Measuring hydrological alteration and periodicity in river
The periodicity analysis on the time series data using wavelet transformation has not very old and it’s a modified form of Fourier transformation. In the case of Fourier transformation, it reveals the information in one dimension. If it gives information about the time domain, the scale domain will be lost and vice versa. The wavelet transformation can able to give both time and scale domain information (Wang et al., 2018; Liu et al., 2016; Amezquita-Sanchez & Adeli, 2015). This is why wavelet transformation has become a popular technique to solve time series problems (Amezquita-Sanchez & Adeli, 2015). The non-stationary time series data (mean, variance, covariance, and autocorrelation are changed over time and not able to get back to their previous original state) are most appropriate to run the wavelet analysis to explore the variability of the data. Therefore, the wavelet transform method is always applied to the hydro-meteorological time series data because of its non-stationary nature.
Goupillaud et al. (1984) first considered wavelets as a family of functions constructed from the translations and dilations of a single function, which is called the ‘‘mother wavelet”. The wavelet transform is defined by Eq. (1)
\({\psi _{a,b}}(t)=\frac{1}{{\sqrt {\left| a \right|} }}\psi (\frac{{t - b}}{a});a,b \in R;a \ne 0\) ------------------(Eq. 1)
Where, the scale parameter is represented by ‘a’ that evaluates the degree of compression, whereas, the translation parameter that computes the time location of the wavelet is represented by ‘b’. The ‘a’ parameter in the mother wavelet will be characterized by higher frequencies (smaller support in the time domain) when\(\left| a \right|\)will be less than 1. When \(\left| a \right|\)will is more than 1, then \({\psi _{a,b}}(t)\)has a larger time width than \(\psi (t)\) that will corresponds to lower frequencies. Thus, wavelets have time widths that are adapted to their frequency which is the real reason behind the success and exclusive usefulness of the Morlet wavelets in signal processing and time-frequency signal analysis.
Measuring Hydrological Alteration In Wetland Through Water Richness Mapping
Three major hydrological indicators like water presence frequency (WPF), hydro-period (HP), and water depth (WD) were used for computing the water richness of the wetland. WPF refers to the frequency of water appearance in a wetland pixel over a selected period (Sarda and Das, 2018). This analysis is very essential in the seasonally inundated flood plain wetland since the wetland in this region is highly erratic in behavior (Talukdar and Pal, 2019). Before developing the layers, spectral water indices based on wetland delineation were performed for each year following the Normalized differences water index (NDWI). Amongst other water indices, NDWI was reported suitable in the Barind flood plain region by Das and pal (2016). NDWI map of each year was turned into a binary map with 0 to non-wetland and 1 to wetland pixel and finally combined. The percentage of frequency in each period was computed about the selected period. WPF of each phase was classified into high, moderate, and low WPF zones using Eq. (2). High WPF signifies consistent wetland appearance and is ecologically more viable (Pal and Sarda, 2020; Pal et al., 2020). Hydro-period refers to the duration of water stagnation within the wetland. This map was prepared by averaging monthly binary NDWI images of the selected period using Eq. (3). Ecologically a perennial wetland is much more feasible than a non-perennial wetland (Yue et al., 2020). The water depth of wetland is very difficult. Field-level data is scarce. Therefore, following Talukdar and Pal (2019), Debanshi and Pal (2020), and Pal and Sarda (2021) the present work also simulated water depth data from the NDWI map using 36 ground-level data. NDWI-based water depth mapping idea was based on Gao et al. (1996) who established NDWI value indicates the thickness of water. Linear regression between NDWI value and water depth data was conducted and the resultant regression coefficient was used for simulating the NDWI map to obtain water depth data. The computed regression coefficient is y = 0.475 + 14.05x
\(WP{F_j}=\frac{{\sum\limits_{{i=1}}^{n} {{I_j}} }}{n} \times 100\) ……………………………… (Eq. 2)
WPF j = Water presence frequency of jth pixels in a period; Ij= jth pixel having water in the selected NDWI images; n = number of images. This value ranges from 0-100%.
\(HP=\sum\limits_{{i=1}}^{{n=12}} {{I_j}}\) ……………………………… (Eq. 3)
The value ranges from 0 to 12. Value 0 means non-wetland, 1 means only one month there is water stagnation, and 12 means water is available all through the year.
