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Keywords:

  • cokriging;
  • MODIS;
  • Hawaii;
  • Jeju Island;
  • land surface temperature

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Description of interpolation methods
  5. 3. Methods
  6. 4. Results and discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

Cokriging, a multivariate geostatistical interpolation method, uses elevation information as a secondary variable to improve the prediction accuracy of air temperature in mountainous areas. Although the secondary variable plays an important role in cokriging, the performance of interpolation largely depends on the amount of input data. The purpose of this study was to improve air temperature estimation by merging hypertemporal Moderate Resolution Imaging Spectroradiometer land surface temperature (LST) data and ground observations as interpolation data. Two significantly different island environments, tropical Hawaii Island (USA) and temperate Jeju Island (Korea), were selected for interpolation experiments. Spatiotemporal characteristics of air temperature prediction were compared between three cokriging methods and the conventional inverse-distance weighted interpolation. Due to the year-round trade winds, there was significant difference in prediction errors between windward and leeward slopes of Hawaii Island. LST-derived temperature was not regularly sampled from cloud-prone, windward slopes. As a result, prediction reliability was lower on windward slopes than leeward slopes, and overall prediction accuracy decreased in the wet season. Jeju Island is a mid-latitude volcanic island heavily influenced by the Asian monsoons. This climatic setting creates the seasonal variations of air temperature that is far greater than its spatial variations. The environmental lapse rate (ELR) of Jeju Island became much steeper in winter, and prediction accuracy and reliability were reduced due to an increase in the spatial variations of air temperature. With the addition of satellite-derived air temperature data, the root mean square errors of cokriging decreased by 27.3–52.9% for Hawaii Island and 34.6–37.6% for Jeju Island depending on cokriging models. Copyright © 2010 Royal Meteorological Society


1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Description of interpolation methods
  5. 3. Methods
  6. 4. Results and discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

1.1. Problem statement

The map of air temperature is rarely updated on a regular basis in rugged mountainous areas, such as remote volcanic islands, due to a limited number of weather stations, inconsistent data collection, and uneven geographic distributions of the weather stations. In addition, island climates are often significantly influenced by the islands' geographic location, prevailing winds, the orographic effect, monsoons, storm events, and elevation. It is commonly observed that the orographic effect is strong and the spatial variations of air temperature are often large despite the small annual range of air temperature in the tropics (Giambelluca and Nullet, 1991; Daly et al., 1994; Nullet et al., 1995). In mid-latitude regions, seasonal winds, or monsoons, primarily control the air temperature patterns, and the annual range of air temperature is greater than the spatial gradient of the variable (Barry and Chorley, 1987). Therefore, the spatial and temporal variations of air temperature may not be adequately represented unless adequate amount and dense network of input data points are available over mountainous areas (Blandford et al., 2008).

The complex nature of island climates makes it difficult to interpolate temperatures using a simple, univariate, statistical approach, such as the inverse-distance weighted (IDW) interpolation. Conventional statistical methods do not consider the complexity of the surface, and they are often criticized for the lack of accurate information, realism, and a spatial climate knowledge base (Daly et al., 2002). Researchers developed a knowledge-based, multivariate approach by combining human-expert and statistical methods. A well-known example of this method is the parameter-elevation regression on independent slope model (PRISM). PRISM uses point data, a digital elevation model (DEM), other spatial data sets, a knowledge base, and human-expert parameterization to produce repeatable estimates of annual, monthly, and event-based climatic elements (Daly et al., 1994, 2002, 2003, 2008; Johnson et al., 2000). Although these advanced interpolation methods significantly improved the accuracy of estimation, the applications of these methods are still limited to long-term climate data and not adequate for isolated islands, where the network of weather stations is not dense and meteorological records are often incomplete.

This study investigates the potentials of satellite land surface temperature data as estimates of air temperature to improve interpolation results on mountainous island surfaces under tropical and temperate climatic settings. In addition to weather station data, satellite-based air temperature was sampled to increase the density of input data. Using these satellite data combined with the ground observations, the conventional IDW and multivariate kriging methods were experimented and their performance was compared with each other.

