Although more on-farm storage ponds have been constructed in recent years to mitigate groundwater resources depletion in Mississippi, little effort has been devoted to estimating the ratio of on-farm water storage pond size to irrigated crop land based on pond metrics and its hydrogeological conditions. In this study, two simulation scenarios were chosen to determine such a ratio as well as to investigate pond hydrological processes using a Structural Thinking, Experimental Learning Laboratory with Animation (STELLA) model, one scenario with and the other without using pond water for irrigation for a typical pond that represented the average conditions in East Mississippi. Simulation results showed that pond water level changed moderately for conditions without using its water for irrigation, whereas pond water level changed dramatically for conditions with using its water for irrigation. A reasonable ratio of pond size to irrigated soybeans land was 1:18 if the irrigation rate was 2.54 cm/d (or 1 inch/d) and the low limit of the pond water level was drawn to near zero (0.08 m). For the ratio of 1:18, our simulations further revealed that a 1-ha soybeans land could save about 542 m^{3} groundwater each year. This study suggests that the STELLA model is a useful tool for estimating the ratio of pond size to irrigated crop land.

## INTRODUCTION

Groundwater withdrawal in the United States has increased dramatically during the 20th century (Hutson *et al.* 2004) and a consequence of such withdrawals is the depletion of water resources from subsurface aquifers (Konikow 2013). This is also true in Mississippi, especially in the Mississippi Delta. Mississippi is a major state for agricultural crop production in the Southeast United States. In 2012, soybean revenue ($1.16 billion) ranked number one in Mississippi as compared with all other crops, exceeded only by broilers/egg/chickens productions as an agricultural commodity (http://www.dafvm.msstate.edu; http://www.msfb.org). The desire by most producers to stabilize or enhance crop yields through irrigation has led to the overdraft of groundwater resources in many regions of Mississippi (Konikow 2013; Vories & Evett 2014) and around the world (Sahoo & Panda 2014). In these regions, groundwater constitutes 80% of all the freshwaters used for agricultural, domestic, and industrial activities (Hossain 2014). In an effort to better understanding of the irrigation requirements of different crops in the Mississippi Delta, a groundwater usage survey has been performed recently and the average loss of groundwater is about 493,000,000 m^{3}/y from 1987 to 2014 in Mississippi Delta (YMD 2015).

With an increasing concern about groundwater and stream water depletion, more irrigation farm and tail water retention ponds have been constructed in recent years in East Mississippi and the Mississippi Delta. Although there is a high amount of rainfall in Mississippi, only 30% occurs during the period from May to October when the major crops are produced (Kebede *et al.* 2014). The temporal mismatch between annual rainfall and crop water demands is a major reason for using water storage ponds as a source of irrigation water. However, the hydrological processes, water budget, and environmental benefits and consequences of water storage ponds in Mississippi are yet to be fully quantified and exploited. For many agricultural practices, farm pond capacity must be adequate to meet crop water use requirements, which vary with crop species, seasons, soil types, hydrological conditions, and climate environments.

Currently, little effort has been devoted to estimating the ratio of pond size to irrigated crop land in Mississippi. Staff from USDA-NRCS in Mississippi have roughly approximated that the pond size to crop irrigation area is about 1:13 based on the soil-plant-air-water (SPAW) model simulation (personal communication). That is, to irrigate 160 ha of crop land, a 12 ha of pond area is needed with the pond bottom to be 10 ha and the embankment footprint to be 2 ha. However, an accurate estimation of such a ratio based on pond hydrological processes, local climate conditions, and crop irrigation demands has yet to be performed. The knowledge of this ratio is crucial to cost-effective pond size estimation for construction and pond water for irrigation management in Mississippi and the regions with similar land uses and climate conditions.

Recently, we developed a Structural Thinking, Experiential Learning Laboratory with Animation (STELLA) model to assess pond hydrological processes and water budget (Ouyang *et al.* 2016). In this companion study, we applied this model to estimate the ratio of pond size to irrigated soybeans land in East Mississippi. Our specific objectives were to: (1) investigate the annual pattern of pond hydrological processes; (2) determine the ratio of pond size to irrigated soybeans land; and (3) estimate the mitigation of groundwater depletion from the use of on-farm water storage ponds.

