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Observational evidence from two mountainous regions that near‐surface wind speeds are declining more rapidly at higher elevationsthan lower elevations: 1960–2006

Tim R. McVicar,1 Thomas G. Van Niel,2 Michael L. Roderick,3 Ling Tao Li,1

Xing Guo Mo,4 Niklaus E. Zimmermann,5 and Dirk R. Schmatz5

Received 20 December 2009; revised 26 January 2010; accepted 2 February 2010; published 16 March 2010.

[1] Coupling recent observed declines of terrestrial mid‐latitude near‐surface wind speed (u) with knowledge thathigh‐elevation sites rapidly experience climate change ledto an assessment of the regional near‐surface elevationdependence of u (uZ) at two mountainous regions(central China and Switzerland). The monthly uZ werecalculated from 1960–2006. In both regions uZ were higherin winter (∼2.25 m s−1 km−1) compared to summer(∼1.25 m s−1 km−1). For the first time uZ trends werecalculated, the results were strongly seasonal, ranging from∼−0.025 m s−1 km−1 a−1 in winter to ∼−0.005 m s−1 km−1 a−1in summer. For both regions uZ trend results showed that uhas declined more rapidly at higher than lower elevations,even though different u dynamics were observed. The uZtrends have important implications for climatic changes ofcoupled land‐surface/boundary‐layer processes (such asevapotranspiration) at high‐elevation regions where muchof the globe’s fresh water is derived. Citation: McVicar, T. R.,T.G.VanNiel,M. L.Roderick, L. T. Li,X.G.Mo,N. E. Zimmermann,and D. R. Schmatz (2010), Observational evidence from two moun-tainous regions that near‐surface wind speeds are declining morerapidly at higher elevations than lower elevations: 1960–2006, Geo-phys. Res. Lett., 37, L06402, doi:10.1029/2009GL042255.

1. Introduction

[2] Near‐surface wind speed (u) increases as land‐surfaceelevation increases [e.g., McVicar et al., 2007; Miller andDavenport, 1998; Wood, 2000]. At local‐scales it has beentermed “wind speed‐ups” [Miller and Davenport, 1998] and“fractional speed‐up ratio” [Taylor, 1998], and is an im-portant factor for wind energy generation [e.g., Burton et al.,2001], evapotranspiration [e.g., McVicar and Jupp, 1999]and carbon exchange [e.g., Baldocchi et al., 2000]. Re-gionally, the increase of u with elevation is termed the“near‐surface elevation dependence of u” (here abbreviatedas uZ with units of m s

−1 km−1) and has been used tocharacterise variations in scalar u with elevation changes.

This underpins the spatial interpolation of u in mountainousregions allowing physically realistic forms of evapotrans-piration to be calculated [McVicar et al., 2007]. In essence,uZ is the change in horizontal u due to the change in hori-zontal distance on a sloping land‐surface partially governedby changes in air density as land‐surface elevation changes.It is determined using a network of anemometers located at aconstant height above the land‐surface with variable eleva-tion (Figure 1). It is not the vertical gradient of u whichincreases as altitude above the land‐surface increases (due toreduced drag).[3] Recently there has been great interest in the wide-

