Precipitation and Temperature Estimation Error at Alpine Treeline Ecotones Using the Mountain Climate Simulator Model (MT-CLIM)

PRECIPITATION AND TEMPERATURE ESTIMATION ERRORAT ALPINE TREELINE ECOTONES USING THE MOUNTAIN CLIMATE

SIMULATOR MODEL (MT-CLIM)

Darren R. Grafius and George P. MalansonThe University of Iowa

Department of Geography316 Jessup Hall

Iowa City, Iowa 52242

Abstract: In order to improve modeling of alpine treeline responses to climate change,estimations of snowfall at treeline sites are needed. The MT-CLIM climate model wasevaluated for this purpose by extrapolating precipitation and temperature from standardweather stations at lower elevations to 30 alpine SNOTEL study sites across the westernUnited States. Quantification of the topography between the base stations and theSNOTEL sites was used in inverse distance weighting and compared to straight-lineweighting. The predicted temperature and precipitation under different weighting meth-ods were compared to observed data over three months during the winter of 2006–2007.The errors were mapped and their spatial pattern analyzed. Error patterns indicate stronggradients, particularly in the Pacific Northwest, that are suggestive of areas where addi-tional characteristics of atmosphere-land interactions and boundary layer climatologyneed to be considered in modeling applications. [Key words: treeline, mountain, snow,extrapolation, climate, modeling, MT-CLIM.]

INTRODUCTION

The zone of ecological transition from alpine forest to alpine tundra is a dynamicecotone that is affected by many biotic and abiotic factors and exhibits a great dealof variability and unpredictability at local scales. This alpine treeline ecotone is alsoconstrained by broad climate trends and shows clear spatial patterns at continentalscales (Arno and Hammerly, 1984), making it tempting as a potential indicator offuture climate change (e.g., Kupfer and Cairns, 1996). The duality betweenregional-scale trends and local-scale variation, however, involves complex inter-actions and positive feedbacks that prevent treeline from reacting to climate changein a linear manner (Holtmeier, 2003; Zeng and Malanson, 2006; Malanson et al.,2007, 2009). Additionally, while climate drives continental and regional-scalechanges at these ecotones, the local-scale landscape patterns are heavily deter-mined by site geomorphology (Butler et al., 2007).

Snow is of particular interest from an ecosystem process perspective. The accu-mulation and redistribution of snow plays a major role in feedbacks of seedlingestablishment and survival at treeline (Walsh et al., 1994; Hiemstra et al., 2002,2006; Alftine and Malanson, 2004). Snow plays both positive and negative roles fortrees. It shelters plants beneath the snowpack during the winter and provides waterduring the spring, where well-drained slopes often make water availability a limit-ing factor, but too much snow limits growth when lasting long into the spring and

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Physical Geography, 2009, 30, 4, pp. 285-307.Copyright © 2009 by Bellwether Publishing, Ltd. All rights reserved. DOI: 10.2747/0272-3646.30.4.285

286 GRAFIUS AND MALANSON

summer (Holtmeier, 2003). The establishment and survival of seedlings, rather thanthe survival of adult trees, ultimately results in changes to landscape pattern atalpine treeline ecotones. The impact of snow and microtopographical features onseedlings is therefore key to understanding treeline landscape dynamics (Malansonet al., 2007; Resler and Fonstad, 2009). The nature of these impacts takes the formof positive feedback cycles, in which seedlings establish only in sheltered locationswhere they can avoid damaging wind speeds and extreme temperature whileobtaining sufficient moisture. Such locations are provided by microtopography andexisting stands of trees, in the lee of which blown snow can accumulate to provideadditional shelter and moisture. As new trees grow and provide sheltered areas intheir lee for additional seedlings, the positive feedback continues as trees alter theirlandscape to make it more favorable for future trees (Germino et al., 2002; Alftineand Malanson, 2004). Landscape patterns influence landscape processes, which inturn alter landscape patterns (e.g., Zeng and Malanson, 2006), and at alpine tree-line ecotones the majority of this relationship centers around interactions betweenplants and snow (Hiemstra et al., 2002, 2006; Geddes et al., 2005; Malanson et al.,2007, 2009). The ability to measure or at least model characteristics of snow atalpine treeline ecotones is important, especially when coupled with concerns overhow climate change is affecting world ecosystems and the already-documentedupslope migration of snowpack and freezing level height in some regions (Diaz etal., 2003).

