We generated the estimation models for daily mean air temperature based on the year-round LST data (Model I), the seasonal LST data (Model II), and the seasonal LST data for rural areas (Model III).
3.2. Optimal Strategies for Merging Images of Daily Mean Air Temperature Estimated from LSTs
We created maps of
TA values for each day from 2003 to 2013. We obtained a maximum of four
TA images on each clear day (
i.e., the daytime and nighttime LSTs from the TERRA and AQUA MODIS products). However, because of cloud cover, one or more of these datasets was often unavailable for certain parts of the study area, and the resulting map of estimated
TA suffered from gaps.
Figure 4 and
Figure 5 present the proportion of the data available for each pixel in the study area based on the daytime and nighttime TERRA and AQUA MODIS LSTs in 2012 and 2013, respectively. Most of the pixels in the study area had availability values of less than 50%. For example,
Figure 6 shows that on 21 June 2012, the available data amounted to only 18.40, 40.81, 51.04, and 24.29% of the pixels for
TATN,
TAAN,
TATD, and
TAAD, respectively. Fortunately, the available data from the different MODIS products both overlap and complement each other, which makes it possible to merge the data to increase data availability for the study area.
Figure 7 provides examples of merged
TA data for 21 June 2012. The available data coverage in the merged image totaled 75.58%, which represents an increase of 57.18, 34.77, 24.54, and 51.29 percentage points compared with the coverage based only on
TATN,
TAAN,
TATD, and
TAAD, respectively.
Table 4 shows that the RMSEs using Model III were 3.4, 2.0, 3.2, and 2.0 when using
LSTTD,
LSTTN,
LSTAD, and
LSTAN as the estimator, respectively, and the corresponding MAEs were 2.70, 1.56, 2.52, and 1.54. This means that combining the different
TA images calculated using the different LST products will result in a different accuracy.
Table 6 shows the possible strategies for combining
TA images. In strategy 1, for instance, the
TATN image was the initial basis for the merged data. When the
TATN value was missing, it was replaced by the
TAAN value. If both
TATN and
TAAN were missing, they were replaced by the
TAAD value. When all three were missing, they were replaced by the
TATD value. The values in
Table 6 were calculated independently for each grid cell throughout the study area.
Figure 4.
Percentages of available data for daily mean air temperature (TA) in 2012 based on daytime and nighttime TERRA and AQUA MODIS land surface temperatures (LSTs).
Figure 4.
Percentages of available data for daily mean air temperature (TA) in 2012 based on daytime and nighttime TERRA and AQUA MODIS land surface temperatures (LSTs).
Figure 5.
Percentages of available data for daily mean air temperature (TA) in 2013 based on daytime and nighttime TERRA and AQUA MODIS land surface temperatures (LSTs).
Figure 5.
Percentages of available data for daily mean air temperature (TA) in 2013 based on daytime and nighttime TERRA and AQUA MODIS land surface temperatures (LSTs).
Figure 6.
Daily mean air temperature (TA) estimated using the daytime and nighttime land surface temperatures (LSTs) from the TERRA and AQUA MODIS products for 21 June 2012.
Figure 6.
Daily mean air temperature (TA) estimated using the daytime and nighttime land surface temperatures (LSTs) from the TERRA and AQUA MODIS products for 21 June 2012.
Figure 7.
Merged image using the daily mean air temperatures (TAs) estimated using the daytime and nighttime land surface temperatures (LSTs) from the TERRA and AQUA MODIS products for 21 June 2012.
Figure 7.
Merged image using the daily mean air temperatures (TAs) estimated using the daytime and nighttime land surface temperatures (LSTs) from the TERRA and AQUA MODIS products for 21 June 2012.
Based on results in
Table 6, we found that
R2 varies between 0.9073 and 0.9383, the RMSEs range from 2.41 to 2.91, MAE change from 1.84 to 2.24, and bias varies between −0.5049 and −0.3421. The merged results had a higher
R2 and a lower RMSE and MAE if
TATN and
TAAN were used as the first two merged images (strategies 1, 2, 7, and 8). The prediction ability was high in each case, with
R2 > 0.93, RMSE ≤ 2.43, and MAE ≤ 1.87 in all cases. In contrast, if we used
TATD and
TAAD as the first two merged images (strategies 17, 18, 23, and 24),
R2 decreased (to values <0.92) and RMSE and MAE increased (to values ≥ 2.76 and 2.11, respectively). This is because the
R2 between
TA and nighttime LSTs was stronger than those between
TA and daytime LSTs (
Section 3.1). The estimation models based on nighttime LSTs had lower RMSEs and MAEs. The optimal combination of
TA images was provided by Strategy 2; although Strategy 18 produced similar results, the
R2 value was higher for Strategy 2. Therefore, we chose Strategy 2 as the optimal combination of the four
TA images.