spread declining trends of u measured by terrestrial anem-ometers at many mid‐latitude sites over the last 30–50 years[see Jiang et al., 2010; McVicar et al., 2008; Pryor et al.,2009; Roderick et al., 2007, and the references therein].These u declines over time (termed a “stilling” [Roderick etal., 2007]) are usually on the order of −0.010 m s−1 a−1.However, all these analyses were conducted without refer-ence to the impact of elevation changes on u, so a keyquestion is to determine if a systematic change in u has alsooccurred as a function of elevation. Assessing both the cli-matology and temporal trends of uZ (the latter metric havingunits of m s−1 km−1 a−1) in mountainous regions is importantas: (i) mountainous regions arguably experience climatechange more rapidly than adjacent lower areas [Beniston,2005; Bradley et al., 2006; Diaz et al., 2003], especiallywithin ±5 °C of the annual 0 °C isotherm in the extratropics[Pepin and Lundquist, 2008]; (ii) over half the globalpopulation live in catchments with rivers originating inmountainous regions [Beniston, 2005], with this watersupporting about 25% of the global gross domesticproduct [Barnett et al., 2005]; (iii) uZ is used to spatiallyinterpolate u in mountainous regions, which is an im-portant factor for assessing evapotranspiration and inter-ception rates [e.g., Barnett et al., 2005; Kaser, 1982;Lundberg and Halldin, 1994; McVicar et al., 2007]; and(iv) stilling has been identified as a key factor in reducingatmospheric evaporative demand, as measured by panevaporation [Rayner, 2007; Roderick et al., 2009; Roderick etal., 2007; Xu et al., 2006a] and reference evapotranspiration[Gong et al., 2006; Xu et al., 2006a]. As actual evapotranspi-ration (ETa) from many mountainous regions is energy‐limited, meaning ETa is limited by potential evapotranspi-ration (ETp) not water availability [Donohue et al., 2007],declines in atmospheric evaporative demand will lead toincreases in annual stream‐flow yielded from such regions(all else being equal). We assess uZ trends by first calcu-lating the monthly uZ from 1960–2006 at two regions with

1CSIRO Land and Water, Canberra, ACT, Australia.2CSIRO Land and Water, Wembley, Western Australia, Australia.3Research School of Earth Sciences, Australian National University,

Canberra, ACT, Australia.4Institute of Geographical Sciences and Natural Resources

Research, Chinese Academy of Sciences, Beijing, China.5Land Use Dynamics, Swiss Federal Research Institute WSL,

Birmensdorf, Switzerland.

Copyright 2010 by the American Geophysical Union.0094‐8276/10/2009GL042255

GEOPHYSICAL RESEARCH LETTERS, VOL. 37, L06402, doi:10.1029/2009GL042255, 2010

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elevation ranges approximating 3,500 m, and then deter-mine the resultant uZ climatology (with units of m s

−1 km−1)and uZ trends (with units of m s

−1 km−1 a−1). This is the firsttime that uZ trends have been reported, and the use of tworegions provides the opportunity to assess similarities (anddifferences) between them.

2. Material and Methods

[4] Monthly average u data (m s−1) from low‐set anem-ometers (10 m) were acquired from the Chinese Bureau ofMeteorology (82 sites) and MeteoSwiss (37 sites) fromJanuary 1960 throughDecember 2006 (totalling 564months).Data quality conforms to the standards and protocols ofeach organisation with no changes in site locations recordedover the 47‐years, yet there is no information regardingnear‐by land‐cover change. While for many of the monthsdata are observed at each site, there are some missing data;the minimum number of sites available in any month is 78and 31 for the Chinese and Swiss regions, respectively.Both regions have large elevation ranges on the order of3,500 m; site elevations range between 53–3,629 m for theChinese region and 203–3,580 m for the Swiss region. TheChinese region is centred on the Loess Plateau locatedat 33.03–41.95°N and 100.13–114.89°E, and the Swissregion covers most of the country (45.87–47.69°N and6.12–10.27°E). Prior to calculating uZ, the u data werecharacterised by: (i) determining u linear trends and testingsignificance at the probability (P) level P = 0.05 using atwo‐sided Kendall tau test to account for autocorrelationat each region only using sites with complete data (i.e.,no missing months—there were 69 and 25 such sites forthe Chinese and Swiss regions, respectively); and poolingcomplete data from each region to calculate time‐series of(ii) annual u and (iii) seasonal u. Due to the annual u seriesfor the Swiss region being non‐monotonic (see results),the break‐point year was calculated using Pettitt’s [1979]method for the annual series and the influence of varyingstart‐dates on resultant trends was determined.[5] For each of the 564 months, all site u observations

within each region were simultaneously fit using ANUS-PLIN (Version 4.36 [Hutchinson, 2006]). An introduction toANUSPLIN for fitting and interpolating hydrometeorolog-ical and climatological data, its advantages over other ap-proaches, and its widespread use, are summarised in Text S1

