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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

In this study we examine the relationship between remotely sensed, ^{2} coefficient of 0.77 for the model simulations and 0.35 for the MODIS LST. These values improved significantly when time-lags were considered and the few outliers were removed, giving R^{2} values of 0.80 for the model and 0.73 for the MODIS LST. These results show that the WRF model correlates better with the

The importance of the land surface temperature (LST) in surface-based bio-geophysical processes and land-atmosphere interactions is well documented in the literature [_{a}) and LST [

As an attribute of the land surface, LST is influenced by the local land-cover (LC). Therefore, the quality of LST retrievals from satellite observations over various LC types needs to be assured in order to use this data source in the above applications.

Comparative analysis of LST from remote sensing data and modelling approaches in the existing research can be categorized into four groups. The first group attempt to improve LST retrievals via modelling complex LC and terrain features. These studies have examined LC for the purpose of a better approximation of surface emissivity, which rely on vegetation fraction of the surface cover [_{a}[_{a} looking at LST as the intermediate link [

The focus of the first group is physical modelling of the parameters involved in measurement of LST, including the sensor, the atmosphere in between and the properties (such as emissivity) of the target area. The second group attempt to improve accuracy of numerical models through assimilation of satellite observational data into the models. Both of these groups focus on producing or using satellite derived data often without comparison with a similar database. The third and the last group, on the other hand, are usually concerned with validation of satellite observations based on ground-truth data. Other works in the literature, which are concerned with both LC and LST, have exploited the inverse relationship between LST and surface vegetation density (e.g., [

Despite numerous research conducted on the validation of remotely sensed LST from various sensors, such as MODIS (e.g., [

The objective of this paper, therefore, is to examine the relationship between LST observations from MODIS with the modelled dataset and the

The paper is organized as follows. The study area and the used datasets (

The study area is located in a valley of the Waimakariri River basin in the Southern Alps of New Zealand (171°45’29”E, 42°59’39”S). The area is relatively flat with an average elevation of 550 m above sea level (a.s.l.), however, high-rise mountains border the area just to the North and to the South (

The climate of the study area is alpine with large diurnal temperature differences at day and night and freezing temperatures in winter. Based on climate data from the University of Canterbury Cass (UC Cass) Automatic Weather Station (171°45’34”E, 43°02’05”S, 583 m a.s.l.), which is located 3 km to the South of the study area, long-term average T_{a}

Data analysed in this paper fall into one of three categories: (_{inSitu}); (_{Modis}); and (_{wrf}). The first two categories are observational data with different levels of accuracy and precision, while the third category is simulated data generated by the state-of-the-art WRF numerical meteorological model. These data are explained in more detail below.

(^{®} DS1922L iButton, −40 °C to 85 °C sensitivity range, ±0.5 °C accuracy, 0.0625 °C resolution) were used in this experiment to measure GST over five different LC types of the area, allocating at least one iButton for each LC type (shown as b1 to b10 in

Given the shallow depth of installations, these iButton measurements are used as a proxy to compare with the MODIS LST. Although this should be presumably a good approximation, we conducted a time-lag analysis to account for the differences depending on the soil heat capacity and LC type. Besides the iButton point measurements, we also used the model simulations (explained further below) as an independent variable, which is also gridded data with a cell-size similar to the MODIS pixel spacing.

(

(_{wrf}. Spatial locations of the grid-points from this dataset are marked by wrf1 to wrf9 on the map of the study area (

We used raster image analysis in order to overlay the MODIS LST with the LC data from the study area. A certain number of pre-processing steps were required to convert the original LST product in HDF format to raster layers with a versatile projected coordinate system. First of all, raster subsets of the LST product were extracted based on the boundary extent of the study area. LST L3 product is gridded in the global Sinusoidal projection, and the grid containing data for the study area is located at column 30 (h30) east-west and line 13 (v13) north-south. However, in this projection New Zealand falls in the lower-right corner with distortion along east-west direction. Using ESRI ArcGIS projection conversion utilities, “New Zealand Transverse Mercator 2000” coordinate system (Spheroid GRS 1980, Datum: NZGD 2000) was applied on the LST raster subsets. With spatial overlay in GIS, coordinates of LST pixels for each LC type in the study area were determined. These coordinates were used in a code to read LST values from the entire HDF files covering the period of field experiment and constructing LST time-series for each LC type. Data for observation times affected with cloud-cover were automatically filtered out by the code using fill-value attribute of the LST product. Quality control field for each observation helped to determine the level of accuracy of that observation.