At regional scales, weather monitoring stations are generally too sparse anduneven to provide researchers with the degree of coverage desirable for studyingand predicting weather and climate trends (DeGaetano and Belcher, 2007). Alsodue to their relative inaccessibility, mountain areas generally have less rainfall dataavailable for study, especially in less-developed countries (Celleri et al., 2007). Theability to interpolate and extrapolate meteorological data from existing records tolocations, scales, or times where data are sparse is particularly valuable for gener-ating input for models that can have data and variable needs exceeding the avail-ability of observations. In some cases climate interpolation has been used togenerate useful datasets spanning large geographic areas and time scales to try andreduce data availability problems for future researchers (Legates and Wilmott,1990; New et al., 1999, 2000; Jeffrey et al., 2001). Interpolation algorithms oftenhave to deal with a trade-off between the ability to be user-friendly and involve rea-sonably simple and few inputs, and involving as many relevant factors as possibleto strive for accuracy. Too much complexity and too many inputs quickly result invery complex models that are only usable by specialists intimately familiar withthem (Wilks, 2008).

Precipitation can be particularly complicated to interpolate, capable of beingmodeled as a two-dimensional random field but heavily modified by other weatherand topographic variables. Additionally, the error variability of rainfall measure-ments can lead to amounts of random variability in data that can make interpola-tion overly complex (Cheng et al., 2007). Topographical effects, particularly inmountains, can complicate matters further by increasing rainfall variability overshort distances. Reliable precipitation and snowpack data for mountainous regionsare sparse and difficult to obtain (Anders et al., 2007). The recognition of their

ESTIMATION ERROR AT ALPINE TREELINE 287

importance in understanding and modeling high-elevation precipitation andorographic effects can be traced back several decades, along with attempts toextrapolate these effects from recorded data at lower elevations. However, the com-plex interactions of factors like wind direction and topography in mountainousenvironments coupled with very sparse networks for recording actual data hasalways made the modeling of orographic precipitation difficult and highly scaledependent (Hay and McCabe, 1998; Pandey et al., 2000).

Interpolation methods for climate data are based on underlying mathematicaland geostatistical principles of varying complexity, ranging between inverse dis-tance weighting, weighted local regression (Wilks, 2008), splines (Jeffrey et al.2001), and various types of kriging (Phillips et al., 1992; Nalder and Wein, 1998;Goovaerts, 2000; Attorre et al., 2007; Cheng et al., 2007). The more complex meth-ods necessitate information about the data’s underlying covariance/spatial autocor-relation structure before interpolation can take place, the derivation of which canbe complicated as climate data cannot be expected to exhibit isotropy (freedomfrom varying directional effects) or a stationary mean across entire study areas(Phillips et al., 1992; Sampson and Guttorp, 1992). Due to regional and local dif-ferences in the importance of different climate factors, land-atmosphere interac-tions and spatial interdependencies, no single method will always perform the best(Nalder and Wein, 1998). However, comparative studies of different meteorologicalinterpolation approaches have shown kriging methods to have particularly favor-able results in terms of accuracy and robustness in many cases. This is primarily dueto their ability to include and analyze spatial dependence more fully than othermethods (Goovaerts, 2000; Attorre et al., 2007). Lastly, hybrid approaches thatbuild on the strengths of previous methods while paying closer attention to thescales involved in studying interactions between climate and complex topographysuch as PRISM have proven particularly powerful. Kriging methods implicitly relyon the data to represent their own spatial variability, while climate characteristicsespecially in mountainous regions are often too variable for datasets to be assumedto be fully representative (Daly et al., 1994).

The ability to study climate effects over time at alpine treeline ecotones is partic-ularly complicated due to the relative inaccessibility of these sites throughout muchof the year. Additionally, existing networks of meteorological stations are generallynot located at sufficiently high elevations or with as dense coverage as is necessaryto capture the variability present at treeline. The MT-CLIM (Mountain ClimateSimulator) model was developed to meet the need for weather data at remote siteswith complex terrain, particularly to provide data necessary for ecological and landsurface process model inputs, by extrapolating to a study “site” from supplied dataat a nearby “base” station (Glassy and Running, 1994; Thornton et al., 1997; NTSG,2006). The utility of MT-CLIM for providing estimates of meteorological data atinaccessible mountain study sites has made it ideal for many studies of treelineprocesses and ecology (e.g., Cairns and Malanson, 1997). While more complexalgorithms like those used by PRISM may in many cases produce more accurateresults, the point-to-point nature of MT-CLIM makes it more applicable for certainstudies of specific alpine sites. The available data from PRISM and other climatedatasets tend to average climate variables and elevations over their cells and are not


necessarily representative of specific points and altitudes above this average, partic-ularly in mountain environments where climate is highly spatially heterogeneous(Daly et al., 1994). While MT-CLIM predicts on a point-to-point basis, subsequentwork has been done to expand the MT-CLIM logic and algorithms to wider applica-tions such as the ability to generate predictive surfaces across entire study areas andderive estimates of more complex climate variables like solar radiation and humid-ity (Thornton et al., 1997, 2000). At the same time, recognition of the extensivelocal complexity and fine-scale processes of alpine treeline ecotones has led to thedevelopment of models dealing with the dynamics of treeline pattern and snowredistribution by wind (Hiemstra et al., 2006).

