catchment process modelling
3.7.2 Equations used to generate remote sensing based inputs for statistical modelling
MODIS reflectance data were used to calculate vegetation indices (i.e. NDVI, NDWI and EVI), and MODIS radiance data were used to calculate brightness temperatures (BT31 and BT32) and thermal indices (i.e. BTdiff and BTgrad). Vegetation indices were calculated only
on no-cloudy images, while BT and thermal indices were calculated on cloudy images. Cloudy images (or cloudy days) were separated from non-cloudy images (or non-cloudy days) using MODIS cloud mask product.
The calculation procedure and equation for NDVI are explained in Section 3.5.2.1 and Equation (3.24). The calculation of NDWI is similar to the NDVI, except bands used in NDWI. Indeed, while short-wave infrared was used in NDWI calculations, the red band was used for calculating NDVI.
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'˜ =:: − :+ :™š
™š (3.38)
where
λ
SWIR is the reflectance of the short-wave infrared (band 5 of MODIS), andλ
NIR isthe reflectance of the near infrared (band 2 of MODIS).
EVI on a non-cloudy day was calculated using MODIS reflectance of band 1, 2 and 3 (Huete et al., 2002):
7 = › ×: + R :: − : œn
œn− R!:••žœ+ G (3.39)
where : œn is the reflectance of MODIS band 1,
λ
BLUE is the reflectance of MODIS band3, G is the gain factor (2.5), L is the canopy background adjustment (for full canopy, L = 1), and C1 and C2 are the coefficients of the aerosol resistance term, which uses the blue band (i.e. band 3) to correct for aerosol influences in the red band (i.e. band 1). C1 and C2 are respectively equal to 6 and 7.5 respectively, as suggested by Huete et al. (2002).
As explained in Section 3.7.1, BT31, BT32, BTdiff and BTgrad were considered as surrogates
for rainfall in this study. BT31 and BT32, which were calculated from Equation (3.1) for rainfall estimation purposes (Section 3.5.1.1), were used in statistical modelling. These BT31 and BT32 were used to calculate BTdiff.BT31 was also used to calculate BTgrad.
BTdiff was calculated using Equation (3.40):
A •• = 31 − 32 (3.40) The BTgrad was initially introduced by Adler and Negri (1988) and has been used by
Kuligowski (2002) for rainfall estimation. They calculated BTgrad by calculating the
difference of the average temperature and the minimum temperature of a 5×5 pixel window, and dividing it by the pixel resolution. The use of the average can result in reducing the gradient, which in turn has the potential of identifying the cloud as a cirrus cloud which produces no-rain. Therefore, the difference between the minimum and
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maximum values divided by the pixel resolution of a 3×3 pixel window was considered as BTgrad in this study.
3.8
Statistical modelling
Artificial neural networks (ANN) were used in this study as the statistical modelling technique to estimate daily streamflow in both study areas. ANN were used in this study since the relationship between vegetation and thermal indices as well as BT with streamflow is very complex, and ANN have the capability to address complex relationships between inputs and output (Govindaraju and ASCE Task Committee on Application of Artificial Neural Networks in Hydrology, 2000; Maier and Dandy, 2000; Samarasinghe, 2006; ASCE Task Committee on Application of Artificial Neural Networks in Hydrology, 2000).
Possible input variables, which were outlined in Section 3.7.1, were considered in daily streamflow estimation using statistical modelling. Catchment average value of each variable was considered in this study for streamflow estimation rather than at a particular pixel. This was mainly to avoid errors in streamflow estimation with noisy pixels. Furthermore, the catchment average gives a better representation for the varying landuse/landcover conditions in the catchment.
The current day, several past days and 8-day average of possible input variables (Section 3.7.1) were considered in statistical modelling. The lagged variables were considered because of the lagged response of rainfall to streamflow, and rainfall to vegetation. On this basis, vegetation indices of seven lag days, and thermal indices and BT of three lag days were considered in this study. In addition to those variables, the previous 8-day average of NDVI, NDWI and EVI were also considered as input variables to model the current-day streamflow. The missing values of previous days are excluded in estimating 8-day average. By doing so, a seamless time series of 8-day average NDVI, NDWI and EVI was generated. Eight day averages were specifically considered since there is no significant difference in vegetation indices within the 8-day period and that is sufficient enough to fill the gaps caused by the clouds.
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There are 43 variables present as potential input variables for daily streamflow estimation using statistical modelling by considering the current day, lag times and the average of variables. All those 43 variables are shown in Tables 3.5 (for vegetation indices) and 3.6 (for BT and thermal indices).
Table 3.5 Vegetation indices of current day, lag days and 8-day average
Vegetation indices
NDVI NDWI EVI
1-day lag NDVI 1-day lag NDWI 1-day lag EVI 2-day lag NDVI 2-day lag NDWI 2-day lag EVI 3-day lag NDVI 3-day lag NDWI 3-day lag EVI 4-day lag NDVI 4-day lag NDWI 4-day lag EVI 5-day lag NDVI 5-day lag NDWI 5-day lag EVI 6-day lag NDVI 6-day lag NDWI 6-day lag EVI 7-day lag NDVI 7-day lag NDWI 7-day lag EVI 8-day avg NDVI 8-day avg NDWI 8-day avg EVI
Table 3.6 BT and thermal indices of current day and lag days
BT and thermal indices
BT31 BT32 BTdiff BTgrad
1-day lag BT31 1-day lag BT32 1-day lag BTdiff 1-day lag BTgrad 2-day lag BT31 2-day lag BT32 2-day lag BTdiff 2-day lag BTgrad 3-day lag BT31 3-day lag BT32 3-day lag BTdiff 3-day lag BTgrad
The increased number of input variables (43) can cause input replication in ANN modelling. All the indices outlined in Tables 3.5 and 3.6 are based on seven key indices, and these seven indices are based five bands of MODIS. In addition, the introduction of lag time and the average of indices can further enhanced the issue of ANN input replication to ANN modelling. Since replication and the increased number of input variables can made the ANN model very complex (Bowden et al., 2005a), an input variable selection procedure was followed to identify the most influential input variables that should be used in the ANN model for both catchments.
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