The model’s prediction performance is quantitatively evaluated by representative metrics. And the r and RMSE (root mean squared errors) are used to measure the difference between the predicted image and actual image. The formulations of these metrics are as follows:

$r=\frac{{\displaystyle {\sum}_{j=1}^{N}({x}_{j}-\stackrel{\xaf}{x})}({y}_{j}-\stackrel{\xaf}{y})}{{\sqrt{{\displaystyle {\sum}_{j=1}^{N}{({x}_{j}-\stackrel{\xaf}{x})}^{2}{\displaystyle {\sum}_{j=2}^{N}({y}_{j}-\stackrel{\xaf}{y})}}}}^{2}}$ (5)

$RMSE=\sqrt{\frac{{\displaystyle {\sum}_{j=1}^{N}{({x}_{j}-{y}_{j})}^{2}}}{N}}$ (6)

where N is the total number of pixels in the predicted image, x_{j} and y_{j} are the values of the jth pixel in the predicted image and the actual image respectively. And
$\stackrel{\xaf}{x}$ ,
$\stackrel{\xaf}{y}$ represent the mean gray values of the predicted image and the actual image respectively.

3. Result and Discussion

3.1. Prediction Performance

We use the August 02 Landsat NDVI image as validation source and use April 28 and October 21 to predict the August 02 image. Figure 3 shows the actual NDVI image and predicted NDVI image by four spatiotemporal fusion models on August 02, 2015. All the predicted NDVI images are consistent with the actual image from visual comparison, and water boundaries and clear land can be predicted obviously, which demonstrate the practicality of these spatiotemporal models.

3.2. Quantitative Assessment

Scatter plots in Figure 4 indicate the difference between the actual NDVI values and the predicted NDVI values on August 02 2015. We can see that the predicted NDVI values by four spatiotemporal fusion models are all fall close to the 1:1 line, which show all four spatiotemporal fusion models can capture changes in phenology. And the prediction of ESTARFM and STVIFM using one input pair is relatively accurate than that of STARFM and FSDAF using two input pairs, which because two input pairs can provide more spatial details.

To better assess the accuracy of predictions, the metrics r and RMSE were calculated in Table 1. All four methods can get the change details to the base date image to get the prediction. The accuracy of the predicted NDVI image using the STVIFM is the best (r = 0.864, RMSE = 0.1191) and a little better than the accuracy of the predicted NDVI image using ESTARFM (r = 0.867, RMSE = 0.1247). The image predicted by STARFM (r = 0.804, RMSE = 0.1626) and FSDAF (r = 0.810, RMSE = 0.1446) can also produce an accurate result, but these two models got inaccurate predictions on some pixels (Figure 3(b), Figure 3(d)), which demonstrate the predictions using two input pairs is relatively more accurate.

Table 1. Comparison of rand RMSE betweeen actual NDVI and predicted NDVI by using STARFM, ESTARFM, FSDAF, and STVIFMmodelsin the study area on August 02 2015.

Figure 3. (a) Actual Landsat-8 NDVI image; (b)-(d) are the predicted NDVI images of STARFM, ESTARFM, FSDAF, and STVIFM respectively.

Figure 4. Scatter plots of the actual and predicted values for NDVI (darker areas indicate high density, and the line is 1:1 line).

4. Conclusion

This study made a comparison between four spatiotemporal fusion models, STARFM, ESTARFM, FSDAF, and STVIFM using high-and coarse-resolution NDVI data, and quantitatively analyzed the performance of these models using r and RMSE. For the results predicted by all four models, the r varied between 0.804 and 0.867 and the RMSE varied between 0.1191 and 0.1626, which showed that all the selected models can produce reasonable predictions. And we found that STVIFM can capture vegetation change and get the predicted results closed to actual NDVI image than other three methods. In conclusion, the STVIFM is more suitable for producing high spatiotemporal resolution NDVI time series, especially for some vegetation with different growing period.