The positive feedbacks that snow is capable of exhibiting on tree species aretied to fine-scale patterns of microtopography, wind speed and direction, andsnow characteristics such as density that occur at too fine a scale to be captured byMT-CLIM. However, regional differences in precipitation and temperature thataffect snow amount and density may be discerned from spatial patterns in how wellMT-CLIM predicts, or fails to predict, those characteristics at alpine treeline sites.The primary goals of this research are to examine prediction error in the MT-CLIMmodel in a variety of representative alpine locations across the western UnitedStates, and to determine to what extent climate variable extrapolation is affected byintervening distance and topography. The purpose of these questions is to deter-mine how important it is that topography be considered when using this model, andif spatial patterns of error highlight regions where the assumptions that drive themodel may be invalid or in need of modification. Investigation of the spatial char-acteristics of model error is the focus of this study, rather than validation of themodel, as this has already been done extensively by previous authors—e.g., Glassyand Running (1994).

LOCATION, DATA, AND MODEL

Because the mountains of western North America consist of multiple ranges withvarying characteristics, this study chose a network of 30 alpine locations to encom-pass the entire region, shown in Figure 1. These locations are not numerous enoughto be considered exhaustive by any means, but their distribution is intended to berepresentative of the variability of alpine treeline ecotones in the western UnitedStates in order to reflect MT-CLIM prediction characteristics across the study area.The sites used in this study as estimation targets were 30 SNOTEL remote weatherstations, part of a network run by the Natural Resources Conservation Service forthe purpose of gathering snowpack and other weather data at high-elevation sites inthe western U.S. and Alaska (NRCS, 2007). By using the SNOTEL stations as estima-tion sites in MT-CLIM, the recorded data at those sites could be compared to modeloutput to gain a measurement of how much prediction error was present. Thespecific sites used were chosen on the basis of their wide distribution and relativeproximity to treeline location.

The base stations used as model inputs consisted of 54 NOAA weather recordingstations, largely located at airports (NCDC, 2007). The three nearest stations withavailable data to each of the SNOTEL sites were chosen, in some cases using the


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same base station for multiple SNOTEL sites. The decision to use three stations foreach site was initially arbitrary but based on the fact that this number is fairly stan-dard for working with climate interpolation models like MT-CLIM, DAYMET andPRISM (cf. Thornton et al., 1997; Daly et al., 2000). Given the spatial characteristicsof available data, it was further decided that using more than three stations wouldin many cases start to bring base stations into the analysis that were too far away tobe relevant, while using fewer would remove the ability to test the effects of base-site distance on model error. Daily maximum and minimum temperature andmonthly total precipitation from these stations were used as inputs for MT-CLIMestimation.

While the primary design focus of MT-CLIM is on the estimation of particularvariables that are necessary for model inputs but often not readily available fromweather stations, such as humidity measurements and incident solar radiation, themodel also derives daily temperature and precipitation measurements using user-supplied lapse rates (Glassy and Running, 1994; Thornton et al., 1997). For temper-ature estimations, this study used the commonly accepted environmental lapse rateof 6.5°C/km in all cases. Although MT-CLIM allows for a customized lapse rate foreach base-site calculation, the decision was made to use a standard lapse rateacross the entire study area in order to test for variations in the applicability of astandard rate. Precipitation is similarly estimated in MT-CLIM by deriving an oro-graphic precipitation lapse rate from user-supplied long-term average precipitationamounts at the base and site. For the SNOTEL sites, these precipitation data weredirectly available from the site records. For the NOAA base stations they wereacquired from a National Atlas dataset produced by the Natural Resources Conser-vation Service and the Spatial Climate Analysis Service at Oregon State University(Daly et al., 2007). Under the normal intended usage of the MT-CLIM model, userswould only have access to recorded precipitation data at the base stations and notat the estimation sites, thereby being forced to rely on interpolated estimates fromother climate models at the sites in order to derive precipitation lapse rates for themodel. It is in using SNOTEL sites where such data are directly available that thisstudy is able to test the validity of this approach. It is important to clarify that theintent of this study is not to validate this approach as the best method for estimatingclimate variables in mountain environments, but to better understand its error char-acteristics in recognition that for many studies it is the best method available.

Lastly, in order to address topographic and elevation effects, MT-CLIM requiresthe input of slope and aspect data from the site and elevation data from both thebase and the site. These were acquired from the U.S. Geological Survey’s NationalElevation Dataset (USGS, 2006).

METHODS AND RESULTS

The following section is organized to combine methods and results together foreach of the two branches of research that were done for this paper. The first twosubsections explain the methods and results of studying the spatial pattern of errorin running the MT-CLIM model, whereas the last two do the same for a second


objective of investigating temporal and spatial variability in the orographic precipi-tation lapse rate across the study area.

MT-CLIM Methods

For the 30 sites studied, daily maximum and minimum temperatures were exam-ined on the 1st and 15th days of December 2006, January 2007, and February2007, as well as total precipitation for those three months. The differences betweenpredicted and observed values, equating to the model error, were used as the basisfor all the analysis in this part of the study. Skew and other characteristics of theerror were investigated by summary statistics.