of the auxiliary material.1 Following McVicar et al. [2007],as the two regions were over 150 km inland [McVicar et al.,2008], the data were fit using a tri‐variate partial thin platespline, which incorporates a bi‐variate thin plate spline as afunction of longitude and latitude and a “constant lineardependence on elevation.” Other topographic and physiog-nomic controls such as local relative relief, local landscapeshape and aspect were not utilised when determining uZ;these were considered uniform over the 47 years. When u isthe dependent variable being fit with ANUSPLIN the“constant linear dependence on elevation” is uZ, a singlevalue determined using all sites in a region. When airtemperature is fit, the “constant linear dependence on ele-vation” is the environmental lapse rate.[6] For the two regions, uZ was generated for each of the

564 months, from which monthly climatologies and trendswere derived. Trend analysis was performed by fitting alinear regression (ordinary least squares) to each monthlyseries with significance determined using a two‐sidedKendall tau test reported at two P levels (P = 0.05 and P =0.1).

3. Results

[7] Figures 2a and 2b show the locations and elevations ofthe sites used in the analysis. For the Chinese region theaverage u trend of −0.0138 m s−1 a−1 (Figure 2c) was inagreement with results presented for other mid‐latitude sites(see the introduction). Figure 2e shows that stilling has beenexperienced since approximately 1970, and was observed ineach season (Figure S1a). In contrast, over the 47‐years, theSwiss u data increased by 0.0067 m s−1 a−1 (Figure 2d).However, since 1983 annual u has decreased by −0.0086 ms−1 a−1 (Figure 2f); with similar levels of stilling observedseasonally (Figure S1b) and a greater number of sites stillingrecently (Figure S2 and Table S1).[8] The monthly series and climatology of uZ shows a

marked seasonality with the control of elevation beingstronger in winter than summer for both regions (Figures 3a–3d). In summer, when solar loading is highest, mesoscaleconvective circulation is often the dominant process con-trolling near‐surface u [Kossmann et al., 1998], whereas in

Figure 1. Schematic illustrating the near‐surface elevation dependence of u (uZ) concept for two stations.

1Auxiliary materials are available in the HTML. doi:10.1029/2009GL042255.

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winter, synoptic frontal‐scale u dominates [Weber andFurger, 2001; Zhang and Lin, 1992] resulting in a largerwinter uZ (Figures 3c and 3d). As synoptic‐scale frontshave larger spatial extents the land‐surface has greateropportunity to alter near‐surface u by dynamically influ-encing near‐surface pressure and temperature gradients.[9] Figures 3e and 3f show the monthly uZ trends (i.e.,

duZ/dt) for the two regions. All monthly uZ trends werenegative for each month‐region combination, except for

April at the Chinese region. A negative uZ trend means thatu was declining more rapidly at higher elevations thanlower elevations. For the Chinese region only winter months(NDJF) had uZ trends that were significant at the P = 0.05level (Figure 3e). In contrast, the Swiss results (Figure 3f)show significant (P = 0.05) uZ trend declines in 10 months(i.e., all months except June and July). Even though thelong‐term u dynamics are markedly different at the tworegions (Figure 2), both had stronger (meaning more nega-

Figure 2. Data characterisation for the two regions: (a and b) site elevations, (c and d) site annual u trends, and (e and f)regional‐average annual u are shown for the Chinese region (Figures 2a, 2c, and 2e) and Swiss region (Figures 2b, 2d, and2f). On Figures 2c and 2d the average (avg), standard deviation (sd), maximum (max), and minimum (min) are shown, andsites with significant trends (P = 0.05) have a ring placed around the dot depicting the trend.

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tive) uZ trend declines in winter (∼−0.025 m s−1 km−1 a−1)than summer (∼−0.005m s−1 km−1 a−1); see Figures 3e and 3f.