## MODEL DESCRIPTION AND SIMULATION SCENARIOS

*et al.*2016). As shown in Figure 1, this model includes rainwater collection, runoff water gathering, surface water evaporation, irrigation water use, pond water spillway release, and soil seepage and infiltration losses. Although an elaborate description of the model can be found in Ouyang

*et al.*(2016) and is beyond the scope of this study, a moderate depiction of the model's major components, including surface runoff, evaporation and infiltration, is given below for readers’ convenience.

*et al.*1992; Mullins

*et al.*1993): where

*R*is the surface runoff rate (cm/h),

*P*is the rainfall rate (cm/h), and S is the watershed retention parameter.

*E*is the evaporation from pond water (cm/h),

*K*

_{1}is the coefficient (dimensionless),

*R*

_{s}is the solar radiation (kJ/cm

^{2}/h), and λ is the latent heat of vaporization (kJ/g).

*et al.*1993): where

*D*

_{inf}is the infiltration rate (cm

^{3}/h), α is the percolation rate coefficient (cm

^{3}/h), θ is the volumetric water content (cm

^{3}/cm

^{3}), and

*f*is the field water capacity (cm

_{c}^{3}/cm

^{3}).

The model has been validated using experimental data in our previous study. The regression equation between the predicted and measured pond water evaporation was *Y*_{Prediction} = 0.98*X*_{Measurement} with *R*^{2} = 0.94 and *p* < 0.001, whereas the regression equation between the predicted and measured pond water level was *Y*_{Prediction} = 0.95*X*_{Measurement} with *R*^{2} = 0.50 and *p* < 0.001. These statistical results represented very good to reasonable correlations between the model predictions and the experimental measurements. Then, the model was applied to estimate diurnal and seasonal pond hydrological processes as well as pond water budget in the Mississippi Delta with promising results. An elaborate description of the mathematical functions and procedures used to develop the model is beyond the scope of this study but can be found in Ouyang *et al.* (2016).

*et al.*2016) and were used as model inputs in this study. It should be noted that the irrigation rate was 2.54 cm/d (or 1 inch/d), which is a very common practice in East Mississippi. Comparison of the simulation results from the two scenarios allowed us to evaluate the impacts of irrigation upon pond hydrological processes and to determine the ratio of pond size to irrigated soybeans land. The simulation period was 10 years started on the first day of 2002 and terminated at the end of 2011, for each scenario an hourly time step was used. All of the input parameters for these scenarios are given in Table 2.

Year | Number of irrigations | Irrigation rate each time (mm) | Total irrigation (mm) |
---|---|---|---|

2002 | 3 | 25.4 | 76.2 |

2003 | 2 | 25.4 | 50.8 |

2004 | 1 | 25.4 | 25.4 |

2005 | 5 | 25.4 | 127.0 |

2006 | 12 | 25.4 | 304.8 |

2007 | 8 | 25.4 | 203.2 |

2008 | 7 | 25.4 | 177.8 |

2009 | 2 | 25.4 | 50.8 |

2010 | 4 | 25.4 | 101.6 |

2011 | 7 | 25.4 | 177.8 |

10-year average | 5.1 | 25.4 | 129.5 |

Year | Number of irrigations | Irrigation rate each time (mm) | Total irrigation (mm) |
---|---|---|---|

2002 | 3 | 25.4 | 76.2 |

2003 | 2 | 25.4 | 50.8 |

2004 | 1 | 25.4 | 25.4 |

2005 | 5 | 25.4 | 127.0 |

2006 | 12 | 25.4 | 304.8 |

2007 | 8 | 25.4 | 203.2 |

2008 | 7 | 25.4 | 177.8 |

2009 | 2 | 25.4 | 50.8 |

2010 | 4 | 25.4 | 101.6 |

2011 | 7 | 25.4 | 177.8 |

10-year average | 5.1 | 25.4 | 129.5 |

The data were obtained from Feng *et al.* (2016) and the number of irrigations each year was determined based on rainfall amount and soil moisture regime.