Because each SNOTEL site had three MT-CLIM predictions from its three nearestbase stations, multiple methods were used to average the three predictions in orderto compare distance and topographical effects. The degree of error at each site wascompared based on one of three averaging methods for the three different predic-tions; a basic mean, an inverse distance weighted average (IDW) in which theweights were the inverse of the straight-line Euclidian distance between the baseand the site with a power of two, and an inverse distance weighted average wherethe weights were the inverse of a derived “topographical distance” with a power oftwo. This topographical distance was calculated in ESRI ArcGIS 9.2 (ESRI, 2006)using the 3D Analyst “surface length” tool that calculates the actual grounddistance between two points, taking topographical features into account. This wasconducted at the resolution of the underlying DEM raster that contained 30-meterpixels. Base station locations, and thus base-site distances, were unfortunatelyheavily determined by data availability but ranged between 19 and 333 kilometers,providing a wide range to test. Vertical distance, the change in elevation betweenthe base and site, was not directly tested because unlike horizontal distanceand intervening topography, vertical distance is already taken into effect by the MT-CLIM algorithm in its calculations of lapse rates and long-term average differences.

As well as being compared statistically, the results of these three averaging meth-ods and their effect on prediction error were mapped to show the spatial distribu-tion of MT-CLIM error across the western U.S. The maps were interpolated inArcGIS 9.2 using a simple inverse distance weighting method with a power of 2,and were made solely for visualizing the spatial pattern of error and not for con-ducting any type of interpolation or analysis, as these would require more datapoints to act as a valid continuous field. Lastly, regression analyses were conductedbetween estimated and recorded data to see how well they agreed.

MT-CLIM Results

Tables 1 and 2 show the summary statistics of the error in predictions made byMT-CLIM. Error in this study was defined as the difference between the observedSNOTEL data and the averaged model predictions for each site, such that positivevalues denote model predictions higher than observed values and negative valuesdenote underprediction. For the purposes of summary statistics all dates were com-bined into a single average data set.


Table 1 shows summary statistics for the prediction error under simple averagingbetween the three MT-CLIM predictions for each SNOTEL site. Both min and maxtemperature measures showed a tendency toward underprediction, while precipita-tion was more closely centered on zero error. However, in all three variables largeanomalies are present as shown by the minimum and maximum values. Table 2shows the summary statistics for the error when averaged by inverse Euclideandistance weighting, and exhibits the same temperature underprediction and highextremes as in the basic averaging method. A third averaging method involving top-ographic distance to test for the potential effects of rain shadows was also consid-ered but produced results that had no significant difference from Euclidean inversedistance weighting. When compared spatially the averaging methods showed thesame patterns and did not exhibit any significant difference. Comparison of a basicaverage of the three model predictions for each site, an average weighted by theinverse of the straight-line Euclidean distance from the site to each base station, andan average weighted by the inverse of the topographically modified distance, wasintended to show if distance and intervening topography played a role in the accu-racy of model prediction. The spatial and statistical patterns remain virtually

Table 1. Summary Statistics for Basic Averaging Errora

AVG Tmax Tmin Prcp

Mean error –4.52 –5.74 0.24

Median error –3.13 –5.77 –1.97

Max error 7.07 14.87 38.47

Min error –29.83 –34.41 –28.59

Standard deviation 6.82 6.23 9.85

aTmax = daily maximum temperature in °C; Tmin = daily minimum temperature in °C; Prcp = total monthly precipitation in cm. Negative values denote model underprediction.

Table 2. Summary Statistics for Euclidian Distance IDW Errora

EUC Tmax Tmin Prcp

Mean error –4.54 –6.14 0.55

Median error –3.14 –5.98 –1.45

Max error 8.78 14.44 49.08

Min error –30.97 –35.06 –27.90

Standard Deviation 6.87 6.42 10.33

aTmax = daily maximum temperature in °C; Tmin = daily minimum temperature in °C; Prcp = total monthly precipitation in cm. Negative values denote model underprediction.


unchanged regardless of which averaging method was used, and a one-wayANOVA with Tukey’s comparison showed no significant differences. Tmax andTmin datasets showed normal distributions while Prcp data were normalized usinga Johnson transformation before comparison.

Figures 2–4 show the average spatial distribution of error for different climatevariables. It is important to note that these figures show interpolations based on theSNOTEL points as marked, and not a continuous field. The choice of displaymethod was made for clear expression of the spatial patterns of error. Figure 2shows the spatial distribution of prediction error for daily maximum temperature(Tmax) using IDW averaging between the three model results. Tmax predictionerror showed consistency across the study dates while exhibiting relative homoge-neity across most of the study area. The notable exceptions are clearly visibleextremes at a few SNOTEL sites where model results consistently underpredictedTmax. The Willow Park site in northwest Colorado is the strongest extreme, with theNiwot site also acting as an anomaly on several dates. The Paradise site on Mt. Rain-ier, Washington, exhibited an uncharacteristically strong underprediction on Febru-ary 1, but this is not readily visible in the average map.