Wetland Water Richness (Wwr) Mapping And Validation
The above-mentioned hydrological components were integrated using both the non-weighted and weighted overlaying methods in the Arc-Gis environment. For weighting the parameters, the analytical hierarchy process (AHP) of Saaty (2004) was followed. AHP is a semi-quantitative approach for pair-wise comparison of parameters or subclasses of a parameter to estimate the weight of the concerned parameters or subclasses. The consistency check of this approach was 3% and therefore be accepted. The hydro-period was discovered to be the most important component (weight: 0.46). Eq. (4) was developed for weighted overlaying. The integrated WWR map was then divided into three classes: high, moderate, and low. Longer hydro-period, deeper wetland, consistent water appearance, defines high WWR class and vice-versa in the case of low WWR.
WCL= \(\sum\limits_{{j=1}}^{n} {{a_{ij}}{w_j}}\)…………………….. (Eq. 4)
Where, aij= ith rank of jth attribute; wj= weighted of jth attribute.
For validating the WWR models, 27 field validation sites from different WWR zones were taken and the employed parameters were observed directly from the field and taken from people’s experiences in this regard (Supplementary Table S3). Based on this, a composite score following the weighted compositing method was computed. The individual/max method was applied for data standardization. For weighting parameters, AHP weight as computed for spatial modeling was applied. AHP weight of the computed field parameters was 0.55 in the case of hydro-period, 0.29 in the case of water depth, and 0.17 in the case of WPF. The consistency check was 1%. A higher composite score signifies good water richness and vice versa. Pearson’s product-moment correlation coefficient was carried out between WWR and field-based WWR score. t-test was done for statistical significance.
Measuring Eco-hydrological Effects In River And Wetland
Ecological thresholding and degree of hydrological failure
Defining the hydrological failure rate and threshold Richter et al. (1998) proposed a range of dispersion metrics for measuring ecological flow status, including the twentieth and eightieth percentiles, one standard deviation (SD), and two standard deviations (SD), among others. Such approaches are commonly used for controlled river flow assessments, but they are rarely used for wetland assessments. Using calibrated water depth, RVA thresholds were set in the case of wetland, Based on the flow level of river water during the pre-dam period, the RVA threshold was determined in the case of the river. SD ± 1 method under RVA was applied to define lower and upper thresholds of ecologically viable water depth. If the depth value is less than Mean-SD1, the state is eco-hydrologically stressed, and if it is greater than Mean + SD1, the state is eco-hydrologically affluent. Depth value within Mean ± SD1 could be considered as a natural range of ecological (optimum) water depth. Based on the above-mentioned thresholds, the failure rate was computed. RVA thresholds of pre-dam periods of the selected seasons were computed and converted into a binary map. 0 was assigned to the pixels beyond the ecological threshold (< Mean + SD1 and > Mean-SD1) and 1 was assigned to the pixels with values within Mean ± SD1. This was done for each year and these were integrated and divided by total years considered in pre and post-dam phases separately. It could be expressed in decimal or percentage. The failure rate varies from 0–1 or from 0 to 100%. A value near 0 means the very least failure rate (ecologically viable) and a value near 100% indicates a high failure rate (ecologically stress).
Eco-deficit/surplus Estimation In Rivers And Mapping In Wetland
Time series data is commonly used for developing the flow duration curve (FDC). Discharge /water level data, water depth data, rainfall data, etc. are used for this. In this case, both discharge data of river and pixel scale water depth data of wetland were used. In FDC mean/median flow/depth was plotted against the exceedance probability. FDC was simply computed using Eq. (5).
\({\text{P=}}\left[ {\frac{{\text{M}}}{{{\text{n+1}}}}} \right]{\text{Χ 100}}\) …………………….. (Eq. 5)
Where, P = the probability that a given flow will be equaled or exceeded (% of the time), M = the ranked position on the time series discharge or depth data (dimensionless), n = the number of events for a period of record (dimensionless)
The flow duration curve (FDC) was used to calculate the eco-surplus and deficit (Vogel et al., 2007). First, median annual water flows duration curves for both unregulated (pre-dam) and regulated (post-dam) hydrological conditions were recorded. When the position of the regulated median FDC is below that of the uncontrolled median flow, the situation is called an eco-hydrological deficit, and the reverse condition can be treated as an eco-hydrological surplus (Talukdar and Pal, 2019). The same method was applied for measuring the eco-deficit/surplus of the wetland using water depth data. Considering the FDC of different hydrological phases, the eco-hydrological condition was studied. A spatial map of the same was done at pixel scale. This approach is common at river scale, however, rare at spatial scale.