1.2. Multivariate approaches

Kriging overcomes the deficiency of univariate interpolation methods and provides more accurate results and measures of prediction reliability considering spatial dependence not only between known points but also between known and unknown points. As one of the kriging methods, cokriging is a widespread multivariate geostatistical method. It reduces estimation variances incorporating two or more input data sets into an interpolation process (Davis, 1986; Hevesi et al., 1992). In mountainous areas, elevation is often used as secondary input data if a primary variable is spatially correlated with it (Martinez-Cob and Cuenca, 1992; Phillips et al., 1992; Ishida and Kawashima, 1993; Martinez-Cob, 1996). A major advantage of cokriging is that a primary attribute can be complemented by secondary attributes that are more densely sampled (Goovaerts, 2000).

The low density, incompleteness, and uneven distribution of ground observations are another limitation to accurate interpolation. This problem can be alleviated by the usage of hypertemporal satellite data. Daily data acquisition is especially beneficial for cloud-prone areas, where remotely sensed data are frequently contaminated by unstable meteorological conditions. Particularly, satellite-measured surface temperature data may be used as additional input to interpolation of air temperature. One of the most commonly used hypertemporal satellite sensors is the Moderate Resolution Imaging Spectroradiometer (MODIS) system. MODIS provides daily satellite coverage of a wide range of electromagnetic spectrum bands and consistent earth-surface monitoring tools with three different spatial resolutions. As the system acquires land surface temperature (LST) data corrected for atmospheric effects with high radiometric resolution and calibration accuracy in multiple thermal infrared bands, it is useful for accurate LST detection (Barnes et al., 1998; Justice et al., 1998; Kaufman et al., 1998).

2. Description of interpolation methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Description of interpolation methods
  5. 3. Methods
  6. 4. Results and discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

2.1. Cokriging

Interpolation is a common surface modelling process for continuous phenomena that are surveyed or measured at a limited number of sampling locations. Traditional local methods (e.g. IDW) work reasonably well only if known values, or control points, are distributed with a pseudoregular pattern. If the number of control points is very small and they are sparsely scattered, values at local peaks and valleys of a surface may not be accurately estimated by the method. Kriging is a generalized least-square regression technique that allows an analyser to account for the spatial dependence between known points, or spatial autocorrelation (Goovaerts, 2000). The method considers spatial dependence of an attribute to find an optimal set of weights in the estimation process at unsampled locations. In kriging, semivariance is used as a measure of the degree of spatial dependence between samples, and it is defined as the sum of the squared differences between pairs of points separated by the distance h (Davis, 1986):

  • equation image(1)

where γ(h) is the mean semivariance between two known points, zi and zi+h, with a distance of h, and n is the number of pairs of sample points separated by h. Once the semivariances for different values of h are calculated, they are plotted against h in the form of a semivariogram. As a result, a semivariogram represents the mean semivariance values against distance intervals an analyst chooses.

Volcanic islands are typically formed by multiple eruptions, and mountainous topography is an important climatic control. An inverse relationship between air temperature and elevation is used in cokriging to reduce the prediction errors of air temperature estimation. A secondary variable is often useful in the multivariate method if a primary variable is undersampled (Issaks and Srivastava, 1989; Goovaerts, 2000). A cokriging estimate is a linear combination of both primary and secondary variables and is given by (Issaks and Srivastava, 1989):

  • equation image(2)

where uo is the estimate of U, the primary variable, at location o; u1, …, un are the primary known values at nearby locations 1 through n; v1, …, vm are the secondary known values at nearby locations 1 through m; ai and bj are cokriging weights.

2.2. Evaluation of kriging

Although kriging is more advanced and complex than IDW, a previous experiment showed that univariate kriging did not outperform IDW in the study area (Park, 2009). The number (or density) of control points and the nature of a phenomenon under investigation are often more important factors than interpolation methods themselves (Declercq, 1996). Mathematical cokriging models were evaluated and compared with IDW in this study. Considering radial patterns of temperature changes on the islands, a directional or drift effect could not be assumed. This study is only limited to basic, plausible fitting models that explain how semivariance changes with distance between two samples. Therefore, an ordinary cokriging approach was used in the analysis.

Unlike conventional interpolation, kriging provides measures of uncertainty of predictions. The variance of estimation is the weighted sum of semivariances for the distances to the points used in the estimation and the constant λ:

  • equation image(3)

where γ(hi0) is the semivariance between the ith known point and the point to be estimated, Wi is the weight associated with point i, n is the number of samples used in the estimation, and λ is the minimum estimation error, called a Lagrange multiplier (Davis, 1986). The standard error(s) of the predicted surface, which is the square root of the estimation variance, provides an explicit expression of the magnitude of estimation errors. Seasonal standard error maps that were produced by cokriging were examined and compared with each other.

3. Methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Description of interpolation methods
  5. 3. Methods
  6. 4. Results and discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

3.1. Study area

Two volcanic islands of tropical and temperate climate regions are selected for interpolation experiments. One is the Island of Hawaii (‘Hawaii Island’ hereafter), Hawaii, USA and the other is the Island of Jeju (‘Jeju Island’ hereafter), Korea (Figure 1). The biome structures of these two islands are well developed vertically, and temperature distribution is an important variable to understand their ecosystems (Vitousek, 2004; Kim, 2008). Hawaii Island is the largest and southernmost island of the Hawaiian archipelago (18°54′34″–20°16′05″N, 154°48′20″–156°03′40″W). Hawaiian climates are characterized by the annual cycles of the cool, wet season (October–April) and the warm, dry season (May–September) due to constant northeasterly trade winds. Two massive mountain systems of Hawaii Island, Mauna Loa (4168 m) and Mauna Kea (4205 m), create a rain shadow on leeward slopes (west). As a result, precipitation of many areas on the dry side is below 500 mm/year, whereas it reaches more than 6000 mm/year on windward slopes (Nullet et al., 1995). Annual temperature ranges are typically less than 5 °C at a given location, but air temperature changes significantly with elevation. A temperature inversion, produced by sinking air in the Hadley Cell, is an important mechanism in vertical temperature distribution. The altitude of a temperature inversion varies between 1500 and 3000 m, but it occurs most frequently at around 2000 m during summer (Giambelluca and Schroeder, 1998). These horizontal and vertical temperature variations make microclimates of the island very complex.

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Figure 1. Study area. The locations of major volcanic mountains and cities are shown on insets

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Jeju Island is a mid-latitude volcanic island located about 140 km south off the coast of the Korean peninsula (33°14′30″–33°15′00″N, 126°32′45″–126°33′15″E). It is a Quaternary shield volcano and mainly composed of basaltic trachytic lavas with minor Cretaceous granite. Nearly 400 scoria cones and tuff rings are scattered across the island (Chough et al., 2000). Half of the land area is covered with forests, and other major land cover types include pasture, grassland, and cropland. Being located adjacent to the West Pacific Ocean, the island is in the transitional region between the temperate and subtropical climate zones. The East Asian monsoon strongly influences the climate of the island. The summer monsoon is characterized by hot and moist air blowing from the West Pacific and East China Sea. In winter, a high-pressure system develops over the northern part of Asia. The dry, cold northwesterly winds spread towards Korea and have direct impacts on the island (Nieuwolt, 1977). Mean air temperature ranges from 4.5 °C in January to 25.9 °C in August, but it is much colder in high elevation near Mt Halla (1950 m). Interpolation methods proposed in this study are experimented on the two significantly different environmental settings. Study results provide an insight into the selection of an interpolation scheme that fits the climatic regime of the islands.

3.2. Climate and DEM data

Daily air temperature data of 2007 were obtained from the National Climate Data Center (http://www.ncdc.noaa.gov) and the Jeju Regional Meteorological Office (http://jeju.kma.go.kr) for the two islands. The density of weather stations is much higher on Jeju Island (9.8/ 1000 km2) than on Hawaii Island (1.2/1000 km2). For Hawaii Island, daily data were obtained from 13 weather stations. To better represent a relationship between air temperature and LST data, additional data were acquired from 31 weather stations of the National Weather Service's Cooperative Station Network in neighbouring islands. However, daily records were not continuously collected at all weather stations. Daily data were missing for more than 60 days during the year at 17 weather stations (38.6%). For Jeju Island, daily temperature data were available from 4 weather stations of the Korean Meteorological Administration's Observation Network and 14 automated weather stations (AWS). On average, 99.5% of the daily observations were recorded for Jeju Island. These daily air temperature data were integrated into 12 periods using the same 32-day composite periods of the LST data, which will be described later. From the twelve 32-day air temperature composites, a linear regression analysis was performed between the air temperature and LST at the weather station locations for both islands. Then, LST data were transformed to air temperature based on their regression equations for the entire year.

