hour data (12 .3 MJmÕ 2 day Õ 1 ), and (4 ) estimated from a publishedmap of national irradiance isolines (12 .5 MJmÕ 2 day Õ 1 ).

3 .2 . Parameter sensitivity

A sensitivity analysis of the SRAD input parameters was performed by runningSRAD with varied parameter values and comparing the output with that of thebaseline SRAD run. The results of the analysis are shown in ® gure 3 . Of the fourparameters varied, cloudiness (® gure 3 (a) and sunshine fraction (® gure 3 (b)) resultedin the most deviation from the baseline irradiance estimates. When compared tobaseline runs, the cloudiness value of 0 .80 (i.e. indicating sparse cloud cover) producedextremely high estimates of irradiance, while the low sunshine fraction value (0 .10 )produced extremely low irradiance estimates. Varying the circumsolar coe� cient(® gure 3 (d )) resulted in irradiance estimates that deviated the least from the baselineestimates.

3 .3 . Scale sensitivity

® gure 4 is a visual representation of the radiation estimates generated for aninclined surface and the growing season period of the Rinker Lake study regionusing, (a) the 100 m DEM, and (b) the 20 m DEM. The 100 m DEM generated animage with a lower resolution, as there is only one estimate of radiation per 100 m2

as compared to 25 estimates per 100 m2 for the 20 m DEM. As a result of this gridcoarsening, the radiation appears smoothed across the more generalised landscape.Radiation has been relatively scaled from least (black) to most (white). North facingand shaded slopes appear darker than south facing slopes. Figures 5 (a) and (b) arefrequency histograms displaying the distribution of these radiation values. Althoughthe minimum radiation estimates produced with the 20 m DEM are much lower(5 .7 MJmÕ 2 day Õ 1 ) than those for the 100 m DEM (13 .3 MJ mÕ 2 day Õ 1 ), the number

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Applying SRAD in boreal forest ecosystems 59

Average daily shortwave irradiance (MJ m_2 day_1)

Average daily shortwave irradiance (MJ m_2 day_1)

(a) (b)

(c) (d)

Figure 3 . Sensitivity of four parameters on average daily shortwave irradiance for the growingseason period. Irradiance using high and low ® xed parameter values is compared toirradiance using baseline parameter values (x = mean of 12 monthly parameter values).On each line, the minimum, maximum (end points), and mean values of irradiance forthe study area are indicated.

of points in the 20 m DEM with a value lower than 13 MJ mÕ 2 day Õ 1 comprise only0 .1% of the total number of grid points. Disregarding the di� erence by one order ofmagnitude in the frequency counts, the distribution pro® les of the radiation estimatesproduced using the two DEMs is similar in shape.

Further scale analysis is given in table 1 , which shows the range and mean ofradiation values for an inclined surface derived using both DEMs, for the annualand growing season periods. As expected, ranges and mean values were higher forthe growing season period when compared to annual values for both DEMs. Foreach of the two periods, radiation had identical means across scales (12 .4 MJ mÕ 2

day Õ 1 annually and 16 .4 MJmÕ 2 day Õ 1 for the growing season, note the low standarddeviations associated with the mean radiation values). However the range of valueswas much greater for the 20 m DEM than the 100 m DEM. Table 1 also reportsradiation estimated from both DEMs at the FEC plot locations within the Rinker

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D. W. McKenney et al.60

Figure 4 . Visual representation of average daily shortwave irradiance of the Rinker Lakestudy area for the growing season period using (a) the 100 m DEM, and (b) the 20 mDEM. The amount of irradiance is relatively scaled from least (black) to most (white).Lakes are shown in white with a black border.

Lake study region. Results using this sample of 96 radiation estimates are similar tothose results using all the estimates of radiation. The mean radiation was 12 .4 MJmÕ 2

day Õ 1 annually and 16 .4 MJmÕ 2 day Õ 1 for the growing season period. Di� erenceslie only in the ranges of radiation values, which are much smaller.

A point-by-point comparison was carried out by plotting the radiation estimatesderived with the 20 m DEM, against the radiation estimates derived with the 100 mDEM. All 90 601 grid points common to both DEMs were compared, as well as thesample of 96 radiation estimates corresponding to the FEC plot locations. For bothcases (all grid points and the 96 FEC locations), 88% of the points di� ered by lessthan 0 .5 MJmÕ 2 day Õ 1 for the annual calculation, and 91% of the points di� eredby less than 0 .5 MJ mÕ 2 day Õ 1 for the growing season calculation. Figure 6 displaysthe distribution of the radiation estimates generated using both DEMs, at the 96plot locations for the growing season. Nine per cent of the plots have values thatdi� er by more than 0 .5 MJ mÕ 2 day Õ 1 .

4 . Conclusions

The SRAD model was shown to generate estimates of incident surface radiationin a boreal forest landscape that are consistent with generalised values from othersources. This validation exercise was limited due to the lack of in situ long-termradiation observations at Rinker Lake itself. For the same reason it was not possibleto validate the estimates of radiation as modi® ed by slope angle, aspect and

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Applying SRAD in boreal forest ecosystems 61

Average daily shortwave irradiance (MJ m_2 day_1)

Average daily shortwave irradiance (MJ m_2 day_1)

(a)

(b)

Figure 5 . Frequency distribution of average daily shortwave irradiance for the growingseason period determined using (a) the 100 m DEM, and (b) the 20 m DEM.

topographic shading (though note that the existing AES network of radiometers arelocated on horizontal surfaces, and that this is standard international practice).However, given the agreement with the estimate of average radiation on a horizontalsurface, and the well-established physics underpinning how SRAD models topo-graphic e� ects, we are con® dent that the estimates of radiation on an inclined andshaded surface are likely to be robust.

