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The performance on prediction by mathematical models which represent the conceived image of a system such as hydrology is oftentimes represented through calibration and verification processes. Oftentimes a best fit between observed and predicted flows is obtained through correlation coefficient (R
^{2}) and the Nash Sutcliffe model efficiency (NSE) by minimizing the average Root Mean Square Error (RMSE) of the observed versus simulated flows. However, these days, a new paradigm is emerging wherein accounting for the flow variability for the protection of freshwater biodiversity and maintenance of goods and services that rivers provide is paramount. Therefore, from an ecohydrology perspective, it is not clear if the existing method of model calibration meets the needs of the riverine ecosystem at its best. Thus, this study investigates and proposes a methodology using entropy theory to gage the calibration of Soil and Water Assessment Tool (SWAT) from an ecohydrology perspective characterized by the natural flow-regime paradigm: Indicators of Hydrologic Alteration.

Mathematical models of watershed hydrology are employed to simulate the effects of various conservation programs and to determine suitable conservation programs for given watersheds and agronomic settings [

Model calibration is the process of estimating model parameters by comparing model predictions for a given set of assumed conditions with observed data for the same conditions [^{2}) and the Nash Sutcliffe model efficiency (NSE) coefficient. The R^{2} value measures how well the simulated versus observed regression line approaches an ideal match and ranges from 0 to 1, with a value of 0 indicating no correlation and a value of 1 representing that the predicted dispersion equals the measured dispersion [

However, there is now a broad acceptance that it is in society’s best interests to recognize that rivers and adjacent wetlands need adequate water to sustain ecological processes and associated goods and services [

Therefore, performing the calibration process just by looking at the above discussed statistical measures of observed versus predicted flows may not portray how well the predicted system will meet the need of the riverine ecosystem that is defined as a function of temporal variations in river flows. Getting a best fit between observed and predicted flows through NSE or R^{2} by minimizing the average Root Mean Square Error (RMSE) of the observed versus simulated flows may lose the vital core needed to sustain the riverine ecosystem.

Moreover, in SWAT and in contemporary hydrological models, to capture the spatial variability, the watershed is subdivided into few subwatersheds/subbasins. The modeler can define as many or as few subwatersheds as desired according to the critical source area (CSA), the threshold at which stream network appears. This has been exercised as a trial and error process. Presently, there are no standard protocols for deciding what scheme to adopt to capture the spatial variability through subwatersheds. Each subwatershed is then further di-

Group | Regime Characteristics | 32 Parameters |
---|---|---|

Group 1:Magnitude of monthly water conditions | Magnitude Timing | Mean value for each calendar month |

Group 2:Magnitude and duration of annual extreme water conditions | Magnitude Duration | Annual min/max of 1 day means Annual min/max of 3 day means Annual min/max of 7 day means Annual min/max of 30 day means Annual min/max of 90 day means |

Group 3:Timing of annual extreme water conditions | Timing | Julian date of each annual 1 day minimum and maximum |

Group 4:Frequency and duration of high and low pulses | Frequency Duration | Number of high and low pulses each year Mean duration of high and low pulses |

Group 5: Rate/frequency of consecutive water-condition changes | Rates of Change | Means of all positive differences between daily values Means of all negative differences between daily values Number of rises Number of falls |

vided into a number of hydrologic representative units (HRU) based on unique combinations of land use and land cover (LULC), and soil types within the subwatershed. To simplify the hydrological system further, an HRU threshold is applied to remove smaller HRUs.

However, the question is whether these conventional calibrated flows at the selected spatial scales (i.e., CSA and HRU threshold) best represent the need of the riverine ecosystem that is characterized through IHA. Furthermore, which one of the considered scales has to be considered as the best model that best represent the need of the riverine ecosystem. It is also worth mentioning that such calibrated models are employed subsequently to analyze the water management scenarios to reflect the real nature. Thus, will these calibrated models mimic the nature that’s being observed at the gage location subsequently at subwatershed scale from an ecohydrology perspective? Therefore, there has to be a way to gage this to ensure that the best calibrated model reflects the need of the riverine system at its best. In other words, there has to be a way to gage the alteration on the need of the riverine system caused by the best calibrated model. Thus, it is the objective of this study to investigate the SWAT calibration at different spatial scales from an ecohydrology perspective characterized by the natural flow-regime paradigm: Indicators of Hydrologic Alteration.

SWAT is a river basin or watershed scale model developed by the United States Department of Agriculture(USDA)―Agricultural Research Service(ARS) to predict the impact of land-management practices on water, sediment and agricultural chemical yields in large complex watersheds with varying soils, land use and management conditions over long periods of time [

The study area is Kings Creek, a tributary of the Cedar Creek River basin, Texas (^{2} as delineated from a USGS streamflow gaging station (32.513˚N, 96.3286˚W). Its elevation ranges from 107 m to 190 m and its land use is mainly hay (34%) and range (34.5%). The remaining areas were composed of agricultural, forest-deciduous, etc. The average annual precipitation in the study area is 975 mm.