USGS DEM was used as a secondary variable of cokriging. A 30-m resolution DEM was downloaded from the National Elevation Dataset (NED) website (http://ned.usgs.gov/) and resampled to 100 m. The annual mean air temperature has a strong, inverse relationship with elevation (r2 = 0.97 for Hawaii Island and r2 = 0.95 for Jeju Island). Annual mean environmental lapse rate (ELR) was 6.3 °C/km on Hawaii Island and 7.1 °C/km on Jeju Island (Figure 2).

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Figure 2. Annual mean environmental lapse rates on Hawaii Island (USA) and Jeju Island (Korea). An inverse relationship is clearly shown on both islands with slightly different annual mean lapse rates. For Hawaii Island, the highest location was excluded in calculating the regression line because it is above the temperature inversion layer

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3.3. Satellite LST data

MODIS LST 8-day composite products (MOD11A2) were downloaded from the EROS Data Center for 2007 (https://wist.echo.nasa.gov). Two image tiles (h03v06 and h03v07) were mosaicked together to cover the main Hawaiian Islands. Two LST composite images of Hawaii Island (18 February 2007 to 25 February 2007 and 6 March 2007 to 13 March 2007) were missing. Therefore, 44 total LST 8-day composite images were processed. Only one tile (h28v05) was required for Jeju Island, and 46 composites of the island were available for the year. Each 8-day composite image contains the mean LST of 8 days in that composite period excluding cloudy days for both daytime and night-time. Each composite data set also includes quality-control information, which is used to extract days under clear-sky conditions. Using this information, individual days that were included in the computation of each 8-day LST composite image are determined. Four consecutive 8-day composites were averaged to create twelve 32-day composite images.

As LST is influenced by various thermal conditions of the surface, determination of a relationship between LST and air temperature requires close examination of data acquisition days and times at data collection locations for both satellite- and ground-based temperature data. Correlation analysis was performed for both daytime and night-time LST data to determine a relationship between LST and air temperature measured at the weather stations. For the selection of sample points, the overall range of distance between neighbouring weather stations was considered. Mean distance between neighbouring weather stations (e.g. eight nearest weather stations) measured as short as 21 km. Hence, a similar grid spacing of 20 km was initially selected, and it was successively reduced to 10 and 5 km (Figure 3). After these grid layers were generated, an LST value for each grid point was extracted from each LST composite for further analyses.

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Figure 3. Regularly gridded sampling points (white dots) are overlaid on the hillshading images of the islands. Sampling grids are created with three different spacings (5, 10, and 20 km), but only 5 km grids of January and July are provided as an example. Solid triangles represent the locations of weather stations. The density of LST-derived data points is lower on windward slopes (east) than leeward slopes (west) of Hawaii Island ((a) and (b)). There is no noticeable change in the data density of Jeju Island ((c) and (d))

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3.4. Parameterization of cokriging

Cokriging was applied to weather station data and LST-derived temperature estimates with three different spacings (5, 10, and 20 km) using the Geostatistical Analyst extension of ESRI ArcGIS 9.3. LST-derived temperature estimates were chosen at 312, 91, and 35 sampling locations for Hawaii Island, and 77, 19, and 5 sampling locations for Jeju Island based on the same three sampling grids. However, only a certain number of LST-derived data were included in interpolation depending on the number of LST values available at the grid points. To determine the number of LST pixel observations needed per composite period to represent air temperature statistically, correlation analysis was conducted between 32-day mean LSTs and the mean air temperature of the same composite periods. For Hawaii Island, 14 observations were needed for each 32-day composite period to obtain a correlation coefficient higher than 0.95 (Park, 2009). For Jeju Island, LSTs were strongly correlated with air temperature (r > 0.95) regardless of the number of LST observations. Based on a regression equation between LST and ground-based air temperature, LST estimates of air temperature were calculated (Figure 4). Finally, four separate data sets with different spacings were used as input to interpolation. The first data set includes weather station data only (13 and 18 weather stations for Hawaii Island and Jeju Island). The other three data sets include weather station data and LST-derived temperature data from 5, 10, and 20 km grids, respectively.