The linear mixing model is used for unmixing the LST pixels with mixed LC types in the study area (_{i}_{i}_{i}_{i}_{i}

We defined the WRF model domain’s central point in a way that model grid-cell centres were located as close as possible to the LST pixel centres. Subtle tuning of the model domain’s central point moved coordinates of the model grid points close to the corresponding coordinates of LST pixel in the study area. However, due to the difference in the pixel-size of the MODIS LST (928 m) with the grid cell-size of the model (1 km), a difference of about 100 to 300 m in the positions of the grid cells and LST pixels was inevitable (blue and red points in _{Modis}, point layers derived from LST_{wrf}, and

Since LST is affected by viewing angle (

Time-series of the input data sources (LST_{Modis}, LST_{wrf} and LST_{inSitu}) were constructed in order to apply correlation and regression analysis on the alternate pairs of the three datasets (listed below). Since the frequency of MODIS observations is limited to four times a day, which is further limited to cloudless days, subsets of the other two datasets were selected accordingly (depending on the latitude, more than four MODIS observations is also possible, but the L3 V5 product contains LST values from only four observations [

Three alternate correlation calculations have been followed in the regression analysis at all times: LST_{Modis} correlated to LST_{inSitu} (denoted as MOD^{∼}_{wrf} to LST_{inSitu} (shown as WRF^{∼}_{Modis} to LST_{wrf} (shown as MOD^{∼}WRF). The regression coefficient of determination (R^{2}) was used to show the strength of correlation between each of the two datasets.

We also tested how the removal of possible outliers in the measurements improves the correlation results from the regression analysis. A scatter plot by itself is a non-parametric test for the existence of the outliers [

In this section, the results from the correlation analysis between the spatially averaged time-series of the three datasets are presented. First, we compared spatially averaged high resolution time-series of the WRF simulations with the _{wrf} and LST_{inSitu} 30-minute data showed a relatively strong (R^{2} = 0.71) correlation (^{2} = 0.35 for the MODIS LST and R^{2} = 0.77 for the WRF simulations (

Time-lags were considered to account for the delay in warming and cooling of the surface as measured by the iButtons 1–2 cm below the surface versus instantaneously observed by the satellite. Taking the MODIS acquisition time as reference, lags of ±100 minute were applied on the ^{2} values were calculated for each lag. For the correlation of model simulations with the

Considering time-lags, correlations were generally deteriorated with lags of more than 90 minutes. The best agreement between the WRF model simulations with the

Several tests were made to improve the correlation values between the MODIS LST and the _{wrf} and LST_{inSitu} were well inside the cut-off margins, it turned out that the source of the outliers to be in the MODIS LST dataset. The same outliers are also visible in the scatter plots (

According to the overpass times (

We looked at relative humidity (RH) and other parameters from the model, but we did not find any meaningful pattern to explain the reason for the outliers. Since high amounts of atmospheric water vapour limits the accuracy of LST retrievals [_{a}_{a}_{a}_{a}

To prevent swamping and masking effects (see [^{2} coefficient. Removing the largest outlier (obs. 12 in ^{2} from 0.35 to 0.51, removing the second largest outlier (point 8) improves R^{2} to 0.53, and removing the third outlier (point 3) improves R^{2} to 0.62 (

Time-series of the MODIS LST and the model simulations over 5 LC classes were correlated individually versus the corresponding series of the

Another point for consideration was the LC type BS. The height of the bush in the area is about 1 to 1.5 m from the base, with a moderate density of the scrub over the surface. Considering this point, the authors were concerned that the values of LST recorded by MODIS observation on this particular LC type are not exactly a representative of the skin temperature of the soil, but rather affected by the temperature near the top of the bush. Although the field experiment was conducted in mid-autumn, the bush maintained considerable foliage, which could have affected temperature measurements as well as solar radiation reaching the ground. Two iButtons were placed at this site, one on top of the bush (b5) and another one on the ground (b4). The corresponding data recorded at this site are referred to as “Bush-Scrub-Ground” (BSG) and “Bush-Scrub-Top” (BST). Correlation of these measurements with the corresponding MODIS LST pixel (LST5) showed higher agreement for BST compared with BSG (^{2} = 0.77), with another peak at 60 min, then it dropped significantly when time-lag increased to 90 min (_{Modis} were analysed: LST9 with homogeneous LC and LST4 with mixed LC. Both of them showed highest agreement with the _{a}, LST4 showed the strongest correlation (R^{2} = 0.68) than all LC types at all time-lags (_{wrf} and LST_{inSitu}, as well as LST_{Modis} with LST_{wrf} were observed when ≈30 min time-lag was applied.