Table 6.
Possible image merging strategies to create maps of daily mean air temperature (TA) using the TERRA and AQUA MODIS land surface temperatures (LSTs) and their accuracy using the validation datasets from 2012 to 2013.
Table 6.
Possible image merging strategies to create maps of daily mean air temperature (TA) using the TERRA and AQUA MODIS land surface temperatures (LSTs) and their accuracy using the validation datasets from 2012 to 2013.
Strategy | Base Image | Second Image | Third Image | Fourth Image | R2 | RMSE | MAE | bias |
---|
1 | TATN | TAAN | TAAD | TATD | 0.9381 | 2.42 | 1.84 | −0.4549 |
2 | TATN | TAAN | TATD | TAAD | 0.9383 | 2.41 | 1.84 | −0.4190 |
3 | TATN | TAAD | TAAN | TATD | 0.9352 | 2.48 | 1.90 | −0.5033 |
4 | TATN | TAAD | TATD | TAAN | 0.9338 | 2.51 | 1.92 | −0.5049 |
5 | TATN | TATD | TAAN | TAAD | 0.9361 | 2.45 | 1.87 | −0.4215 |
6 | TATN | TATD | TAAD | TAAN | 0.9341 | 2.49 | 1.91 | −0.4541 |
7 | TAAN | TATN | TAAD | TATD | 0.9367 | 2.43 | 1.87 | −0.4501 |
8 | TAAN | TATN | TATD | TAAD | 0.9369 | 2.42 | 1.87 | −0.4141 |
9 | TAAN | TAAD | TATN | TATD | 0.9299 | 2.54 | 1.94 | −0.3851 |
10 | TAAN | TAAD | TATD | TATN | 0.9253 | 2.63 | 2.00 | −0.4348 |
11 | TAAN | TATD | TATN | TAAD | 0.9281 | 2.57 | 1.96 | −0.4073 |
12 | TAAN | TATD | TAAD | TATN | 0.9250 | 2.62 | 2.00 | −0.3756 |
13 | TAAD | TAAN | TATN | TATD | 0.9170 | 2.76 | 2.13 | −0.4245 |
14 | TAAD | TAAN | TATD | TATN | 0.9124 | 2.84 | 2.19 | −0.4743 |
15 | TAAD | TATN | TAAN | TATD | 0.9190 | 2.74 | 2.10 | −0.4443 |
16 | TAAD | TATN | TATD | TAAN | 0.9124 | 2.84 | 2.19 | −0.4743 |
17 | TAAD | TATD | TATN | TAAN | 0.9097 | 2.89 | 2.22 | −0.4794 |
18 | TAAD | TATD | TAAN | TATN | 0.9079 | 2.91 | 2.24 | −0.4647 |
19 | TATD | TAAN | TATN | TAAD | 0.9167 | 2.76 | 2.11 | −0.3739 |
20 | TATD | TAAN | TAAD | TATN | 0.9136 | 2.81 | 2.15 | −0.3421 |
21 | TATD | TATN | TAAN | TAAD | 0.9183 | 2.74 | 2.09 | −0.3769 |
22 | TATD | TATN | TAAD | TAAN | 0.9162 | 2.78 | 2.13 | −0.4095 |
23 | TATD | TAAD | TAAN | TATN | 0.9073 | 2.91 | 2.24 | −0.3562 |
24 | TATD | TAAD | TATN | TAAN | 0.9091 | 2.89 | 2.22 | −0.3709 |
The LSTs from MODIS TERRA and AQUA are retrieved only under clear-sky conditions. LSTs under cloudy conditions would differ from those obtained under a clear sky. In contrast,
TA is available irrespective of cloud conditions. It is therefore important to analyze the influence of clouds on the estimation of
TA.
Table 7 summarizes the difference between the measured and estimated
TA under four different cases of cloud conditions. In Case 1, pixels from all four datasets are cloud-free. In Case 2, pixels from three of the four datasets are cloud-free. In Case 3, pixels from two of the four datasets are cloud-free. In Case 4, pixels from only one of the four datasets are cloud-free. Case 5 means that pixels are contaminated with clouds in all four LST products, so LST is instead estimated by means of interpolation between adjacent pixels (we will describe the interpolation method in
Section 3.3). In Case 2, Case 3 and Case 4, missing pixels due to cloudiness in different datasets were filled with corresponding cloud-free pixels in another dataset which means that
TA could have been overestimated (
i.e., because
LST would be lower as a result of the shade created by clouds). In Case 5, missing pixels were interpolated from surrounding cloud-free pixels, leading to a positive bias. The bias also varied seasonally. In winter, as the vegetation coverage is lower, bare soil and built structures receive more solar radiation, which causes a slightly higher bias when daytime
LST is merged into the map. In summer, vegetation and water reduce the temperature difference during the daytime and nighttime. The results show no obvious relationship among the four cases because the LSTs from the MODIS Terra and Aqua have already been filtered to eliminate cloud cover using the QC data. Under these circumstances, the data merging method proposed in this study has no consistent bias that must be adjusted to account for cloudiness.
