Recursive Digital Filter Method Research Articles

Stream analysis for a sub-catchment of Red River (Vietnam) using isotopic technique and recursive digital filter method

River streams, in general, comprise of two flows: quick flow and baseflow. The baseflow is closely related to geological catchment properties, and understanding the baseflow contribution to stream flow is very important in the planning of water resources management. The baseflow in a sub-catchment of the Red River in Vietnam was quantified using the isotopic technique, and results were compared with Eckhardt’s recursive digital filter (RDF) method. Results of the isotopic approach showed that groundwater is recharged from regions at 300 to 800 m above mean sea level. The upstream baseflow gains from Holocene and Pleistocene aquifers throughout the year, contributing to 65 ± 4 % of the river discharge. On the contrary, the midstream baseflow contributes 44.6 ± 6.5 % of the river’s annual discharge to both Holocene and Pleistocene aquifers. The downstream is more complicated, where the baseflow loses to the Pleistocene aquifer and gains 73 ± 17 % of the river's annual discharge from the Holocene aquifer. The loss of baseflow was attributed to the high rate of groundwater mining.Maintaining the vegetative cover over the recharge areas is recommended to reduce runoff and increase groundwater potential so that the baseflow could sustain the river stream.

Evaluation of recharge estimation methods applied to fissure and karst aquifers of the Lagoa Santa Karst Environmental Protection Area, Brazil

AbstractThe Lagoa Santa Karst Environmental Protection Area is known worldwide as the place where the oldest human fossil in the Americas was found. Beyond its archaeological richness is speleological, faunistic and floristic richness across this remarkable karstic landscape. It is also a region with important aquifers for public and private water supply. Located in the state of Minas Gerais, Brazil, despite its environmental relevance, the area is characterized by increased anthropic environmental impacts. Regarding the relationship between surface water and groundwater, in order to investigate the annual input of water into the aquifers, this study aimed to estimate the annual recharge rate in the hydrological years 2017 to 2021 using three methods: the recession curve displacement method of Rorabaugh (International Association of Scientific Hydrology, 1964, 63:432–441), the recursive digital filter method by Lyne and Hollick (Institute of Engineers Australia National Conference, 1979, pp. 89–93), and the method based on water‐table fluctuation in tubular wells proposed by Healy and Cook (Hydrogeology Journal, 2002, 10(1):91–109). The average percentage of rainfall that is recharged into the aquifer, considering the overall period studied from 2017 to 2021, found with the three methods was 13%, 9% and 9%, respectively, which indicates that recharge rates within the study area are low and that higher values are observed within karst basins in comparison with basins located in pelitic zones. Overall, the methods yielded coherent values among each other and were compared with previous studies in the area. In relation to the automatized recursive digital filter method, the automatized recession curve displacement method was more adherent because it considers daily streamflow measurements. The WTF method was handy for the local recharge rate analysis and enabled an evaluation of recharge rates in each aquifer unit. Despite the similarity of the values obtained in the methods, they are likely underestimated due to the high pumping rates of groundwater. Furthermore, it is recommended to deepen the correlation between lithotype, karst geomorphology, and its dissolution processes to improve the understanding of recharge processes.

A new approach to use of wavelet transform for baseflow separation of Karst springs (case study: Gamasiyab spring)

Today, groundwater is the essential resource the whole water sector demands. The spring baseflow discharge analysis can significantly help us better manage water resources. This study was focused on the separation baseflow discharge of the Gamasiyab karstic spring (western Iran) using the wavelet transform (WT). The recursive digital filter (RDF) method with different algorithms has been used to compare the approach performance. Forty-nine years (1968–2018) of the recorded springs’ daily discharge data were used for this aim. The isotopic content (IC) method was used to determine the best RDF algorithm and WT for baseflow separation. The IC of the monthly samples taken in 2017–2018 was measured. The results showed that the WT had the adjusted coefficient of determination (R_{{{text{adjusted}}}}^{2}) of 0.95 and root mean square error (RMSE) of 0.552 (m3/s) compared to the IC index method. The best algorithm in the RDF method was related to the Eckhardt algorithm with R_{{{text{adjusted}}}}^{2} of 0.97 and RMSE of 0.670 (m3/s), which had the best performance compared to the IC index method. Results showed that in most samples, the values of the separated baseflow by the WT are closer to the isotopic values. Also, based on the RMSE criterion, the WT has a lower RMSE than the RDF method and is known as the best method in this study. The results showed that the WT accurately separated the spring baseflow discharge and could split the baseflow of rivers.