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Figure 4. Correlations between LST and air temperature. Only night-time LST had a significant relationship with air temperature on Hawaii Island. On Jeju Island, however, both daytime and night-time LST had a strong direct relationship with air temperature. As a result, the mean LST of Jeju Island had the strongest relationship with mean air temperature

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Spatial dependence decreases as a distance between two locations increases, and sample points beyond a certain distance have little or no correlation with a point value to be estimated. Therefore, it is a common practice to select the number of control points that will be used in the prediction of an unknown value. For sample-point search, a quadrant strategy was used for all data sets (Slocum et al., 2009) because it was reported that the prediction errors and the variance of estimation were reduced when sample points were selected from all cardinal directions (Park, 2009). Four control points or the minimum of two sample points that fell within each of the four cardinal sectors of a search circle were used.

Selection of a mathematical fitting model of a semivariogram is an important task in kriging. Previous studies showed that data characteristics, visual inspection, and cross-validation were important in a model-selection process (Webster and Oliver, 2001; Jarvis et al., 2003). This study aims to find a cokriging model that is effective and advantageous over mountainous surface using satellite-based temperature data in addition to weather station data. A semivariogram cloud of each composite data set was fitted with three common models, including spherical, exponential, and Gaussian models, to determine the best option for the island settings. A spherical model shows a gradual decrease in spatial dependence of a variable as a distance between two points increases. An exponential model applies when the spatial dependence decreases exponentially with increasing distance and erratic changes in air temperature over short distance occur. In a Gaussian model, the spatial dependence also vanishes at an infinite distance. The unique feature of this model is its parabolic shape at the origin (Figure 5). The result of these kriging models was evaluated by cross-validation.

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Figure 5. Schematic illustration of spherical, exponential, and Gaussian models that may fit the semivariogram of a variable in kriging

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3.5. Cross-validation

Cross-validation allows an investigator to compare interpolation methods by providing diagnostic statistics that indicate the quality of each method. It withholds one data point and predicts the value at that location using the rest of data points. Then, the predicted value is compared with the known value. After completing the procedure for each known point, an indicator of prediction quality is computed. In addition to visual inspection of an interpolation result, two different statistics are commonly used as the important means of evaluation, including the root mean square error (RMSE) and the standardized RMSE (SRMSE) (Chang, 2008):

  • equation image(4)
  • equation image(5)

where n is the number of points, zio is the known value of point i, zie is the estimated value of point i, si2 is the variance of estimation at point i, and s is the mean prediction standard error. RMSE is a mean offset value between predicted and known values. Therefore, an optimal interpolation method should have the smallest RMSE. SRMSE provides the assessment of uncertainty of predictions by estimating the variability of the predictions from known values. If SRMSE is close to 1, it means that RMSE is close to s and the interpolation method is correctly assessing the variability of the predictions. Both weather station data and LST sample data were used in the process.

4. Results and discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Description of interpolation methods
  5. 3. Methods
  6. 4. Results and discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

4.1. Acquisition time and density of satellite-measured input data

Daytime and night-time satellite LST data were compared with each other in terms of their relationships with air temperature. Daytime LST data of Hawaii Island had only a weak correlation with air temperature. Intense radiation received on the barren surface is converted to sensible heat fluxes on Hawaii Island, and it raises surface temperature (Juvik et al., 1993), which significantly deviates from air temperature. The temperature inversion in high elevation creates dry conditions, and this phenomenon also enhances LST deviations from air temperature due to little latent heat fluxes on the surface. It is believed that a significant amount of lava fields with various ages and complex assemblage of diverse land cover types are responsible for the large variations of LST and a poor correlation between daytime LST and air temperature. Night-time LST data, on the other hand, had a strong inverse relationship with air temperature (Table I). For Jeju Island, daytime and night-time LST data had the highest correlation with daily maximum (r = 0.88) and minimum (r = 0.96) air temperature, respectively (Figure 4). The mean LST (the average of daytime and night-time LSTs) had an improved correlation coefficient (r = 0.98) with the mean air temperature. This high correlation is attributed to the relatively uniform emissivity of gentle slopes mostly covered with grasslands (Palluconi et al., 1990; Kawashima et al., 2000; Chung and Yun, 2004; Park et al., 2005).

Table I. Correlations between LST and air temperature (mean, maximum, and minimum)
 Hawaii IslandJeju Island
 LST_dayLST_nightLST_dayLST_nightLST_mean
  • Pearson's correlation coefficients are computed for daytime, night-time, and mean LSTs.