In this section, the results from the regression analysis between the MODIS LST, the WRF model and the

Correlations between the MODIS LST and the ^{2} = 0.63) compared with the iButton on the ground (BSG in ^{2} = 0.18), whereas during night a stronger correlation (R^{2} = 0.94) is observed at the ground (BSG in

On the contrary, the WRF model simulations showed generally higher correlations with the

Although the MODIS LST and the WRF model simulations are both gridded datasets, our results showed that the latter correlates better with the

The iButtons were buried very close to the surface well shielded from direct radiation. Even though they measure different physical properties, each dataset have already been adjusted to approximate the surface skin temperature. These adjustments include surface emissivity and directional effects in the MODIS LST product (see [^{2} values over different LC types at least 14% (such as GT) and up to 26% (such as BG in

Consideration of geographic characteristics of the test-site also helps to understand the difference between the MODIS LST and iButton measurements, which is discussed below as how it affects the LST retrieval process.

Uncertainties involved in the retrieval of LST can be related to (

(_{a} analysis by [

(

(_{a}, provided in the MODIS atmospheric product is also used to improve LST retrieval accuracy [_{a} on LST retrievals. It must be noted that the iButton on the bush had been strongly affected by the near-surface T_{a}. Bush canopy provides protection against solar heat during day and excess emission during night, hence the iButton on the ground might have been negatively or positively biased at day and night, respectively (this can be interpreted from GST variations measured by BushG iButton in _{a} is relatively warmer than the surface skin. Since the MODIS LST correlates better with the warmer temperatures inside the bush at night, it is suspected that the LST product actually has a bias towards T_{a} at night. Similarly, higher day-time correlations of LST with the iButton on top of the bush, as well as bare-soil (which has faster heating rate), is an indication of the fact that the MODIS LST correlates better with T_{a} during day.

Consequently, there is the possibility that the algorithm used in the extraction of MODIS LST does not perform well in the mountainous regions, where the solar radiation regimes are different (see [

The MODIS LST product over a mountainous region in the Southern Alps of New Zealand was analysed in comparison with the ^{2} = 0.35, F-statistics = 12.36, p-value = 0.0020, 99% confidence) correlation between the MODIS LST and the ^{2} = 0.77, 99.9% confidence) between the model simulations and the ^{2} = 0.80 with 99.9% confidence) were higher than the MODIS LST (R^{2} = 0.73 with 99.9% confidence). It is, therefore, concluded that the MODIS LST, if assimilated in the WRF model without any prior assessment for the outliers and the local effects, will not provide any improvement for LST simulations over an alpine region. Longer time-series, however, are required to draw more robust conclusions about the applicability of the MODIS LST product for improving WRF simulations over alpine complex terrain. We suggest outliers in time-series of the MODIS LST to be investigated based on

This research is funded by the University of Canterbury (UC) in New Zealand. We acknowledge free access to the MODIS LST product provided by the US NASA. Warehouse Inventory Search Tool (WIST) and Reverb were used to download the LST product. LC satellite imagery data were obtained from US Geological Survey (USGS) publicly available web resources via Earth Explorer. The authors wish to acknowledge Rob Agnew from the New Zealand Institute for Plant & Food Research for his iButton data-loggers. We also express our thanks to Justin Harrison for his help and expert advice on the field work. We appreciate the valuable comments from four anonymous reviewers, which significantly improved this manuscript.

Minimum and maximum ground temperature measurements from 5 iButtons over Grassland LC type (30-min rate, May 2011). Night observations (7 pm–7 am) are distinguished by the grey-line overlaid on the plot.

Comparison of GST time-series measured over 5 LC types plus the iButton on top of the bush (30-min data, May 2011). The broken grey-line is overlaid on the plot to distinguish day and night measurements; it is assigned 0 for night (7 pm–7 am) and 20 °C for day (7 am–7 pm).

The mean (dots) and ±1

View zenith angles (

View zenith angles (

(

Time-series and trend-lines of LST_{inSitu}, LST_{Modis} and LST_{wrf}. Series are produced by spatially averaging points over various LC types in the study area (except for LST3, which is excluded due to its higher elevation, LST1 to 10 in _{Modis} series). Series only contain the values from times that were coincident with the MODIS LST observations.

Regression residuals’ plot revealing the outliers in the MODIS LST dataset (controls are roughly equal to ±1.5

Scatterplots with line-fits of LST_{inSitu}, LST_{Modis} and LST_{wrf} time-series, first row: all observations (outliers are bordered by a larger square), second row: outliers removed. (

Variations of regression R^{2} statistics from correlations between iButton GST measurements over 5 LC types and time-series of the corresponding MODIS LST pixels using ±100 minute time-lags (1 min increments). Full names of LC types in this figure are listed in

Correlations of day and night time-series of the three datasets over various LC types considering different time-lags (BG: Barren-Gravel, BST: Bush-Scrub-Top, BSG: Bush-Scrub-Ground, NF: Native-Forest, G: Grassland and GT: Grass-Tussock).