Performance evaluation of an automated method for hydrograph separation in Mellah catchment, Northeastern Algeria

This paper explains a procedure based on the master recession curve (MRC) for hydrograph separation into individual flow components, using the recession constant K. To evaluate the performance of this computational technique, the results of the baseflow component were compared to the baseflow component obtained from the recursive digital filter (RDF) method. The study has revealed that the results of baseflow achieved by both methods show similarity to a great extent, and the baseflow values agree better with (R2 > 0.77). Moreover, automated baseflow separation underestimates the simulated baseflow from RDF method by as much as 2.35%, or overestimates it by up to 23.55%, during rainfall. These methods were applied to a set of hydrometric measures in the Mellah catchment, Algeria. The results proved that the proposed method gives a better estimate of flow components.

Can the two-parameter recursive digital filter baseflow separation method really be calibrated by the conductivity mass balance method?

Abstract. The two-parameter recursive digital filter method (Eckhardt) and the conductivity mass balance (CMB) method are two widely used baseflow separation methods favored by hydrologists. Some divergences in the application of these two methods have emerged in recent years. Some scholars believe that deviation of baseflow separation results of the two methods is due to uncertainty of the parameters of the Eckhardt method and that the Eckhardt method should be corrected by reference to the CMB method. However, other scholars attribute the deviation to the fact that they contain different transient water components. This study aimed to resolve this disagreement by analyzing the effectiveness of the CMB method for correcting the Eckhardt method through application of the methods to 26 basins in the United States by comparison of the biases between the generated daily baseflow series. The results showed that the approach of calibrating the Eckhardt method against the CMB method provides a “false” calibration of total baseflow by offsetting the inherent biases in the baseflow sequences generated by the two methods. The baseflow sequence generated by the Eckhardt method usually includes slow interflow and bank storage return flow, whereas that of the CMB method usually includes high-conductivity water flushed from swamps and depressions by rainfall, but not low-conductivity interflow and bank storage return flow. This difference results in obvious peak misalignment and periodic deviation between the baseflow sequences obtained by the two methods, thereby preventing calibration. However, multi-component separation of streamflow can be achieved through comparison. Future research should recognize the deviations between the separation results obtained by the different methods, identify the reasons for these differences, and explore the hydrological information contained therein.

Baseflow estimation in typical catchments in the Yellow River Basin, China

Abstract Baseflow is crucial to maintaining river flow during low-rainfall periods. The baseflow estimation is important to water supply and ecological environmental protection in the Yellow River Basin (YRB), China. This paper comprehensively assessed the applicability of four single-parameter digital filtering, recursive digital filtering, and HYSEP (streamflow hydrograph separation) methods across four typical catchments in the Yellow River Basin: the Zuli River Basin, the Kuye River Basin, the Tuwei River Basin, and the Jingle sub-basin. We also investigated annual and monthly variations in baseflow. We found the standard deviation and coefficient of variation of baseflow index through recursive digital filter were relatively small. And the baseflow process line was smoother and more reasonable in typical year and typical storm-flood events, which conformed to the damping and hysteresis effect of the underlying surface. Thus the recursive digital filter method had the best performance, which was recommended for baseflow separation in the YRB. The estimated baseflow index of typical basins were between 0.354 and 0.502. In addition, inter-annual baseflow showed a decreasing trend and intra-annual baseflow was characterized by uneven distribution, which was subject to the characteristics of each basin.

Calibration of surface runoff parameters with the hydrologic tank model using recursive digital filter and master recession curve

There are two basic methods to calibrate the hydrological model: (1) the trial and error procedure; (2) the automatic calibration. The problem in the calibration method is the determination of the initial value of the parameters. This poses a problem for beginner model users. This paper presents the calibration results of surface runoff parameters in the hydrological tank model using recursive digital filter method and the master recession curve. The results indicate that the Recursive Digital Filter as a surface runoff separation method can be used for the initial approach to calibrate the tank model parameters

The cumulative effects of forest disturbance and climate variability on streamflow components in a large forest-dominated watershed

Assessing how forest disturbance and climate variability affect streamflow components is critical for watershed management, ecosystem protection, and engineering design. Previous studies have mainly evaluated the effects of forest disturbance on total streamflow, rarely with attention given to its components (e.g., base flow and surface runoff), particularly in large watersheds (>1000 km2). In this study, the Upper Similkameen River watershed (1810 km2), an international watershed situated between Canada and the USA, was selected to examine how forest disturbance and climate variability interactively affect total streamflow, baseflow, and surface runoff. Baseflow was separated using a combination of the recursive digital filter method and conductivity mass balance method. Time series analysis and modified double mass curves were then employed to quantitatively separate the relative contributions of forest disturbance and climate variability to each streamflow component. Our results showed that average annual baseflow and baseflow index (baseflow/streamflow) were 113.3 ± 35.6 mm year−1 and 0.27 for 1954–2013, respectively. Forest disturbance increased annual streamflow, baseflow, and surface runoff of 27.7 ± 13.7 mm, 7.4 ± 3.6 mm, and 18.4 ± 12.9 mm, respectively, with its relative contributions to the changes in respective streamflow components being 27.0 ± 23.0%, 29.2 ± 23.1%, and 25.7 ± 23.4%, respectively. In contrast, climate variability decreased them by 74.9 ± 13.7 mm, 17.9 ± 3.6 mm, and 53.3 ± 12.9 mm, respectively, with its relative contributions to the changes in respective streamflow components being 73.0 ± 23.0%, 70.8 ± 23.1% and 73.1 ± 23.4%, respectively. Despite working in opposite ways, the impacts of climate variability on annual streamflow, baseflow, and surface runoff were of a much greater magnitude than forest disturbance impacts. This study has important implications for the protection of aquatic habitat, engineering design, and watershed planning in the context of future forest disturbance and climate change.