Figure 3 shows the same map for daily minimum temperature (Tmin). Tminshowed less consistency from one date to the next, with a great deal of both spatialand temporal variability across the study area and interval. The same issue of individ-ual stations acting as anomalies appears to be present, but the problem persists acrossmore sites than it did for Tmax and the intensity of the error varied widely betweendates. There was some consistency between dates as to which way prediction errorwent when it existed—i.e., some sites consistently were either close to the mean orunderpredicted, while other sites were either close to the mean or overpredicted.

Fig. 2. Average IDW prediction error for daily maximum temperature in °C. Negative values denotemodel underprediction.


The South Colony SNOTEL site in southern Colorado can be seen on the averagemap to be the strongest consistent source of underprediction for Tmin.

Figure 4 shows the average spatial pattern of error for total monthly precipitationusing IDW averaging. More than Tmax and Tmin, precipitation showed a fairly

Fig. 3. Average IDW prediction error for daily minimum temperature in °C. Negative values denotemodel underprediction.

Fig. 4. Average IDW prediction error in cm/month for total monthly precipitation in cm. Negativevalues denote model underprediction.


consistent pattern whereby most of the study area remains more or less homo-geneous save for several sites in the Pacific Northwest. This region, in particular theWaterhole site in the Olympic Peninsula, consistently showed strong overpredic-tion of precipitation. The Leavitt Lake site in central California also appeared as amore isolated extreme in underprediction.

Figures 5–7 show regression analyses comparing observed values with modeledones for each of the three weather variables used. Figure 5 shows how well Tmaxobservations correlated with model predictions, which had the lowest R2 value ofthe three variables and the linear equation y = 0.2088x + 0.9412 + ε, where ε rep-resents the error or deviation from the regression line. The low R2 value of 0.06,however, is disproportionately affected by the two anomalies visible on the graph,Willow Park and Niwot, the same two sites that were noted as being visibleextremes in Figure 2. A second analysis with these two points removed (darkertrendline) returned a more representative R2 value of 0.64 and the equation y =0.5796x + 1.6823 + ε.

Figure 6 shows the same analysis for Tmin with the equation y = 0.5893x –1.1099 + ε. These data were not affected by strong anomalies the way Tmax was,showing an R2 of 0.60 and exhibiting a dispersed but definite trend in prediction, ifslightly skewed toward underprediction. Finally, Figure 7 shows the correlation forprecipitation, which had the equation y = 0.4952x + 5.3294 + ε and at 0.71 thehighest R2 value. The trend for this graph however, is toward overprediction and afew anomalies are present, particularly the aforementioned Leavitt Lake site.

Fig. 5. Correlation between observed and modeled Tmax. Initial regression equation (dashed line) y =0.2088x + 0.9412 + ε. Anomaly corrected regression equation (thick solid line) y = 0.5796x + 1.6823 +ε. Thin solid line is 1:1 line shown for comparison.


Orographic Precipitation Lapse Rate Methods

In pursuit of a better understanding of the error patterns in MT-CLIM’s precipita-tion estimation, the isohyet differences between bases and sites were mappedacross the study area in the form of an orographic precipitation lapse rate. This rate

Fig. 6. Correlation between observed and modeled Tmin. Regression equation y = 0.5893x – 1.1099 +ε. Thin solid line is 1:1 line shown for comparison.

Fig. 7. Correlation between observed and modeled Prcp. Regression equation y = 0.4952x + 5.3294 +ε. Thin solid line is 1:1 line shown for comparison.


directly expresses the degree to which precipitation amount decreases or increasesas elevation increases. This was calculated as:

The resulting rate is a measure in centimeters of precipitation per kilometer ofelevation change, and is arranged such that a large negative number denotes astrong precipitation increase with rising elevation, and a large positive numberdenotes a decrease with elevation. This was done to map the underlying patternsbeing used by MT-CLIM to derive its estimations of precipitation. Calculation andmapping of this value was undertaken for both the long-term isohyets used as modelinput and the “actual” observed orographic precipitation lapse rate betweenrecorded precipitation data at the bases and sites for the period of this study. For thelatter, both the average monthly precipitation for the three-month study interval andeach individual month were examined to allow investigation of short-term variabil-ity. As with the previous figures, the surface for visual analysis was interpolatedfrom the SNOTEL sites in ArcGIS using an IDW method with a power of 2. A differ-ence map between the long- and short-term average rates was also derived. Finally,the resulting long- and short-term rate distributions were compared.

