Uncertainty Analysis of Distributed Sub-Daily Agro-Hydrological Modeling of a Sugarcane Farming System with Combinational Free/Controlled Subsurface Drainage Management

Agro-hydrological models play an important role in water resource management. However, their predictions always suffer from various sources of uncertainty, including model structures, parameters, and input and output data. Model structural uncertainty is caused by the fact that the model cannot perfectly represent the natural processes involved in the studied system. Parameter uncertainty indicates that many model parameters are not directly measurable or can only be obtained with unknown errors. Measurement uncertainty in input and output data is due to unknown measurement errors and incommensurability errors. Hence, it is important to assess the degree of uncertainty involved in agro-hydrologic modeling. The generalized likelihood uncertainty estimation (GLUE) method has been widely used for uncertainty analysis in hydrologic modeling because of its simplicity, ease of implementation, and less strict statistical assumptions about model errors. In GLUE, parameter uncertainty accounts for all sources of the model uncertainty. The drawback of the GLUE is its prohibitive computational burden imposed by its random sampling strategy, which hinders the efficient application of the method. In this study, a hybrid high-dimensional uncertainty analysis method was developed, combining GLUE with an evolutionary optimization algorithm, Unified Particle Swarm Optimization (UPSO), to improve the computational efficiency of the GLUE framework. UPSO is a modification of Particle Swarm Optimization (PSO) that aggregates its local and global variants, combining their exploration and exploitation capabilities without additional objective function evaluations. The hybrid GLUE-UPSO framework was used for uncertainty analysis of SWAP distributed sub-daily agro-hydrological modeling for a sugarcane farming system with combinational free/controlled subsurface drainage management.

The source code of the SWAP model was modified and extended to consider the duration of the irrigation events, simulation of sub-daily reference evapotranspiration, sub-daily precipitation interception, ratooning, and implementation of subsurface controlled drainage during the simulation period. The GLUE-UPSO framework was coded in FORTRAN and C++ and integrated into SWAP source code. The developed framework was applied to a dataset collected from a field with a combinational free/controlled (70-cm depth) subsurface drainage management located at Shoaybiyeh Sugarcane Agro-industrial company farms, Khuzestan province, Iran. The simulation was performed from 2010-07-19 to 2011-12-11 (481 days) for planted sugarcane (CP48-103 cultivar). A soil profile of 550 cm depth (depth of impermeable layer) was specified during simulations. The soil profile was divided into two layers. To consider the heterogeneity of irrigation scheduling at different parts of the studied field, the field area ( 21 ha) was divided into ten homogeneous simulation units, termed as hydrotopes. Hydrotopes have similar agro-hydrological properties except for irrigation scheduling. The model was calibrated, using the measured soil moisture profile, soil solute concentration profile, groundwater level, subsurface drainage outflow, drainage outflow salinity, Leaf Area Index (LAI), cane yield, and sucrose yield in a parallel manner. The weighted average of simulated values derived for each hydrotopes was compared with the corresponding measured data. Totally, 45 parameters were estimated through the GLUE-UPSO framework. The accuracy of the model in calibration and validation stages was evaluated, normalized root mean square error NRMSE and Nash-Sutcliffe model efficiency coefficient EF. The behavioral parameters were identified, using NRMSE > 0.2 for solute transport (soil water solute concentration and drainage outflow salinity) and EF > 0.7 for hydrological (soil water content, water table level, and drainage outflow) and biophysical (cane yield, sucrose yield, and LAI) simulations. For each parameter set, the objective function values were used as the likelihood measure to calculate the corresponding likelihood weights. The 95% prediction uncertainty (95PPU) bands were calculated at the 2.5% and 97.5% levels of the cumulative posterior distribution (realized from the weighted behavioral parameter sets) of the simulated state/flux variables.

The results revealed a significant nonuniqueness of the calibrated parameters and the necessity of an uncertainty assessment for the SWAP simulations. Strong parameter correlations highlighted the need for calibration of the model parameters against diverse calibration data in a simultaneous manner. The 95% prediction uncertainty bands obtained for the model's hydrology (soil water content, water table level, sub-surface drainage outflow), solute transport (soil water solute concentration and sub-surface drainage outflow salinity), and biophysical (leaf area index, cane, and sucrose dry yield) components enveloped 41-87%, 18-67%, and 75-100% of the corresponding total observed data (including both calibration and validation datasets), respectively, with a r-factor (the ratio of the average thickness of the 95PPU band to the standard deviation of the corresponding measured variable) of 0.71-1.14, 0.33-1.14, and 0.84-0.98. The results indicated that the hybrid GLUE-UPSO framework offers an efficient alternative to provide traditional calibrated parameters as well as uncertainty analysis of computationally expensive hydrologic models.