Annual baseflow variations as influenced by climate variability and agricultural land use change in the Missouri River Basin

The Missouri River system has a large water storage capacity, where baseflow plays an important role. Understanding historical baseflow characteristics with respect to climate and land use impacts is essential for effective planning and management of water resources in the Missouri River Basin (MORB). This study evaluated statistical trends in baseflow and precipitation for 99 MORB minimally disturbed watersheds during 1950–2014. Elasticity of baseflow to climate variability and agricultural land use change were quantified for the 99 studied watersheds. Baseflow was derived from daily streamflow records with a recursive digital filter method. The results showed that baseflow varied between 38 and 80% (0 and 331mm/year) of total streamflow with an average of 60%, indicating that more than half of streamflow in the MORB is derived from baseflow. The trend analysis revealed that precipitation increased during the study period in 78 out of 99 watersheds, leading to 1–3.9% noticeable increase in baseflow for 68 of 99 watersheds. Although the changes in baseflow obtained in this study were a result of the combined effects of climate and land use change across the basin, upward trends in baseflow generally coincide with increased precipitation and agricultural land use trends in the basin. Agricultural land use increase mostly led to a 0–5.7% decrease in annual baseflow in the basin, except toward east of the basin where baseflow mostly increased with agricultural land use increase (0.1–2.0%). In general, a 1% increase in precipitation and a 1% increase in agricultural land use resulted in 1.5% increase and 0.2% decrease in baseflow, respectively, during the study period. These results are entirely dependent on the quality of data used; however, they provide useful insight into the relative influence of climate and land use change on baseflow conditions in the Great Plains region of the USA.

Data requirements for using combined conductivity mass balance and recursive digital filter method to estimate groundwater recharge in a small watershed, New Brunswick, Canada

Summary Estimation of baseflow and groundwater recharge rates is important for hydrological analysis and modelling. A new approach which combines recursive digital filter (RDF) model with conductivity mass balance (CMB) method was considered to be reliable for baseflow separation because the combined method takes advantages of the reduced data requirement for RDF method and the reliability of CMB method. However, it is not clear what the minimum data requirements for producing acceptable estimates of the RDF model parameters are. In this study, 19-year record of stream discharge and water conductivity collected from the Black Brook Watershed (BBW), NB, Canada were used to test the combined baseflow separation method and assess the variability of parameters in the model over seasons. The data requirements and potential bias in estimated baseflow index (BFI) were evaluated using conductivity data for different seasons and/or resampled data segments at various sampling durations. Results indicated that the data collected during ground-frozen season are more suitable to estimate baseflow conductivity ( C bf ) and data during snow-melting period are more suitable to estimate runoff conductivity ( C ro ). Relative errors of baseflow estimation were inversely proportional to the number of conductivity data records. A minimum of six-month discharge and conductivity data is required to obtain reliable parameters for current method with acceptable errors. We further found that the average annual recharge rate for the BBW was 322 mm in the past twenty years.

Regression Modeling of Baseflow and Baseflow Index for Michigan USA

Baseflow plays an important role in maintaining streamflow. Seventeen gauged watersheds and their characteristics were used to develop regression models for annual baseflow and baseflow index (BFI) estimation in Michigan. Baseflow was estimated from daily streamflow records using the two-parameter recursive digital filter method for baseflow separation of the Web-based Hydrograph Analysis Tool (WHAT) program. Three equations (two for annual baseflow and one for BFI estimation) were developed and validated. Results indicated that observed average annual baseflow ranged from 162 to 345 mm, and BFI varied from 0.45 to 0.80 during 1967–2011. The average BFI value during the study period was 0.71, suggesting that about 70% of long-term streamflow in the studied watersheds were likely supported by baseflow. The regression models estimated baseflow and BFI with relative errors (RE) varying from −29% to 48% and from −14% to 19%, respectively. In absence of reliable information to determine groundwater discharge in streams and rivers, these equations can be used to estimate BFI and annual baseflow in Michigan.