4. Discussion

[10] Results presented in Figures 2e, 2f, and S2 and Table S1show that u is dynamic. Values of u linear trends depend onthe start date and observation length. While the 47‐yearincreasing Swiss u trend of 0.0067 m s−1 a−1 (Figure 2d)appears to contradict previous mid‐latitude terrestrial stillingresults (see introduction), this is caused by very low u beingmeasured in the 1960s, hence linear trends over the entireseries are increasing. From 1983–2006 the annual u trenddecreased by −0.0086 m s−1 a−1 (Figure 2f) in line withprevious results.[11] Previously, monthly time‐step uZ climatology has

only been reported for central China using fewer sites (58)over a shorter observation length (21‐years) [McVicar et al.,2007]. Here our results, using 82 sites from a 47‐year series,have similar seasonality and magnitudes to those previously

presented. Additionally, here the seasonality and magni-tudes of the monthly uZ climatology are similar for the tworegions (Figures 3c and 3d). In the only other assessment ofuZ we found, Zhang and Lin [1992, p. 206] reported anannual mean uZ of 2.22 m s

−1 km−1 for 6 paired−sites, whereone site of each pair was located near a mountain summit. Ourannual mean of 1.61 m s−1 km−1 (derived from Figure 3c) hasa similar magnitude; with their value being higher as theyonly use 6 paired‐sites with large elevation differentialswhere uZ would be exaggerated.[12] This is the first time that long‐term trends in uZ in

mountainous regions have been calculated; extending pre-vious efforts assessing climatic change in mountainous re-gions which have primarily focused on air temperatures,freezing height levels and precipitation [e.g., Beniston,2003; Bradley et al., 2009; Durand et al., 2009]. WithHegerl and Solomon [2009] noting that “climate change”means more than “global warming,” and given the above-mentioned impact of stilling reducing atmospheric evapo-

Figure 3. Data analysis of monthly uZ for the two regions: (a and b) time series, (c and d) climatology, and (e and f) trendsare shown for the Chinese region (Figures 3a, 3c, and 3e) and Swiss region (Figures 3b, 3d, and 3f). The legend for c appliesto d, with r2 being the correlation coefficient and RSD being the Root Squared Difference (units = m s−1 km−1) between theobserved and line‐of‐best‐fit monthly uZ mean values.

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rative demand over many mid‐latitude terrestrial surfaces, itis vital that u be characterised for mountainouswater‐yieldingregions, and importantly here significant (P = 0.05) uZ trendshave been detected for two such regions. Results for bothregions, despite experiencing markedly different u dynamics(Figures 2e and 2f), showed declining uZ trends (meaningthat u was declining more rapidly at higher elevations thanlower elevations) that were significant (P = 0.05) for wintermonths at the Chinese region and for 10 months in Swit-zerland (Figures 3e and 3f). Trends at the Chinese region arelikely driven by the interplay of factors governing the eastAsian monsoon including: (i) relative sea‐surface and land‐temperature changes [Xu et al., 2006b]; and (ii) interannualvariations of the El Niño‐Southern Oscillation and NorthAtlantic Oscillation (NAO) [Wu et al., 2009]. In Switzerlandit is likely that changes in the NAO are influencing uZ trends[Beniston, 2005]. Additionally, at both regions, the observedincreasing altitude of the tropopause [Santer et al., 2003]could be a factor contributing to decreasing uZ trends. Weacknowledge that both: (i) analysis at other mountainousregions; and (ii) detailed modelling at these two regions toattribute cause(s) are required; here we primarily detect andreport the trend. Such u‐trend‐elevation analysis and mod-elling will need to use data that are highly‐resolved hori-zontally, using either a network of sites (as used here) or highresolution rasters, as using coarsely resolved rasters willmean that sub grid‐cell elevation changes will be averaged,thereby likely dampening the uZ trend signal to below noiselevels. Additionally, complimentary to the u‐trend‐elevationanalysis conducted here, u‐trend‐height analysis can beperformed using: (i) sites with anemometers at multipleheights; and/or (ii) pressure‐corrected raster outputs at dif-ferent heights above the land‐surface. Our results providefurther weight to previous recommendations that all aspectsof the wind climate need to be better understood throughenhanced measurement, analysis and modelling [McVicar etal., 2008; Pryor et al., 2009], especially for the globallyimportant headwater catchments.