Input data on topography were extracted from a digital elevation model (DEM). The 30 m DEM used in delineating the watersheds was taken from the NHDPlus dataset, an integrated suite of application-ready geospatial data products envisioned by the U.S. Environmental Protection Agency. Soil dataset was obtained from the USDA-NRCS State Soil Geographic Data Base (STATSGO). Digital land use/land cover data for the Kings Creek watershed was obtained from the National Land Cover Dataset (NLCD). The observed daily streamflow data used for calibrating SWAT was obtained from the USGS National Water Information System (NWIS). The study area was set up to run on a daily time step. As shown in

The percentile of subwatershed scale was obtained by considering the lower most CSA (1000ha) as the 0%

and the upper most CSA (5000 ha) as the 20%. The percentile of HRU scale was obtained by considering an equal threshold on landuse and soil. In other words, a 5% HRU scale represents a 5% landuse and 5% soil. Surface runoff was calculated using the Soil Conservation Service (SCS) curve number method. The Penman- Monteith method was used to determine potential evapotranspiration. Channel water routing was performed using the Muskingum routing method.

Manual and automatic calibration methods were combined for calibrating SWAT using the measured stream flow data at (32.513˚N, 96.3286˚W). For this analysis, twenty years, from 1 January 1963 to 31 December 1982, of meteorological and hydrometric flow data were utilized, including two years of “warm-up” period. The objective function was to minimize the RMSE of observed versus simulated flows. RMSE was defined as:

where n is the number of time steps, Q_{obs,i}_{ }is the observed streamflow at time i, and Q_{sim,i} is the simulated streamflow at time i. The NSE was used to evaluate SWAT’s overall performance at calibration and validation. The NSE was defined as:

The following parameters were tuned during the calibration process: Curve Number (CN), Soil Available Water Capacity (SOIL_AWC), Soil Evaporation Coefficient (ESCO), Base-Flow Alpha Factor (ALPHA_BF), and Groundwater Revap. Coefficient (GW_REVAP). The model validation was done using the calibrated parameters. The model validation involved re-running the model using input data different from the data used in calibration. Four years of observed flow data from 01 January 1983 to 31 December, 1986, were used to validate the model.

Among the considered spatial scales, 5% of subwatershed scale and 0% of HRU scale produced the best NSE value of 0.865 and 0.823 for the study area during the calibration and validation, respectively. Whereas 20% of subwatershed scale and 20% of HRU scale produced the lower most NSE of 0.781 and 0.727 during the calibration and validation respectively. Although the variation of NSE among the considered spatial scales was not that significant, the altered level of NSE, which is the absolute deviation with respect to the highest NSE, was high with the increased HRU scale at the high subwatershed scale as highlighted in

Having calibrated and validated SWAT for the combination of CSA and HRU threshold as presented in

in accord with the Principle of Maximum Entropy (POME), subject to known constraints. In Equation (3) E is the Shannon entropy,

probabilities constitute the probability distribution

where C_{j} is the jth constraint, m is the number of constraints, and

In practical applications, functions

Non-Satisfaction Level (NSL) for an “nth” parameter was defined as

where

The computed values of average NSL for IHA group-1 which provides the general measure of habitat availability or suitability and an expression of environmental contingency [

The average NSL for IHA group-2 which measures the structuring of river channel morphology, physical habitat conditions, and aquatic ecosystems by abiotic versus biotic factors [

However, it is reasonable to say that these NSLs of 32 parameters may have priorities among themselves. Some of the parameters may not be of important, even though they define the underlying riverine ecosystem. Thus, there has to be a way to consider this to reflect the overall status of the alteration on ecohydrology with the SWAT simulation, which could go in parallel with the NSE.

The values of NSLs of biological parameters were aggregated based on [

where the computed value of entropy for each of the 32 parameters is the argument (a_{i}), b_{j} is the jth largest of a_{i},

and w_{j} are a collection of weights such that w_{j} ?[0,1] and

The methodology used for obtaining the OWA weighting vector was based on [

maximize:

subject to:

The Orness characterizes the degree to which the aggregation is like an “OR” operator. For the analysis an Orness value of 0.75 was assumed in this study to ensure that the impact of all the IHA parameters is considered in the index development and to avoid assigning equal weights as some of the parameters may have more influence on defining the underlying ecosystem. Then, an array of weights w_{j} was generated using Equations (10) and (11).

As shown in

and 0% of HRU threshold) which gave the highest NSE was relatively low even though it did not yield the lowest aggregated NSL. Furthermore, the lowest aggregated NSL was observed at 0% subwatershed scale and 0% HRU scale. In other words, the lowest aggregated NSL occurs with the hydrological system without any simplification on HRU. Moreover, the ability of the model to reflect the need of the riverine ecosystem tends to decrease as the subwatershed scale increased. This is justified with the average NSE that tends to decrease as the subwatershed scale increased.

This study shows how the conventional calibration process by minimizing the RMSE of the observed versus simulated flows of a hydrological model like SWAT can be gauged on its ability to retain the need of the riverine ecosystem characterized by the natural flow-regime paradigm: Indicators of Hydrologic Alteration. The outcome of this study shows the followings:

1) The ability of the calibrated model to reflect the need of the riverine ecosystem tends to decrease as the subwatershed scale (i.e., CSA threshold) increased.

2) The best calibrated model does not yield the best result for the selected study area from an ecohydrology perspective. However, the deviation is not that significant.

3) The model without any simplifications on HRU and CSA threshold gives the best result for the selected study area from an ecohydrology perspective.

4) The proposed methodology can be used as a surrogate when there is a tie to select the best simulation along with spatial scales.

The authors would like to thank Texas Water Resources Institute and U.S. Geological Survey for providing the financial support to conduct this research.

SivarajahMylevaganam,RaghavanSrinivasan,Vijay P.Singh, (2015) Long Term Soil and Water Assessment Tool (SWAT) Calibration from an Ecohydrology Perspective. Open Journal of Applied Sciences,05,344-354. doi: 10.4236/ojapps.2015.57035