Table 7.
Bias between measured and estimated daily mean air temperature (TA) under different cloud conditions for the merged data from four MODIS datasets using data from 2012 and 2013. Cases: 1 = pixels from all four datasets are cloud-free; 2 = pixels from three of the four datasets are cloud-free; 3 = pixels from two of the four datasets are cloud-free; 4 = pixels from one of the four datasets are cloud-free; 5 = pixels are contaminated with clouds in all four datasets and must be estimated by means of interpolation of data from adjacent pixels.
Table 7.
Bias between measured and estimated daily mean air temperature (TA) under different cloud conditions for the merged data from four MODIS datasets using data from 2012 and 2013. Cases: 1 = pixels from all four datasets are cloud-free; 2 = pixels from three of the four datasets are cloud-free; 3 = pixels from two of the four datasets are cloud-free; 4 = pixels from one of the four datasets are cloud-free; 5 = pixels are contaminated with clouds in all four datasets and must be estimated by means of interpolation of data from adjacent pixels.
Case | Whole Year | Spring | Summer | Autumn | Winter |
---|
1 | −0.4837 | −0.8475 | −0.3088 | −0.3207 | −0.2039 |
2 | −0.6341 | −0.3766 | −1.0319 | −0.4779 | −0.7821 |
3 | −0.3775 | −0.2540 | −0.6404 | −0.0127 | −1.0149 |
4 | −0.3979 | −0.0953 | −0.4046 | −0.4798 | −0.7197 |
5 | 0.0646 | −0.1483 | −0.1535 | 0.4003 | 0.3944 |
3.3. Temporal and Spatial Fusion of Daily Mean Air Temperature Using Time Series Images
Figure 8 demonstrates the spatial distribution of data availability for each pixel using data for the whole year in 2012 and 2013. The merged image greatly improved the spatial coverage by the available data.
Table 8 presents the annual data availability percentages for the
TA images throughout the study area for the merged images and for images derived from daytime and nighttime TERRA and AQUA MODIS LSTs in 2012 and 2013. The results show that the merged image greatly improved the spatial coverage by the available data, reaching values of 55.46% in 2012 and 44.92% in 2013. But the percentages of available data were 22.08%, 17.94%, 22.48%, and 18.65% for
TATN,
TAAN,
TATD, and
TAAD images in 2012. They were 28.85%, 25.23%, 31.30%, and 27.84%, respectively, in 2013. The available data in the merged images therefore increased by 33.38, 37.52, 32.98, and 36.81 percentage points in 2012 and by 16.07, 19.69, 13.62, and 17.08 percentage points in 2013 compared with the corresponding
TATN,
TAAN,
TATD, and
TAAD images. However, given the fact that data for an average of half of the pixels were unavailable even after merging the images, it is clearly necessary to obtain fuller spatial coverage to improve the accuracy of estimation of
TA.
Figure 8.
Percentages of data availability for daily mean air temperature (TA) in 2012 and 2013 for merged images based on the validation dataset.
Figure 8.
Percentages of data availability for daily mean air temperature (TA) in 2012 and 2013 for merged images based on the validation dataset.
Table 8.
Percentages of the daily mean air temperature (
TA) images for the merged dataset (all four MODIS LST products combined using strategy 2 in
Table 6) and for images derived from daytime and nighttime TERRA and AQUA MODIS LSTs in 2012 and 2013.
Table 8.