5. Conclusion

[13] Using u observations from near‐surface (10 m) an-emometers from 1960 to 2006 for two terrestrial mid‐latitude regions with large elevation ranges, monthly uZ hasbeen determined. For both regions, the resulting climatologywas seasonal, varying from ∼2.25 m s−1 km−1 in winter to∼1.25 m s−1 km−1 in summer. For the first time uZ trendswere calculated: the results were strongly seasonal rangingfrom ∼−0.025 m s−1 km−1 a−1 in winter to ∼−0.005 m s−1km−1 a−1 in summer. A negative uZ trend means that u hasdeclined more rapidly at higher elevations than at lowerelevations. Across the two regions, the vast majority ofmonths showed declining uZ trends over the 47‐year serieseven though the long‐term u dynamics were markedly dif-ferent. Given that recent stilling is a primary factor reducingatmospheric evaporative demand over many mid‐latitudeterrestrial surfaces and the high reliance on water resourcesderived from such mountainous headwater catchments, it isimportant to determine how widespread declining uZ trendsare globally. Most headwater catchments are energy‐limitedso reductions in u will serve to reduce rates of ETa partially

compensating for increases in ETa due to increasing airtemperatures.

[14] Acknowledgments. We thank the editor and two reviewers forinsightful comments on an earlier draft.

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1

Auxiliary material for Paper 2009GL042255

Observational evidence from two mountainous regions that near-surface wind speeds are

declining more rapidly at higher elevations than lower elevations: 1960-2006

Tim R. McVicar1*, Thomas G. Van Niel2, Michael L. Roderick3, Ling Tao Li1, Xing Guo Mo4,

Niklaus E. Zimmermann5 and Dirk R. Schmatz5

1 CSIRO Land and Water, GPO Box 1666, Canberra, 2601, ACT, Australia

2 CSIRO Land and Water, Private Bag No. 5, Wembley, 6913, WA, Australia

3 Research School of Earth Sciences, The Australian National University, Canberra, 0200, ACT,

Australia

4 Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of

Sciences, Datun Road, AnWai, Beijing 100101, China

5 Land Use Dynamics, Swiss Federal Research Institute WSL, Zuercherstrasse 111, CH-8903

Birmensdorf, Switzerland

McVicar, T.R., Van Niel, T.G., Roderick, M.L., Li, L.T., Mo, X.G., Zimmermann, N.E. and

Schmatz, D.R. (2010) Observational evidence from two mountainous regions that near-surface

wind speeds are declining more rapidly at higher elevations than lower elevations: 1960-2006.

Geophysical Research Letters, 37, L06402, doi:10.1029/2009GL042255.

March 2010

2

DJF (−0.0105, −0.0089)MAM (−0.0006, −0.0075)JJA ( 0.0009, −0.0075)SON (−0.0041, −0.0080)

(a)

DJF (0.0079, −0.0066)MAM (0.0129, −0.0095)JJA (0.0062, −0.0076)SON (0.0078, −0.0102)

(b) Auxiliary Figure S1. Regional-average u is shown seasonally for: (a) the Chinese region; and (b)

the Swiss region. Region-average trends to and from the break-point year are shown as (trend

from 1960 to the break-point, trend from the break-point to 2006); the trends have units of m s-1

a-1. The break-point years are 1982 (China) and 1983 (Swiss), both significant at the P = 0.001

level.