  • a

    Correlation is significant at the 0.01 level (one-tailed).

  • b

    Number of observations.

Mean_air0.27a0.96a0.87a0.96a0.98a
nb222205216212208
Max_air0.33a0.94a0.88a0.95a0.97a
n222205216212208
Min_air0.21a0.94a0.84a0.96a0.97a
n222205216212208

The addition of LST-based temperature estimates increased the density of input data and improved the prediction accuracy significantly. The prediction errors were strongly influenced by the number of input data. The mean RMSE rapidly decreased as the density of input data points increased for Hawaii Island. The density of input data increased from 1.2/1000 to 2.4/1000, 5.4/1000, and 17.5/1000 km2 as 20, 10, and 5 km grid data were added, respectively. The mean RMSE of all methods improved from 4.51 to 1.51 °C as the mean number of data points increased from 12.9 (weather station data only) to 182.8 (weather station + 5 km-grid data). For Jeju Island, the density of input data increased from 9.8/1000 to 12.4/1000, 19.1/1000, and 46.3/1000 km2 as LST-derived data were added to the weather station data. As a result, RMSE decreased from 1.87 to 1.21 °C (Figure 6). Prediction errors were more strongly influenced by the number of input data points on Hawaii Island, where the density of input data points is lower than Jeju Island. Prediction errors quickly decreased until data density reached 10/1000 km2, but there was only marginal change beyond the density value of 20/1000 km2 (Figure 6). This threshold value is equivalent to the grid intervals of 7 km (one sample point every 7 km) approximately. Therefore, additional input data, such as 5 km interval or finer data points, would not reduce prediction errors substantially unless there are many cloud-contaminated pixels in the satellite data.

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Figure 6. A relationship between annual mean RMSE and the density of input data. RMSE decreases exponentially as the input data density increases

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4.2. The impact of temperature variations on cokriging

Although cokriging is dependent on a correlation between primary and secondary variables, the spatial variability of air temperature also influences the performance of the interpolation method. Spatial variations of air temperature, represented by its standard deviation (SD), were significant (4–5 °C) in all months on Hawaii Island although their seasonal changes were small (Figure 7). It reflects the complex nature of the island's geography, including rain shadow, temperature inversions, tall mountain systems, and the size of the island. ELR describes the vertical change of air temperature, and higher ELRs tended to increase the correlations between air temperature and elevation (Figure 8). Despite an improved correlation between the two variables, higher ELRs caused prediction errors to increase in winter. This is because high ELRs increased the spatial variance of air temperature and led to greater prediction errors (Figure 9). On Hawaii Island, mean prediction errors seasonally varied even if the annual range of air temperature was small. This seasonal pattern is associated with the cycles of dry and wet seasons. In the wet season (winter), more frequent cloudy conditions decreased the density of satellite-derived temperature estimates and produced higher RMSEs (Figure 10(a)).

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Figure 7. Seasonal changes of ELR and the standard variations (SD) of air temperature for both islands. Spatial temperature variations are larger on Hawaii Island than Jeju Island, but seasonal variations of temperature SD are greater on Jeju Island. ELR is typically higher in winter than in summer, and its seasonality is also greater on Jeju Island than Hawaii Island

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Figure 8. Correlations between air temperature and elevation increase as ELR increases. The annual range of ELR is much greater on Jeju Island than on Hawaii Island

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Figure 9. Prediction errors (RMSE) have a positive relationship with air temperature SD. Hawaii Island, which is bigger and taller than Jeju Island, has greater temperature variations and prediction errors

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Figure 10. Mean RMSEs resulted from three ordinary cokriging models and the IDW method are compared with each other. RMSE scores are lower in summer than in winter on both islands (a and b). This pattern corresponds to the seasonality of temperature variations and ELR in Figure 7

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The seasonal patterns of ELR and temperature variations of Jeju Island were more apparent than those of Hawaii Island (Figure 7). Knowing that the density of input data points was relatively stable for the island, the seasonal change of prediction errors is attributed to the strong monsoonal impact on meteorological conditions (Figure 10(b)). Park and Jang (2008) recently reported that cokriging improved the prediction accuracy relative to univariate ordinary kriging, and the magnitude of improvement increased as a correlation between elevation and air temperature became stronger. Although they did not analyse vertical temperature change and its seasonal pattern, the prediction errors of cokriging significantly increased in winter months. In October and January, for example, correlations between air temperature and elevation were higher than those in summer months. This result shows that a correlation between primary and secondary variables is not the only major factor in a cokriging process.