Parameter | Value | Source |
---|---|---|

Hydrological conditions | ||

Curve number | 89 | Rawls et al. (1992) |

Hourly rainfall (cm/h) | Time series measurements | Local weather station |

Effective land area for runoff (cm^{2}) | 15,297,117,277 (or 153 ha) | Estimated |

Pond drainage (cm^{3}/h) | 0.00005 | Estimated |

Lateral seepage (cm^{3}/h) | 0 | Estimated |

Evaporative coefficient K_{1} in Equation (3) | 0.0022 | Calibrated |

Hourly solar radiation (kJ/cm^{2}/h) | Time series data | Measured |

Hourly air temperature (°C) | Time series data | Measured |

Pumping for irrigation rate (cm^{3}/h) | Time series measurements | Estimated |

Irrigation area (cm^{2}) | varied for different ratios | Assumed |

Pipe flow | ||

Manning roughness coefficient, n | 0.01 | Maidment (1992) |

Bottom slope of pipe | 0.003 | Measured |

Radius of the pipe (cm) | 60 | Measured |

Pond Matrix | ||

Bottom pond width, a (cm) | 1.60E + 04 | Measured |

Bottom pond length, b (cm) | 2.02E + 04 | Measured |

Maximum top pond width, Wm (cm) | 2.00E + 04 | Measured |

Maximum top pond length, Lm (cm) | 2.53E + 04 | Measured |

Maximum pond height, Hm (cm) | 2.00E + 02 | Measured |

Pumping low limit of pond level (cm) | 5.00E + 01 | Measured |

Maximum pond volume (cm^{3}) | 6.51E + 10 | Calculated |

Initial pond volume (cm^{3}) | 6.50E + 10 | Assumed |

Pipe spill level | 1.80E + 02 | Measured |

Pond spill level | 1.99E + 02 | Measured |

Parameter | Value | Source |
---|---|---|

Hydrological conditions | ||

Curve number | 89 | Rawls et al. (1992) |

Hourly rainfall (cm/h) | Time series measurements | Local weather station |

Effective land area for runoff (cm^{2}) | 15,297,117,277 (or 153 ha) | Estimated |

Pond drainage (cm^{3}/h) | 0.00005 | Estimated |

Lateral seepage (cm^{3}/h) | 0 | Estimated |

Evaporative coefficient K_{1} in Equation (3) | 0.0022 | Calibrated |

Hourly solar radiation (kJ/cm^{2}/h) | Time series data | Measured |

Hourly air temperature (°C) | Time series data | Measured |

Pumping for irrigation rate (cm^{3}/h) | Time series measurements | Estimated |

Irrigation area (cm^{2}) | varied for different ratios | Assumed |

Pipe flow | ||

Manning roughness coefficient, n | 0.01 | Maidment (1992) |

Bottom slope of pipe | 0.003 | Measured |

Radius of the pipe (cm) | 60 | Measured |

Pond Matrix | ||

Bottom pond width, a (cm) | 1.60E + 04 | Measured |

Bottom pond length, b (cm) | 2.02E + 04 | Measured |

Maximum top pond width, Wm (cm) | 2.00E + 04 | Measured |

Maximum top pond length, Lm (cm) | 2.53E + 04 | Measured |

Maximum pond height, Hm (cm) | 2.00E + 02 | Measured |

Pumping low limit of pond level (cm) | 5.00E + 01 | Measured |

Maximum pond volume (cm^{3}) | 6.51E + 10 | Calculated |

Initial pond volume (cm^{3}) | 6.50E + 10 | Assumed |

Pipe spill level | 1.80E + 02 | Measured |

Pond spill level | 1.99E + 02 | Measured |

## RESULTS AND DISCUSSION

### Pond hydrological processes

^{3}/d/pond in winter to 50 cm

^{3}/d/pond in summer. The highest rate of pond evaporation (63 cm

^{3}/d/pond) was found in the summer of 2007 when it was in dry conditions with less rainfall (Figure 3(a)). A zero rate of pond evaporation was also observed because the STELLA model assumed no evaporation occurred with rain and during the night. The annual pond evaporation pattern happened because of the annual cycles of solar radiation and air temperature with more intensive radiation and warmer temperatures during summer compared with winter. Results showed that annual pond evaporation was controlled by air temperature and solar radiation.