3

46°N

47°N

7°E 8°E 9°E 10°E

avg = 0.0067sd = 0.0250max = 0.0426min = −0.0686n = 25

u Trend (m s−1 a−1) −0.06−0.04−0.02 0.00 0.02 0.04

0.06

46°N

47°N

7°E 8°E 9°E 10°E

avg = 0.0047sd = 0.0212max = 0.0403min = −0.0505n = 25

u Trend (m s−1 a−1) −0.06−0.04−0.02 0.00 0.02 0.04

0.06

46°N

47°N

7°E 8°E 9°E 10°E

avg = 0.0049sd = 0.0145max = 0.0299min = −0.0279n = 25

u Trend (m s−1 a−1) −0.06−0.04−0.02 0.00 0.02 0.04

0.06

46°N

47°N

7°E 8°E 9°E 10°E

avg = 0.0037sd = 0.0173max = 0.0414min = −0.0399n = 25

u Trend (m s−1 a−1) −0.06−0.04−0.02 0.00 0.02 0.04

0.06

46°N

47°N

7°E 8°E 9°E 10°E

avg = −0.0037sd = 0.0224max = 0.0408min = −0.0757n = 25

u Trend (m s−1 a−1) −0.06−0.04−0.02 0.00 0.02 0.04

0.06

46°N

47°N

7°E 8°E 9°E 10°E

avg = −0.0106sd = 0.0347max = 0.0594min = −0.1440n = 25

u Trend (m s−1 a−1) −0.06−0.04−0.02 0.00 0.02 0.04

0.06

Auxiliary Figure S2. Influence of start-date on linear trend statistics for the Swiss region, for all

plots the data ends in 2006. Start-date varies from: (a) 1960; (b) 1965; (c) 1970; (d) 1975; (e)

1980 and (f) 1985. The average (avg), standard deviation (sd), maximum (mx), and minimum

(mn) are shown on all plots, and sites with trends significant at the P = 0.05 level determined

using a two-sided Kendall tau test have a ring placed around the dot depicting the trend. The

number of stations for each significant-trend category (i.e., (i) ‘significant and negative’; (ii)

‘non-significant and negative’; (iii) ‘non-significant and positive’; and (iv) ‘significant and

positive’) are provided in Table S1.

4

Auxiliary Table S1. For the Swiss region number of stations in each significant-trend category

(i.e., (i) ‘significant and negative’; (ii) ‘non-significant and negative’; (iii) ‘non-significant and

positive’; and (iv) ‘significant and positive’) influenced by different start-dates is shown. The

values in brackets are the percentage of the 25 sites which have continuous monthly records

over the 47-years. The trends are linear and significance was determined at the P = 0.05 level

using a two-sided Kendall tau test.

Date Range Significant &

Negative

Non-significant &

Negative

Non-significant

& Positive

Significant &

Positive

1960 - 2006 6 (24%) 3 (12%) 4 (16%) 12 (48%)

1965 -2006 6 (24%) 4 (16%) 6 (24%) 9 (36%)

1970 -2006 5 (20%) 3 (12%) 8 (32%) 9 (36%)

1975 -2006 4 (16%) 7 (28%) 7 (28%) 7 (28%)

1980 -2006 9 (36%) 7 (28%) 7 (28%) 2 (8%)

1985 -2006 13 (52%) 6 (24%) 4 (16%) 2 (8%)

5

Auxiliary Text S1: Introduction to ANUSPLIN: Theory and Applications

THEORY

Wahba and Wendelberger [1980] primarily developed thin-plate spline interpolation, with

Wahba [1990] extending the theoretical development to include covariates (or parametric sub-

models) the resultant model being termed a partial thin-plate spline. Hutchinson [1991; 2006]

has implemented these algorithms in ANUSPLIN (comprising 8 FORTRAN binary executables

suitable for Windows, Unix and Linux operating systems) primarily to fit and spatially

interpolate hydrometeorological and hydroclimatological variables. ANUSPLIN can provide a

spatially varying dependence on covariate(s), usually the covariate is spatially-dense elevation

data derived from a Digital Elevation Model (DEM). Using the elevation data as a covariate

means that the dependent data are fit using a tri-variate partial thin plate spline, which

incorporates a bi-variate thin plate spline as a function of longitude and latitude and a constant

linear dependence on elevation. If the elevation data were used as another independent variable

(i.e., in addition to geographic position indicated by longitude and latitude) this means the

dependent data are fit using a tri-variate thin plate spline as a function of longitude, latitude and

elevation. In the above examples, note that a thin plate spline means no covariate is used

whereas a partial thin plate spline means that a covariate is used.