Percentages of the daily mean air temperature (TA) images for the merged dataset (all four MODIS LST products combined using strategy 2 in Table 6) and for images derived from daytime and nighttime TERRA and AQUA MODIS LSTs in 2012 and 2013.
| | Data Availability (%for Coverage, Percentage Points for Increase) |
---|
Year | Merged coverage | TATN | TAAN | TATD | TAAD |
---|
coverage | increase | coverage | increase | coverage | increase | coverage | increase |
---|
2012 | 55.46 | 22.08 | 33.38 | 17.94 | 37.52 | 22.48 | 32.98 | 18.65 | 36.81 |
2013 | 44.92 | 28.85 | 16.07 | 25.23 | 19.69 | 31.30 | 13.62 | 27.84 | 17.08 |
Ideally, the
TA for crop growth monitoring and model simulation should take advantage of complete datasets. In reality, noise and missing pixels create gaps in the data that must be filled somehow. Aiming to achieve improved accuracy of
TA will require efforts to reduce the loss of data and fill gaps, thereby providing better coverage of the whole study region. The daily mean temperature images before the date of the estimation are obtained if their data are available. These images carry important information for the
TA estimation for the present day. We therefore proposed a method to fill gaps in the data based on the assumption that atmospheric conditions would be uniform within a relatively small window surrounding a pixel for which data is missing. This means that the
TA difference of a target pixel between data
t and data
t-1 is equal to the mean
TA difference of surrounding pixels between data
t and data
t-1. To minimize the uncertainty in the error introduced by cloudiness and gaps between swaths, we exploited a possible strategy based on finding the optimal window size by extending the process into a larger geographic area. The optimum window size was obtained from statistical analysis of the difference between
TA estimated from the MODIS LST and
TA measured by the meteorological stations.
Figure 9 displays the change in the quality of the estimate as a function of the window size used for the spatial filling.
Figure 10 illustrates this estimation procedure (using a window size of 9 × 9 pixels as an example). The
R2 increased with increasing window size. In the contrast, RMSE, MAE, and bias decreased with increasing window size. The magnitude of the bias reached its minimum at a window size of 33 × 33 pixels. We therefore used a grid of 33 × 33 pixels centered on the pixel with missing data in our subsequent analysis. The mean difference in
TA among these pixels is calculated as follows:
where
is the mean
TA difference among the pixels with available data both at the date of estimation (
i.e., at time
t) and the date before the estimation (
i.e., at time
t–1).
N is the number of pixels with available
TA values both at the date of estimation and the date before estimation.
and
are the
TA values for the pixel in line
i and column
j of the image at times
t and
t–1.
can be estimated as follows:
We used this approach to generate a time series of filled pixels using data for the whole year derived from the 14 rural meteorological stations in both 2012 and 2013.
Figure 11 shows the resulting relationship between the estimated and measured
TA. Overall, the approach produced good results: a strong and statistically significant relationship (
R2 = 0.8971) with a low MAE (2.35) for data from all seasons. Using the filled dataset increased data coverage to 78.23% and 86.02% in 2012 and 2013, respectively. The model showed a seasonal pattern of error. In summer, the
R2 was relatively poor and the distribution of the data was more concentrated than in other seasons which led to a lower RMSE. In turn, the higher LST increased turbulence in the atmospheric boundary layer, thereby affecting heat transfer from the land surface into the ambient air and subsequently to the upper atmosphere. In contrast, the land surface receives less solar radiation in winter, thereby weakening turbulence. The retrieval of
TA is simpler at night because solar radiation does not affect the thermal infrared signal.
Figure 12 demonstrates the day-to-day variation of the measured and estimated daily mean air temperature in 2012 and 2013 at the 14 rural meteorological stations. Judging from the similarity of the measured and estimated air temperatures (
i.e., the difference was small and centered on 0 °C), the estimation model generally showed good agreement with the measured
TA and was able to reflect the annual pattern of
TA fluctuation. We found no systematically positive or negative biases between the estimated and measured values (
Figure 11 and
Figure 12).
Figure 9.
Analysis the optimal size (pixels) of the window used for the spatial filling method illustrated in
Figure 10.
Figure 9.
Analysis the optimal size (pixels) of the window used for the spatial filling method illustrated in
Figure 10.
Figure 10.
Flowchart for calculation of missing pixel values caused by cloud cover and other problems using the merged images from the day before the estimation date The red square represents the pixel for which TA will be calculated based on data from the previous day.
Figure 10.
Flowchart for calculation of missing pixel values caused by cloud cover and other problems using the merged images from the day before the estimation date The red square represents the pixel for which TA will be calculated based on data from the previous day.
Figure 11.
Relationships between the estimated and measured daily mean air temperature (TA) for whole-year data and for data from the spring, summer, fall, and winter.
Figure 11.
Relationships between the estimated and measured daily mean air temperature (TA) for whole-year data and for data from the spring, summer, fall, and winter.
Figure 12.
Annual variation in the measured and estimated daily mean air temperature (TA) in 2012 and 2013 based on the data from the 14 rural meteorological stations.
Figure 12.
Annual variation in the measured and estimated daily mean air temperature (TA) in 2012 and 2013 based on the data from the 14 rural meteorological stations.