Estimation of annual baseflow at ungauged sites in Indiana USA

Summary This study developed regression models for predicting baseflow and baseflow index (BFI) (baseflow/total streamflow) at ungauged sites by using long-term baseflow data, land use, and watershed physiographic characteristics. Baseflow data were derived from daily streamflow records with a recursive digital filter method for baseflow separation for 22 watersheds in Indiana. Filtered average annual baseflow varies between 150 and 320 mm for the study watersheds. BFI varies between 0.40 to 0.88 with an average of 0.60, suggesting that 60% of long-term streamflow in Indiana is likely supported by ground water discharge and shallow subsurface flow. Three regression equations (one for baseflow and one for BFI) were developed and evaluated in the study watersheds. Results showed that the models reasonably estimate baseflow with relative errors (RE) ranging from 0% to 30%, except in one watershed where the RE was 50% during the validation period. These equations can be used to estimate baseflow and BFI at ungauged sites in Indiana. The present work would have implications for improving the capabilities of simple hydrologic/water quality models, and support planning and management of water resources. The methodology used in this study can be applied in other locations and regions.

Baseflow separation in a small watershed in New Brunswick, Canada, using a recursive digital filter calibrated with the conductivity mass balance method

AbstractBaseflow separation is important for obtaining critical parameters for hydrological models. As measuring the baseflow component directly is difficult, various analytical and empirical baseflow separation methods have been developed and tested. The recursive digital filter (RDF) method is commonly used for baseflow separation due to its simplicity and low data requirement. However, parameters used in the RDF method are often determined arbitrarily, resulting in high uncertainty of the estimated baseflow rate. A more accurate method is the conductivity mass balance (CMB) method, which is established based on the differences in physical processes between baseflow and surface runoff. In this research, the output of the CMB method was used to calibrate the parameters of an RDF model, and the calibrated RDF model was used to estimate monthly, seasonal and annual baseflow rate and baseflow index for the past 19 years using streamflow discharge records. The characteristics of the baseflow hydrographs were found to be consistent with the hydrological and hydrogeological conditions of the research area. Research results indicated that the accuracy of the RDF model has been greatly enhanced after being calibrated with the CMB method so that the RDF model can provide more reliable baseflow separation results for a long‐term study. Copyright © 2012 John Wiley & Sons, Ltd.

Filtered smoothed minima baseflow separation method

Summary The smoothed minima baseflow separation method of the United Kingdom Institute of Hydrology (UKIH) is coupled with the recursive digital filter (RDF) to develop the filtered smoothed minima baseflow separation (FUKIH) method in which the daily streamflow time series is first separated by the UKIH method and then filtered by the RDF. In the FUKIH method, the sharp peaks and troughs generated by linear interpolation in the UKIH method are removed and a smooth hydrograph representing the baseflow generating mechanisms is obtained. The application to daily streamflow time series from the Filyos river in the Western Black Sea region, Turkey, shows that the FUKIH baseflow sequence traces the UKIH method during the recession period of the hydrograph while it traces the RDF during the ascension. The FUKIH baseflow sequence has delayed peaks rather than peaks taking place right under the total streamflow peaks. This is plausible as it is known baseflow consists of delayed flow with longer time of concentration than the total streamflow hydrograph. A low-flow characteristic used in the comparison of baseflow separation methods, the ratio of the quantiles with exceedance probabilities of 90% and 50%, Q90/Q50, is found to be the same for FUKIH and RDF. This suggests the FUKIH method is able to reproduce the results of the RDF method. The advantage of the FUKIH over the RDF is that it requires only one pass filtering in the forward direction instead of three (forward–backward–forward filtering) in the RDF.

Regional estimation of base flow for the conterminous United States by hydrologic landscape regions

Information on base flow availability and/or contributions is needed to develop water quantity and water quality management strategies. Base flow availability varies over space and time in a region due to climate, topography, landscape, and geological characteristics. In this study, base flow index (BFI) (base flow/total stream flow) was estimated from daily streamflow records using a recursive digital filter method and interpolated to produce a raster grid map for the conterminous United States. When compared for validation, BFI estimated by recursive digital filter method showed good agreement overall with the USGS smoothed minima BFI method. Estimated base flow index and volume were analyzed, with Hydrological Landscape Regions (HLRs) developed for the United States to identify the mean hydrologic flow response within HLR. They were also used to determine relationships with hydro-geologic descriptive variables and used for defining the HLRs based on Pearson’s correlation table and a stepwise multiple regression. These descriptive variables used in defining the HLRs include relief, effective rainfall, potential evapotranspiration and percentage of sand. The regression results indicated that relief and percentage of sand were highly correlated to base flow index, and the amount of base flow volume can be related to gradient and the amount of effective rainfall. The regression results also suggested that the descriptive variables used in constructing the HLR can be used to define mean values of shallow ground water flow within the regions. Further testing is needed to ascertain if such relationships could be used to define flow within an HLR.