Daily changes in pond water spill (Figure 3(c)) for the simulation scenario without using pond water for irrigation over a 10-year period corresponded well to rainfall events (Figure 3(a)), i.e., the rate of pond water spill increased with the rate of rainfall. The highest rate of pond spill was 11,559 m^{3}/d/pond during early 2004 when the highest rate of rainfall was 0.42 cm/d. This occurred because the sources of water entering the pond were from rainwater interception directly by pond as well as from rainwater collection indirectly by pond through surface water runoff. Figure 3(d) showed the moderate variations in pond water level over the 10-year period. It seems that pond water level was relatively stable under natural conditions and without using pond water for irrigation.

Comparison of Figures 3(d) and 4(d) revealed that a dramatic decline in pond water level occurred when the pond water was used for irrigation. Although such declines varied from year to year, a lowest pond water level of 0.08 m was observed in the summer of 2007 during the entire 10-year simulation period. This was just because there were lower rainfall rates (Figure 4(a)) plus the use of pond water for irrigation (Figure 4(e)) during the summer of 2007. Comparison of Figures 4(d) and 4(e) further demonstrated that a decline of pond water level corresponded well to the use of pond water for irrigation. The ratio of pond size to the irrigated soybeans land for the results shown in Figure 4 was 1:18 and the irrigation rate was 2.54 cm/d (or 1 inch/d). In other words, if the low limit of pond water level was above 0.08 m, a 1-ha pond with an average depth of 2 m could irrigate 18 ha soybeans land over a 10-year simulation period. This simulation finding is very useful to farmers and water resources managers for on-farm water storage pond construction and soybeans irrigation.

### Ratio of pond size to irrigated soybean land

Figure 5(c) further revealed that the maximum ratio of pond size to irrigated soybeans land could be extended to 1:23 for the entire 10-year period if the pond water level was occasionally drawn to zero. Within this ratio, there were only two dry conditions in 2007 when the pond water was drawn to zero, while for the rest of the time, the pond water level was always above 0.28 m (Figure 5(c)).

### Water resources conservation estimation

^{3}of pond water was used to irrigate 72 ha of soybeans land over a 10-year period if the ratio was 1:18. In other words, about 542 m

^{3}of ground or surface water was saved per hectare of soybeans each year if these waters were used for irrigation. Although there were no data available for East Mississippi, it has been reported that the average loss of groundwater is about 493,000,000 m

^{3}/y from 1987 to 2014 in the Mississippi Delta. If a 10,000-ha of soybean land is irrigated with pond water in the Mississippi Delta, it would reduce the loss of groundwater by 11% (5,420,000/4,930,000,000 = 11%) when the ratio of pond size to irrigated soybeans land was 1:18. Results showed that on-farm water storage pond is one of the promising alternatives to conserve groundwater resources.

## SUMMARY

In this study, a STELLA model developed previously was applied to investigate the annual pattern of pond hydrological processes, determine the ratio of pond size to irrigated crop land, and estimate the mitigation of groundwater depletion due to the use of an on-farm storage pond.

A typical annual pond evaporation pattern, with increasing from winter to summer followed by decreasing from summer to next winter, was observed for a 10-year simulation period. The annual pond evaporation was controlled by air temperature and solar radiation and the pond water level was relative stable for conditions without using pond water for irrigation. In contrast, dramatic changes in pond spill and water level were observed for conditions with using pond water for irrigation. A reasonable ratio of pond size to the soybeans irrigation land area was estimated to be 1:18 if the irrigation rate was 2.54 cm/d (or 1 inch/d) and the average pond water level was above 0.08 m. A maximum ratio of pond size to irrigated soybeans land could be 1:23 for the entire 10-year period if the pond water level was occasionally drawn to zero.

We postulated that if a 10,000-ha soybean land was irrigated with pond water under the ratio of 1:18, it could reduce the loss of groundwater by 11%. This study showed that on-farm water storage pond is one of the promising alternatives to conserve groundwater resources. Results suggested that the STELLA model is a useful tool to estimate the pond size for desired crop irrigation land. Further study is warranted to estimate the optimal contributing drainage watershed area for runoff water collected by the pond.

## ACKNOWLEDGEMENTS

This project (62-2015) was funded by Mississippi Soybean Promotion Board.