Orographic Precipitation Lapse Rate Results

Figure 8A shows an interpolated surface of the orographic precipitation lapserate used across the study area by MT-CLIM to estimate precipitation at each of thesites. Precipitation is less directly correlated with altitude changes than temperatureand more heavily modified by local and regional climate trends, making this ratemore spatially heterogeneous than the more common temperature environmentallapse rate. However, in mountain environments and particularly in arid regions likemuch of the American West it is of vital importance. Here it provides a measure ofhow great the difference in average precipitation was between bases and sites,modified by difference in elevation. Positive values, light tones in the map, denotestation pairs where high elevation site precipitation was lower than at the basestations. Most of the map however shows negative values, where precipitation washigher at higher elevations, with the most intensely negative rates being found atstations in the Pacific Northwest and the Many Glacier site in northern Montana.

Figure 8B shows this same orographic precipitation lapse rate but based on theactual three-month average recorded values at bases and sites during the studyperiod rather than the long-term isohyet values. While the short-term data are moreheterogeneous in space and time, the rate shows a slight trend of consistent nega-tive values in the Pacific Northwest region.

Figure 9 shows a difference map between the long- and short-term average rates.Where negative values are shown in the map, long term rates were lower than shortterm rates, leading to model overprediction relative to observed values. The patternshown in this map is largely consistent with the pattern of error in MT-CLIM estima-tion of precipitation across the study area.

Orographic prcp lapse rate base precipitation cm( ) SNOTEL site precipitation cm( )–site elevation km( ) base elevation km( )–( )

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------=


Lastly the distributions of the long- and short-term orographic precipitation lapserate distributions were compared using a one-way ANOVA test with Tukey’s com-parisons after being normalized with a Johnson transformation. Ultimately the testreturned a p-value of 0.779, showing that there was not a significant differencebetween the means of the distributions. Table 3 shows the summary statistics of thedistributions.

Fig. 8. Maps of orographic precipitation lapse rates in cm/km elevation used across the study area,(A) calculated by MT-CLIM from base and site long-term isohyets as annual average and (B) derivedfrom actual recorded short-term three-month average data at the bases and sites.


DISCUSSION

MT-CLIM Modeling Error Characteristics

The summary statistics of the model error highlight a few important results. Theoverall trend of negative values in both Tmax and Tmin shows that the entire studywas skewed toward underprediction in temperature, with MT-CLIM generallyproducing lower estimates than what was observed at the study sites. Giventhat both temperature and precipitation are dealt with in MT-CLIM according to

Fig. 9. Map showing difference of long-term average orographic precipitation lapse rates andshort-term three-month study period average rates. Negative values denote long-term rates lower thanshort-term rates, leading to long-term predictions higher than short-term observations and model over-prediction.

Table 3. Summary Statistics for Precipitation Lapse Rate Distributionsa

PLR Long-term 3-month Dec. Jan. Feb.

Mean –5.55 –5.67 –6.05 –4.66 –6.29

Median –4.20 –5.50 –5.90 –3.29 –5.25

Max –1.61 0.48 4.47 –0.34 –0.19

Min –16.88 –13.54 –15.22 –15.77 –20.79

Standard deviation 3.62 3.42 4.27 4.12 4.54

aPrecipitation lapse rates in cm/km, where more extreme negative numbers denote greater increase in precipitation with elevation.


user-supplied lapse rates, it is therefore likely that the temperature lapse rates usedin this study were inappropriate. The commonly accepted environmental lapse rateof 6.5°C per kilometer of elevation was used, but it is possible that local andregional climate factors altered the actual lapse rate between bases and sites, or thatlocal variability was too great for an overall standard lapse rate to be valid. Thisstandard lapse rate is intended to work at global climate scales and long timescales, while the actual lapse rate can vary greatly at finer spatial scales as well asby season and type of weather pattern (Lundquist and Cayan, 2007; Blandford etal., 2008). MT-CLIM allows for the user to supply a custom lapse rate for each runof the model, so if more were known about the temperature relationships betweeneach base-site pair it is possible that temperature predictions would improve. Giventhat applications for ecological studies in mountain regions generally will not havethese data, regional synoptic analyses are necessary in order to determine appropri-ate lapse rates. The intent in this study was to examine the extent of the error causedwhen using MT-CLIM to make do without those specific data.

The Tmax predictions in Figure 2 show a trend of general homogeneity acrossmost of the study area, showing that for most base-site pairs the model estimationswere relatively consistent, even if according to the statistical results they were con-sistently skewed toward underprediction. This reinforces the notion that the mainproblem in predicting Tmax in this study was a systematic error that might be solvedor minimized by using a more appropriate environmental lapse rate as a modelinput. The existing literature confirms the idea that a single standard environmentallapse rate is not always applicable, especially in mountain environments (Looking-bill and Urban, 2003; Lundquist and Cayan, 2007; Blandford et al., 2008). How-ever, the commonly accepted rate used in this study of 6.5°C per km has beenfound elsewhere to cause overprediction of daily average and minimum tempera-tures, as opposed to the underprediction found in this study, which remains unex-plained (Blandford et al., 2008).