An important difference between kriging and other local methods is that kriging produces a variance measure for each point estimated to indicate the reliability of the interpolation (Chang, 2008). The standard error of the predicted surface is mapped in Figure 11. The standard error was higher on windward slopes than leeward slopes on Hawaii Island. Seasonally, prediction errors were greater in January than July on the tropical environment because the number of input data points is smaller in the wet season (winter months) than the dry season. On Jeju Island, however, control points were almost evenly distributed in summer and winter. Unlike Hawaii Island, there was no directional pattern on the standard error map of the island, but the reliability of interpolation was still strongly dependant on the density of input data. For example, standard errors were higher along the coastline and in areas where data points were missing, such as the highlands of Mt Halla on the January map (Figure 11).

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Figure 11. The SEs of cokriging are compared with input data points selected by 5 km grids. LST-derived temperature estimates are frequently missing on the windward slopes of Hawaii Island ((a) and (b)), and the number of missing data points is higher in winter (January) than in summer (July). Input data points are fairly evenly distributed on Jeju Island, and there is no spatial trend of SE. Instead, cokriging SE varies significantly from January (c) to July (d) on Jeju Island

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4.3. Selection of interpolation models

Cokriging models did not improve the prediction errors relative to IDW when the two lowest-density input data sets were used in interpolation for Hawaii Island (Table II). The density of input data points still remained as low as 2.4/1000 km2 even after LST-derived 20 km grid points were added to cokriging. When the other two finer-grid samples were used as input data, however, the cokriging models outperformed the IDW method substantially. For example, the mean prediction error of the three cokriging models was smaller than that of IDW by 29.6–31% for the 10 km grid data and by 32.3–35.8% for the 5 km grid data. For Jeju Island, cokriging methods outperformed the IDW method at all density levels (9.8/1000–46.3/1000 km2) by 3.2–18.2%. Among those cases, where cokriging methods worked better than IDW, the Gaussian model performed almost always better than the other two models, whereas the exponential model had the highest RMSE scores (Figure 10). Considering strong correlations between elevation and air temperature (−0.97 to − 0.99 based on 32-day composite data), erratic changes in air temperature over short distance were not expected to exist, and spatial dependence of two points was assumed to decrease progressively with increasing distance between them. Visual representation of variograms for both islands is shown in Figure 12, where semivariance increases slowly near the origin.

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Figure 12. Semivariograms (January) fitted with a Gaussian model for Hawaii Island (a) and Jeju Island (b)

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Table II. The annual mean of RMSE and RMSSE computed from IDW, spherical, exponential, and Gaussian models of cokriging
LocationHawaii IslandJeju Island
GridScoreIDWSphericalExponentialGaussianIDWSphericalExponentialGaussian
StationsRMSE4.464.894.534.901.981.841.891.77
 SRMSE1.071.011.110.860.860.82
20 kmRMSE3.583.473.743.601.761.611.711.54
 SRMSE0.720.700.860.880.870.90
10 kmRMSE3.422.522.642.491.631.381.461.39
 SRMSE0.700.580.770.830.780.89
5 kmRMSE2.091.441.371.371.341.151.241.11
 SRMSE0.540.400.670.870.700.93
MeanRMSE3.392.983.072.991.681.501.571.45
 SRMSE0.740.670.820.860.800.88

The Gaussian and spherical models showed similar RMSE scores. For the two finest densities of sample points, the prediction errors of the two cokriging models were not significantly different from each other. However, the Gaussian model produced a more reliable result compared to the spherical model. The SRMSE of Jeju Island showed that uncertainty of predictions of the Gaussian model was smaller than that of the spherical model by 19.7 and 21.2% based on the 10 and 5 km grid data sets. The difference was even greater for Hawaii Island. The uncertainty of predictions of the model was 19.9 and 43.5% lower than that of the spherical model for the two data sets. This result reveals that the Gaussian model better represents temperature changes over the surface terrain, which causes the semivariance of the variable to change gradually.