As mentioned previously, some parameters were di� cult to derive in the absenceof local solar radiation and meteorological data. Consequently, the errors associatedwith the parameters are unknown and it is possible inaccuracies may have occurred.

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D. W. McKenney et al.62

Table 1 . A comparison of radiation estimates for an inclined surface, produced using the20 m DEM and the 100 m DEM for the Rinker Lake study area. Radiation range andmean with standard deviation are given for all points from both DEMs, as well as fora sample of radiation estimates from both DEMs corresponding to the 96 RinkerLake FEC plot locations.

20 m DEM 100 m DEM 20 m DEM 100 m DEMall points all points FEC plots FEC plots

n= 2 253 001 n= 90 601 N= 96 n= 96

Annual radiation (MJmÕ 2day Õ 1 )Range 4 .5 ± 15 .0 9 .5 ± 13 .9 10 .6 ± 13 .7 11 .3 ± 12 .9Mean Ô standard deviation 12 .4 Ô 0 .4 12 .4 Ô 0 .2 12 .4 Ô 0 .4 12 .4 Ô 0 .2

Growing season radiation (MJmÕ 2 day Õ 1 )Range 5 .7 ± 18 .1 13 .3 ± 17 .6 14 .6 ± 17 .4 15 .3 ± 16 .8Mean Ô standard deviation 16 .4 Ô 0 .4 16 .4 Ô 0 .2 16 .4 Ô 0 .4 16 .4 Ô 0 .2

20m DEM average daily shortwave irradiance (MJ m_2 day_1)

100m

DEM average daily shortwave irradiance (MJm

_2day

_1)

Figure 6 . Average daily shortwave irradiance for the growing season period at the 96 RinkerLake FEC plot locations (E ). Irradiance determined at the 20 m scale is plottedagainst irradiance determined at the 100 m scale. Reference lines indicate di� erence inirradiance between the two scales at no di� erence ( ) and 0 .5 MJmÕ 2 day Õ 1

( Ð Ð ).

However, great care was taken in deriving the parameters, and common experienceseems to re¯ ect the trends seen in the monthly variations of the parameters (such asNovember being the lowest sunshine fraction month). Analysis of the parametersshowed that the model was most sensitive to varying, (1 ) the sunshine fraction, and(2 ) cloudiness. The sunshine fraction is not di� cult to determine for a location ifsunshine hour data are available, and in most cases, the nearest meteorological

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Applying SRAD in boreal forest ecosystems 63

station to the area of interest should provide adequate information. The cloudinesshowever, may be quite di� cult to determine, for reasons outlined in the Methodssection. Considering that the cloudiness has a large e� ect on the radiation estimates,and that it may not be easily determined, great care should be taken in deriving thecloudiness parameter. The model was least sensitive to the circumsolar coe� cient.Sensitivities to parameters may vary for areas of interest with terrain that is markedlydi� erent from this application of the model. However, it is safe to assume that theseconclusions will hold for similarly rugged boreal topographies.

In relation to the growing season period of calculation, the radiation valuesgenerated at the 20 m scale that are less than 13 MJ mÕ 2 day Õ 1 are not representedat all at the coarser 100 m scale. However these values are rare, comprising only0 .1% of the landscape. It is important to note that the mean value of radiation forthe study area was determined to be 16 .4 MJ Õ 2 day Õ 1 , regardless of the scale of theDEM. A point-by-point comparison of the gridded radiation estimates generated atthe two scales showed that 9% of the grid points di� ered by more than 0 .5 MJmÕ 2

day Õ 1 for the growing season. Similarly, the radiation at 9% of the FEC plots di� eredby more than 0 .5 MJ mÕ 2 day Õ 1 when estimates at the two scales were compared.

Constructing a 20 m resolution DEM for a landscape is a time-consuming exer-cise. There is also a concomitant increase in the data ® le size and the ® le processingtime as the resolution of the DEM is increased. We note that a national DEM at a100 m resolution is presently being developed for all of Canada (see Sims et al. 1997afor a preliminary discussion). Hence there is a trade-o� between using a readilyavailable 100 m DEM to model radiation, versus the cost and computational com-plexity of developing a 20 m resolution DEM for each new project. The resultssuggest that about 10% of the cells will di� er by >0.5 MJ mÕ 2 day Õ 1 . Consequently,for most applications the 100 m resolution DEM should su� ce.

The results encourage us to think that we now have the ability to generatereliable spatially-distributed estimates of radiation across the entire Canadian borealforest zone at scales commensurate with a landscape-level of ecological analysis. Theresults are also encouraging as radiation is one of the few environmental forcingfunctions for which we can obtain actual rather than index values. The moistureregime for example, is very di� cult to model in boreal forest ecosystems, even withthe aid of DEMs, and a more generalised relative index approach is commonly taken(for example, Mackey et al. 1996 ). Similar problems arise in spatial analysis of thenutrient regime. Ongoing research is aimed at incorporating these radiation valueswith DEM-based estimates of the topographic controls on water ¯ ow (see Wilsonand Gallant 1997 ) to better predict patterns of moisture distribution in the landscape.

Acknowledgments

The authors wish to thank the following individuals for their technical assistanceand advice; Art Groot, Ken Baldwin, Norm Szcyrek, Lisa Venier and Yonghe Wangat the Canadian Forest ServiceÐ Sault Ste. Marie; Mike Hutchinson, John Gallantand Ian Mullen at The Australian National University. John Wilson formerly of theMontana State University at Bozeman, and Tim Bullock at the AtmosphericEnvironment Service, Canada. Daniel McKenney was a Visiting Fellow at the Centrefor Resource and Environmental Studies in the ® nal stages of the manuscriptpreparations.

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