However, users are not restricted to only using elevation as a covariate in ANUSPLIN,

assuming alternative (and possibly additional) covariate(s) exist which capture more of the

spatial process when fitting and interpolating the dependent data. The ability of other

covariate(s) to capture more of the spatial process is determined when goodness-of-fit statistics

are maximal when evaluating various covariate(s) choices. Here we provide three examples of

6

not exclusively using elevation as a covariate to fit dependent data. Firstly, precipitation has

been fit and interpolated using: (i) aspect only; or (ii) aspect and elevation as covariates

[Hutchinson, 1995; 1998a; 1998b; Sun, et al., 2008]. This means the dependent data

(precipitation) were fit: (i) using a tri-variate partial thin plate spline, which incorporates a bi-

variate thin plate spline as a function of longitude and latitude and a constant linear dependence

on aspect; or (ii) using a quart-variate partial thin plate spline, which incorporates a bi-variate

thin plate spline as a function of longitude and latitude and constant linear dependencies on

aspect and elevation. Secondly, moisture availability, the ratio of actual to potential

evapotranspiration, has been fit and interpolated using three remotely-sensed based covariates

of: (i) fractional vegetation cover; (ii) net radiation; and (iii) the surface-air temperature

differential [McVicar and Jupp, 2002]. This means the dependent data (moisture availability)

were fit using a quint-variate partial thin plate spline, which incorporates a bi-variate thin plate

spline as a function of longitude and latitude and constant linear dependencies on fractional

vegetation cover, net radiation, and the surface-air temperature differential. Thirdly and finally,

pan evaporation has been fit and interpolated using: (i) net radiation; (ii) vapor pressure deficit;

and (iii) wind speed as covariates [McVicar, et al., 2007]. This means the dependent data (pan

evaporation) were fit using a quint-variate partial thin plate spline, which incorporates a bi-

variate thin plate spline as a function of longitude and latitude and constant linear dependencies

on net radiation, vapor pressure deficit, and wind speed.

ANUSPLIN simultaneously uses all site observations in a region by providing the best-fit to the

dependent data by minimising the objective function, usually the generalised cross validation

statistic, within the interacting constraints of the: (i) number of independent variables; (ii)

number of independent covariate(s); (iii) model parameters selected; and (iv) number of

dependent site observations within a region [McVicar, et al., 2005]. A full description of the

7

algorithm and how the ANUPLIN diagnostic statistics are calculated and used is available on-

line [see McVicar, et al., 2005, pp14-18], with more generic introductions to the algorithm being

provided elsewhere [e.g., Hutchinson, et al., 2009; Jarvis and Stuart, 2001, among others]. At

each site within the region independent geographic co-ordinate pairs, independent covariate(s)

values, and the dependent variable values are needed. User directives and examples for the

individual programs that comprise ANUSPLIN are provided in the user notes [Hutchinson,

2006].

Those more familiar with regression modelling can, broadly speaking, consider that ANUSPLIN

generates a spatially varying offset (as if there was no-elevation present) which is additively

modified by a single slope across the whole region (capturing the relationship between the

dependent data and elevation) multiplied by the spatially varying land-surface elevation.

Generically, fitting some dependent data using a tri-variate partial thin plate spline with

elevation as a covariate means:

the fit of dependent data(long, lat) = slope*elevation(long, lat) + offset(long, lat);

where (long, lat) indicates that the variable in question is spatially distributed.

When fitting maximum air temperature (Tmax) using a tri-variate partial thin plate spline with

elevation as a covariate means:

Tmax(long, lat) = ELR*elevation(long, lat) + offset(long, lat);

where ELR is the environmental lapse rate (denoted slope in the generic example above).

When fitting wind speed (u) using a tri-variate partial thin plate spline with elevation as a

covariate means:

u(long, lat) = uZ*elevation(long, lat) + offset(long, lat);

8

where uZ is the “near-surface elevation dependence of wind speed” (denoted slope in the

generic example above).

As can be seen above, uZ is to wind speed as the environmental lapse rate is to air temperature.

Examples of the spatially varying offset (as if there was no-elevation present) when

interpolating air temperature are provided in Figure 4 of McVicar et al. [2007]. Monthly

climatologies of the relationships between the dependent data and elevation when fitting, in turn,

maximum and minimum air temperatures, wind speed and vapor pressure as the dependent data

are presented in Figure 3 of McVicar et al. [2007].