The spatial patterns of January and July maps created by the Gaussian cokriging method were evaluated for both islands (Figure 13). Overall, temperature patterns were well represented, showing low temperatures at four major volcanic mountain peaks of Hawaii Island. Isotherms on leeward slopes and dry highlands were much smoother than those on windward slopes due to the higher density of satellite-derived sample points on the leeward slopes. As annual temperature ranges are small on the tropical island, there was little change in temperature patterns between January and July. A strong association between air temperature and elevation is also clear on Jeju Island, showing steeper temperature gradients in the north–south direction than the east–west direction. The seasonal impact of the Asian monsoons on the island is well expressed by a large temperature difference between the 2 months.

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Figure 13. Cokriging results for January ((a) and (c)) and July ((b) and (d)) temperatures. Isohyets are typically parallel to contours and represent a strong relationship with elevation. Seasonal temperature change is pronounced by the Asian monsoons on Jeju Island while an annual temperature range is small on Hawaii Island

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5. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Description of interpolation methods
  5. 3. Methods
  6. 4. Results and discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

As spatial climate data sets are required for various scientific models in agriculture, hydrology, natural resource management, and ecology, estimates of climatic data should be processed as a primary component and prepared in fine resolution. The optimal interpolation method of a climatic variable depends on the physical nature of the phenomenon, topographical characteristics, and the geographic scale of a study (Daly, 2006). Typically, the network of weather stations on a remote mountainous terrain is not dense enough to represent its dynamic temperature patterns regardless of interpolation techniques. Focusing on tropical and temperate islands, this study showed that hypertemporal satellite-derived surface temperature might be used as additional sample data for interpolation of air temperature. The MODIS LST data products are a useful, systematic data source for detailed climate interpolation on mountainous environments, providing explicit gridded estimates of air temperature over adjustable periods of data compositing.

Study results showed that the usage of satellite-derived temperature estimates in interpolation is beneficial and promising for areas where the density of weather station networks is low. Integration of remote sensing data into a prediction process improved estimation errors (Smith et al., 2005). With the addition of satellite-derived air temperature data, the RMSE of cokriging decreased by 27.3–52.9% for Hawaii Island and 34.6–37.6% for Jeju Island depending on cokriging models. Cokriging generally improves the interpolation accuracy of mountainous areas using elevation data as a secondary variable because elevation is strongly correlated with air temperature. However, higher correlations between them did not necessarily improve interpolation performance. It should be noted that steeper ELRs (greater decrease in temperature with height) tend to increase the spatial variations of air temperature and have an adverse impact on interpolation results, increasing prediction errors.

Despite the obvious value of MODIS LST data, cloud contamination is the primary cause of satellite data loss. As this issue is problematic in wet environments producing a temporally intermittent view of satellite imagery, scientific limitations of satellite data applications in temperature interpolation should be acknowledged. Factors influencing prediction accuracy and reliability vary depending on climatological settings of an area of interest. Air temperature estimation was sensitively influenced by the number of input data, which varied through time and space because the frequency of cloudy days was undulated seasonally and topographically on the mountainous landscape. Even the daily time stamps of MODIS LST data could not completely overcome the cloudy conditions of the tropical environment. Many missing LST pixels were caused by prolonged cloudy periods, and the spatial patterns of temperature interpolation could be biased towards clear-sky days. On Hawaii Island, the availability of satellite data is strongly influenced by the annual cycles of dry and wet seasons. As a result, prediction reliability decreased in the wet season (winter months) as the number of satellite-derived input data points decreased due to frequent cloudy conditions. This limitation is further complicated spatially because the mountain effect is dominant in the island. The orographic effect often creates a rain shadow on leeward slopes of a mountain and it increases the spatial variations of air temperature on the tropical island. This spatial disparity contributes to the uneven distribution of prediction errors. In future studies, a detailed analysis of the impact of cloudy days on the reliability of temperature interpolation might be needed. Further investigation on this issue should better evaluate the usefulness and the value of the satellite application for a wide range of climatic environments.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Description of interpolation methods
  5. 3. Methods
  6. 4. Results and discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

The author thanks Drs Soojin Park (Seoul National University, Korea) and Taeho Kim (Cheju National University, Korea) for their generous help in obtaining and preparing DEM and daily meteorological data for Jeju Island, Korea. The author also thanks two anonymous reviewers for their constructive suggestions and comments on this article.

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  2. Abstract
  3. 1. Introduction
  4. 2. Description of interpolation methods
  5. 3. Methods
  6. 4. Results and discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
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