The Tmax predictions are also characterized by the strong anomalous effectsconsistently present at two of the sites and one in particular, Willow Park, CO andto a lesser degree Niwot, CO, both visible as dark patches in the otherwise lightgrey map. The reasons for this are unknown, but there are several possibilities. Anerror in the recording data at either those sites or one of their bases, or perhaps abase station shared by both in this analysis, could cause such an effect, although itdoes not appear to be an effect exactly shared inasmuch as the Niwot site showedthis effect in only four of the six dates, while the Willow Park site showed it at alldates. Another possibility is that there is some local process in that region causingtemperature differences over distance or elevation to behave differently than in therest of the study area that the study did not take into account. One possibility islocal temperature inversions, discussed below.

The spatial pattern of Tmin estimation error showed a greater deal of variabilitythan the Tmax estimation from date to date, with a strong effect by one extremenegative value at the South Colony CO site consistently skewing the statistics.Strong differences due to anomalies or possibly regional effects are present at somedates and absent in others, making it difficult to form any solid conclusions, despitethe relative homogeneity of the average map across all dates. Temperature inversions


during winter nights may play a role in MT-CLIM prediction error and can particu-larly be conceived how Tmin estimates, occurring at night when an inversionwould be present, would be lower than actual if a valley-bottom base station wereaffected by an inversion and the site was not (Whiteman et al., 1999, 2004). Thisfactor could explain anomalies at individual sites where it was taking place, causingthe base-site temperature gradient to deviate from the standard environmental lapserate used in this study. By the opposite effect, local over-predictions could occurwhere SNOTEL sites are situated in local basins suffering inversions while basestations are not.

The map of precipitation error is where a discernible spatial pattern begins toemerge. Most of the study area is more or less homogeneous with a few smallanomalies, while several adjacent sites in Washington and Oregon showed a con-sistent trend of greater overprediction than the rest of the study area. The way thischaracteristic is shared across several nearby sites rather than being a single anom-alous point suggests that there may be a regional difference in the Pacific Northwestthat is causing this consistent difference, at least during some months. This regionaltrend was more or less absent in February. The reason for this trend cannot be com-pletely determined but this region is known to receive particularly high amounts ofprecipitation relative to the rest of the study area, due to its location on the conti-nent with respect to global climate circulation combined with the orographiceffects of several mountain ranges (Daly et al., 2002). Model error in this case rep-resents, in part, a departure from the expected relationship between base and siteprecipitation deriving from the differences in isohyet values between them. Putanother way, the algorithm of MT-CLIM calculated that there would be more precip-itation than observed because of differences between long-term and short-termprecipitation lapse rates, discussed below.

Effects of Distance and Topography on Model Performance

While the effect of distance and topography was one of the interests of this study,the comparison of the three averaging methods did not produce significant results.Both summary statistics and spatial pattern showed minimal differences in outputdata whether the three calculations for each site were averaged normally, averagedusing Euclidean IDW, or using topographic IDW. While distance should beassumed to play a role in estimation accuracy at some level given the spatial auto-correlation shown by climate and other natural systems, the scales used in thisstudy failed to capture any significant effects of it.

Orographic Precipitation Lapse Rate Characteristics

The spatial pattern of the orographic precipitation lapse rate derived and used byMT-CLIM showed interesting trends and reinforced those visible in the precipitationerror maps. While the sparse network available for this study prevents strong con-clusions from being drawn about regional trends, the patterns displayed were sug-gestive and may indicate such trends that would warrant further study. The apparentregional trend of the Pacific Northwest having different precipitation characteristics


than the rest of the study area is clearly visible, with the high negative rates in Figure8 specifically showing that precipitation values rise more quickly as elevationincreases than in the rest of the country. Several individual sites elsewhere in thecountry also showed particularly high negative outlying rates in individual months,but these points did not show the high MT-CLIM errors that the Pacific Northwestsuggested as a region. It is therefore possible that these extreme rates are simplyvalid local characteristics that produced accurate model results, unlike the North-west. In the Pacific Northwest, the more extreme lapse rates led to overpredictionof the actual precipitation present at those sites, suggesting that those lapse rates,and thus the overall relationships between base and site long-term average precip-itation, differed between the study period and historically. If so, this is not wellrepresented in Figure 8B, in which the observed orographic precipitation lapse ratewas seen to be generally but not intensely negative across the study area, with aregional trend of being more largely negative across the Pacific Northwest. Thisnegative rate, present in both the short-term and long-term maps, implies thatprecipitation was in most cases higher at higher elevations where the SNOTEL sitesare located, than at lower elevations where the base stations were situated. This isconsistent with existing knowledge about orographic precipitation in mountainousregions that air masses rising against mountain slopes release more precipitation athigher altitudes than lower ones (Daly et al., 1994; Hay and McCabe, 1998; Pandeyet al., 2000; Dettinger et al., 2004). As such, the over-prediction of precipitation inthe Pacific Northwest seems to be caused primarily by a difference in the intensityof this relationship between long-term historical trends and the short-term onesobserved in the study, rather than by the relationship being absent or fundamentallydifferent. Given the sparse network of data points used in this study, local differ-ences between bases and sites may have played a role in this pattern. However,given the geographic location and characteristics of this pattern, the authors believethat the vertical properties of air masses coming off the ocean are more likely tocause these differences from the rest of the study area.