Specifications of iButton measurement sites. All iButtons were buried at a depth of 1–2 cm in the soil except iButtons 1 & 5.

b1 | Forest | Dense native Beech trees with ≈10 m canopy height |

b2 | Grassland | Native grass-turf with ≈5 cm height |

b3 | Grassland | ” |

b4 | Matagauri bush/scrub | Native bush with ≈50% density and ≈1.5 m height |

b5 | Matagauri bush/scrub | ” (this iButton was fixed on top of the bush) |

b6 | Grassland | Native grass-turf with ≈5 cm height |

b7 | Grassland | ” |

b8 | Grassland with tussocks | ” mixed with native tussock with ≈20 cm height |

b9 | Grassland | Native grass-turf with ≈5 cm height |

b10 | Barren-gravel | Bare soil with gravel on the inactive river banks |

Fractional abundance vectors (_{i}_{i}

_{i} | ||||||
---|---|---|---|---|---|---|

Barren-gravel | 0.35 | 0.70 | 0.10 | 0.15 | 0.10 | LST9 |

Bush-scrub | 0.25 | 0.05 | 0.50 | 0.00 | 0.05 | LST5-6 |

Forest | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | LST3 |

Grassland | 0.15 | 0.20 | 0.40 | 0.85 | 0.10 | LST2 |

Grass-Tussock | 0.00 | 0.05 | 0.00 | 0.00 | 0.75 | LST8 |

Basic statistics from spatially averaged time-series of the three dataset.

8.49 | 6.98 | 7.99 | |

3.26 | 4.33 | 3.63 |

Regression statistics from spatially averaged data, with and without outliers. P-values from the correlations between MODIS LST and iButton series are also provided, where the smaller the p-level, the more significant the relationship. (

^{∼}inSitu |
^{∼}inSitu |
^{∼}WRF | ||||||

^{2} |
^{2} |
^{2} |
||||||

| ||||||||

0min | 0.35 | 3.57 | 0.0020 | 12.36 | 0.77 | 1.79 | 0.56 | 2.92 |

30min | 0.40 | 3.44 | 0.0008 | 15.10 | 0.80 | 1.68 | 0.62 | 2.73 |

60min | 0.47 | 3.23 | 0.0002 | 20.20 | 0.79 | 1.71 | 0.60 | 2.80 |

90min | 0.51 | 3.10 | 0.0000 | 24.10 | 0.67 | 2.13 | 0.52 | 3.06 |

| ||||||||

(a) | ||||||||

| ||||||||

^{∼}inSitu |
^{∼}inSitu |
^{∼}WRF | ||||||

^{2} |
^{2} |
^{2} |
||||||

0min | 0.62 | 2.63 | 0.0000 | 32.84 | 0.77 | 1.79 | 0.69 | 2.38 |

30min | 0.69 | 2.37 | 0.0000 | 45.13 | 0.80 | 1.68 | 0.72 | 2.26 |

60min | 0.73 | 2.22 | 0.0000 | 54.55 | 0.79 | 1.71 | 0.67 | 2.47 |

90min | 0.72 | 2.27 | 0.0000 | 51.43 | 0.67 | 2.13 | 0.56 | 2.83 |

| ||||||||

(b) |

Regression R^{2} statistics over 5 LC types, including the maximum R^{2} values achieved with various time-lags (minute). Time-lags were applied in a range of ±100 minutes, with one-minute increments. R^{2} results from correlations between MODIS and ^{2}, are listed in this table. For the other two correlations, only two time-lags are given.

^{2}@lag |
^{∼}inSitu |
^{∼}inSitu |
^{∼}WRF | |||||
---|---|---|---|---|---|---|---|---|

BarrenGravel(LST4) | 0.42 | 0.51 | 0.62 | 0.68(68) | 0.71 | 0.75 | 0.73 | 0.75 |

BarrenGravel(LST9) | 0.38 | 0.43 | 0.50 | 0.56(69) | 0.71 | 0.75 | 0.43 | 0.46 |

BushScrubT(LST5) | 0.51 | 0.62 | 0.66 | 0.77(19) | 0.67 | 0.74 | 0.65 | 0.67 |

BushScrubG(LST5) | 0.04 | 0.07 | 0.09 | 0.18(74) | 0.31 | 0.33 | 0.65 | 0.67 |

Forest(LST1) | 0.21 | 0.23 | 0.31 | 0.47(80) | 0.48 | 0.50 | 0.64 | 0.70 |

Grassland(LST6) | 0.42 | 0.46 | 0.48 | 0.61(91) | 0.77 | 0.78 | 0.69 | 0.73 |

GrassTussock(LST7) | 0.37 | 0.39 | 0.43 | 0.52(57) | 0.81 | 0.79 | 0.53 | 0.62 |