Previous results have shown that spatial surfaces generated from ANUSPLIN were favourable

when compared to those produced with other interpolation algorithms [Jarvis and Stuart, 2001;

Price, et al., 2000], including kriging [Hutchinson and Gessler, 1994; Laslett, 1994]. For

hydroclimatological data there are two examples: firstly, when interpolating precipitation in

Canada, Price et al. [2000] reported that the ANUSPLIN root mean square error was lower than

the GIDS (Gradient plus Inverse-Distance Squared) counterpart for all months in the

mountainous British Columbia/Alberta region and for 10 months in the flatter Ontario/Québec

region. Given that a previous comparison [Nalder and Wein, 1998] showed the superiority of

GIDS over other interpolation methods (including kriging), the results of Price et al. [2000]

provide a strong argument for using ANUSPLIN. Secondly, Jarvis and Stuart [2001, their Table

2] showed that a tri-variate partial thin plate spline implemented using ANUSPLIN out-

performed: (i) optimal inverse distance weighting; (ii) ordinary kriging; and (iii) trend surface

analysis when interpolating daily maximum and daily minimum air temperatures over England

and Wales.

9

APPLICATIONS

ANUSPLIN is a widely used algorithm, it has been used in the following geographic domains:

(i) globally, specifically for the entire global land surface [e.g., Booth, et al., 2002; Hijmans, et

al., 2005; Jones, et al., 1999; Kelly, et al., 1999; New, et al., 1999; , 2000; New, et al., 2002]; (ii)

North America [e.g., Hutchinson, et al., 2009; McKenney, et al., 2001; McKenney, et al., 2006;

McKenney, et al., 2008; Price, et al., 2000]; (iii) South America [e.g., Booth and Jones, 1998];

(iv) Asia [e.g., Hong, et al., 2005; McVicar, et al., 2007; McVicar, et al., 2002; Sun, et al.,

2008]; (v) Australasia [e.g., Hutchinson, 1995; Hutchinson and Bischof, 1983; Hutchinson, et

al., 1984a; Hutchinson, et al., 1984b; Jeffrey, et al., 2001; McVicar and Jupp, 2002; McVicar, et

al., 2008; Sharples, et al., 2005; Tait, et al., 2006]; (vi) Africa [e.g., Booth, 1998; Booth and

Jovanovic, 2002; Booth, et al., 1989; Hutchinson, et al., 1996]; and (vii) Europe [e.g., Jarvis

and Stuart, 2001].

Finally, ANUSPLIN has been used extensively for spatially interpolating a variety of

hydrometeorological and hydroclimatological variables including: (i) precipitation [e.g.,

Hijmans, et al., 2005; Hutchinson, 1995; Hutchinson, et al., 2009; Jones, et al., 1999;

McKenney, et al., 2001; McKenney, et al., 2006; McKenney, et al., 2008; McVicar, et al., 2007;

McVicar, et al., 2002; New, et al., 1999; , 2000; New, et al., 2002; Price, et al., 2000]; (ii) air

temperatures [e.g., Hijmans, et al., 2005; Hong, et al., 2005; Hutchinson, 1991; Hutchinson, et

al., 2009; Jones, et al., 1999; McKenney, et al., 2001; McKenney, et al., 2006; McKenney, et al.,

2008; McVicar and Jupp, 2002; McVicar, et al., 2007; New, et al., 1999; , 2000; New, et al.,

2002; Price, et al., 2000]; (iii) wind speed and wind run [e.g., Hutchinson, et al., 1984b;

McVicar, et al., 2007; McVicar, et al., 2008]; (iv) vapor pressure [e.g., Jeffrey, et al., 2001;

McVicar, et al., 2007]; (v) solar radiation and atmospheric transmittance (or sunshine hours)

10

[e.g., Hutchinson, et al., 1984a; Jeffrey, et al., 2001; McVicar and Jupp, 2002; McVicar, et al.,

2007]; and (vi) pan evaporation [e.g., Jeffrey, et al., 2001; McVicar, et al., 2007].

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13

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14

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2010_GRL_Letter_042255Wind_Lapse_Rate_Trends_V9_SUPP

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