Cite this paper

Han, Z. and Zhao, W. (2019) Comparison of Spatiotemporal Fusion Models for Producing High Spatiotemporal Resolution Normalized Difference Vegetation Index Time Series Data Sets.*Journal of Computer and Communications*, **7**, 65-71. doi: 10.4236/jcc.2019.77007.

Han, Z. and Zhao, W. (2019) Comparison of Spatiotemporal Fusion Models for Producing High Spatiotemporal Resolution Normalized Difference Vegetation Index Time Series Data Sets.

References

[1] Busetto, L., Meroni, M. and Colombo, R. (2008) Combining Medium and Coarse Spatial Resolution Satellite Data to Improve the Estimation of Sub-Pixel NDVI Time Series. Remote Sens. Environ., 112, 118-131.
https://doi.org/10.1016/j.rse.2007.04.004

[2] Tewes, A., Thonfeld, F., Schmidt, M., Oomen, R., Zhu, X., Dubovyk, O., Menz, G. and Schellberg, J. (2015) Using RapidEye and MODIS Data Fusion to Monitor Vegetation Dynamics in Semi-Arid Rangelands in South Africa. Remote Sens., 7, 6510-6534. https://doi.org/10.3390/rs70606510

[3] Bhandari, S., Phinn, S. and Gill, T. (2012) Preparing Landsat Image Time Series (LITS) for Monitoring Changes in Vegetation Phenology in Queensland, Australia. Remote Sens., 4, 1856-1886. https://doi.org/10.3390/rs4061856

[4] Gevaert, C.M. and García-Haro, F.J. (2015) A Comparison of STARFM and an Unmixing Based Algorithm for Landsat and MODIS Data Fusion. Remote Sensing of Environment, 156, 34-44. https://doi.org/10.1016/j.rse.2014.09.012

[5] Schmidt, M., Udelhoven, T., Gill, T. and Röder, A. (2012) Long Term Data Fusion for a Dense Time Series Analysis with MODIS and Landsat Imagery in an Australian Savanna. J. Appl. Remote Sens., 6, 63512. https://doi.org/10.1117/1.JRS.6.063512

[6] Fensholt, R. (2004) Earth Observation of Vegetation Status in the Sahelian and Sudanian West Africa: Comparison of Terra MODIS and NOAA AVHRR Satellite Data. Int. J. Remote Sens., 25, 1641-1659.
https://doi.org/10.1080/01431160310001598999

[7] Zurita-Milla, R., Clevers, J., van Gijsel, J. and Schaepman, M. (2011) Using MERIS Fused Images for Classification Mapping and Vegetation Status Assessment in Heterogeneous Land-scapes. Int. J. Remote Sens., 32, 973-991.
https://doi.org/10.1080/01431160903505286

[8] Gao, F., Masek, J., Schwaller, M. and Hall, F. (2006) On the Blending of the MODIS and Landsat ETM+ Surface Reflectance. IEEE Trans. Geosci. Remote Sens., 44, 2207-2218. https://doi.org/10.1109/TGRS.2006.872081

[9] Zhu, X., Chen, J., Gao, F., Chen, X. and Masek, J.G. (2010) An enhanced Spatial and Temporal Adaptive Reflectance Fusion Model for Complex Heterogeneous Regions. Remote Sens. Environ., 114, 2610-2623. https://doi.org/10.1016/j.rse.2010.05.032

[10] Zhu, X., Helmer, E.H., Gao, F., Liu, D., Chen, J. and Lefsky, M.A. (2016) A Flexible Spatiotemporal Method for Fusing Satellite Images with Different Resolutions. Remote Sens. Environ., 172, 165-177. https://doi.org/10.1016/j.rse.2015.11.016

[11] Liao, C., Wang, J., Pritchard, I., et al. (2017) A Spatio-Temporal Data Fusion Model for Generating NDVI Time Series in Heterogeneous Regions. Remote Sensing, 9, 1125. https://doi.org/10.3390/rs9111125

[12] Zhukov, B., Oertel, D. and Lanzl, F. (1999) Unmixing-Based Multisensor Multiresolution Image Fusion. IEEE Trans. Geosci. Remote Sens., 37, 1212-1226.
https://doi.org/10.1109/36.763276