This interpretation is consistent with the findings shown in Figure 9, where thedifferences between long-and short-term average rates match closely with thespatial pattern of modeling error, with the sole exception of the Many GlacierSNOTEL site in northern Montana. Additionally, there is a degree of short-term vari-ability in the orographic precipitation lapse rate, showing changing values andpatterns from month to month. This echoes previous findings in literature that in theOlympic Peninsula, particularly, long-term annual precipitation is relatively stablefrom year to year but the short-term variability is large (Anders et al., 2007). Addi-tionally, the accurate measurement of rainfall, especially in mountain regions, haslong been recognized as a difficult and error-prone process. Mean annual precipi-tation measurements represent a particular danger as they are the starting point formany ecological and hydrological studies including this one, and as such, measure-ment errors can propagate through the entire study (Dingman et al., 1988). Becausethis study necessarily compared data from different sources in addition to differ-ences in climate between bases and sites, there remains the possibility that some ofthe error in this study originated as measurement error.


The short-term variability of precipitation in some cases may be considerableenough to call into question the validity of assumptions that short-term precipita-tion estimations can be derived from long-term average precipitation differences;however, a statistical comparison of long-term and short-term rates showed thatthey were not significantly different. The orographic precipitation lapse rate, whilestatistically consistent across time for the entire study area, is visibly variable tosome degree in both space and time, and this variability appears to be the primarycause of the spatial pattern of error in this study. While the statistical measures showno significant differences for the entire study area, the visual patterns show individ-ual locations where this variability may be significant over time. That this variabilityis not taken into account by MT-CLIM to any degree at all could be an importantconsideration to researchers using the model if other spatial and temporal scales docreate a significant difference. Further, climate models that base their functionalityon historical relationships within the climate system are generally ill equipped toaddress future climate change scenarios, inasmuch as stationarity of the climate’sfundamental relationships cannot be assumed in these scenarios (Leung and Ghan,1995; Leung and Wigmosta, 1999).

The implications of these findings to the study and modeling of pattern/processrelationships at alpine treeline ecotones, while not definitive, are important. Therelative inaccessibility of these ecotones for much of the year and the complexityinherent to them often forces researchers to rely on models and estimates of actualprocesses and values. While there is no way around the need for assumptions, theimportance of constantly re-evaluating these assumptions to ensure they are validfor the work at hand cannot be understated. The work presented here suggests thatsome common assumptions about the estimation of precipitation in mountainregions, specifically that they are sufficiently consistent in space and time towarrant the use of long-term average relationships as the basis for such estimation,may not always be valid.

CONCLUSIONS

This study examined the spatial patterns of error in temperature and precipitationextrapolation using the MT-CLIM model in areas of complex alpine topography.Both daily maximum (Tmax) and minimum (Tmin) showed trends of underpredic-tion, with Tmax error remaining relatively homogeneous while Tmin error experi-enced more spatial variability. It is suggested that the consistent underpredictionmay be caused by the use of the standard environmental lapse rate in this study,which may not always be the most appropriate rate at these locations. Precipitationestimation error showed a consistent trend of relative homogeneity across most ofthe study area and overprediction in the Pacific Northwest, due to a departure of theactual orographic precipitation lapse rate from the long-term averages used asmodel parameters. Further analysis of the orographic precipitation lapse ratesinvolved in this study confirmed this difference between the short- and long-termrates. Such variability was largest in the Pacific Northwest, where precipitation isgenerally higher and sharper differences in precipitation amount occur betweenlow and high elevations. The dynamic nature of orographic precipitation lapse rates


suggested by these findings should be taken as a warning for researchers assumingthe applicability of long-term rates to short-term studies. This study also comparedthree averaging methods of MT-CLIM output to test for the impact of distance andtopography on the model’s utility and, as it was studied here, found no significantresults.

Acknowledgments: Thanks to Marc Linderman for comments on an early draft of this paper, toSunday Goshit for discussion on climate patterns in the formative stages of the research, and to the twoanonymous reviewers whose comments were very helpful in guiding revisions. This work was supportedby a USGS cooperative agreement with GPM supervised by Dan Fagre and is a contribution from theMountain GeoDynamics Research Group.

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Precipitation and Temperature Estimation Error at Alpine Treeline Ecotones Using the Mountain Climate Simulator Model (MT-CLIM)