**1. Introduction**

Sorghum is a crop that can be grown as either a grain or cash crop. It is one of the top five cereal crops in the world. Sorghum is also required for the survival of humankind in different parts of the world, especially in Africa and Asia. The United States (US) is the largest producer of sorghum in the world [1]. In the US, sorghum usually grows throughout the sorghum belt from South Dakota to southern Texas [2]. The top five sorghum producing states are Kansas, Texas, Colorado, Oklahoma, and South Dakota. In the US, sorghum grain is primarily used for feeding of livestock and ethanol production, but it is becoming popular in the consumer food industry and other markets [3]. The livestock industry is one of the oldest standing marketplaces for sorghum grain in the US. Sorghum

is utilized in feed rations for poultry, beef, dairy, and swine [3]. Also, a large portion of sorghum is used for biofuel production. It is also exported to the different parts of the world, including Mexico, China, and Japan.

Sorghum grain is highly resistant to drought and can withstand waterlogging better than any other cereal crop. Sorghum has a special fibrous root system, which can extend to a depth of 1.2 to 1.8 m (4 to 6 feet) deep in the soil. More than 75% of water and nutrients taken by root system are from the top 0.9 m (3 feet). Therefore, the deep extension of the root system helps sorghum withstand drought conditions better than any other cash crops [4]. Grain sorghum exhibits yield stability greater than maize. Drought resistance and heat tolerance make it a popular choice for marginal rainfall areas of semiarid zones of Africa where food shortages are common.

Total water use by a sorghum crop depends on the variety, maturation, planting date, and geographical and environmental conditions. It is estimated that the total use of 1750 mm/ha (28 inches of water/acre) water is needed for good sorghum yield of 783 kg/ha (700 lb/acre) [5]. The water use of sorghum depends on the growth stage of the sorghum plant (Table 1). During the early part of plant development, water use is relatively low but water stress during this time can affect plant growth and yield. Rainfall of 25 to 50 mm (1 to 2 inches) in the second week following sorghum pollination would result in the best yield if the period of pollination had adequate soil moisture [5,6]. The period from sorghum pollination to maturity is about 60 days. At the time of growth, a dry spell in the field from 14 to 60 days after pollination may have a small effect on the final harvesting yield of the sorghum crop. If no rain were to occur during the final period of 46 days, the yield of the sorghum crop would be greatly reduced [5,6]. Therefore, rainfall and its timing are important factors for the growth and yield of sorghum.


**Table 1.** Estimated grain sorghum water use by growth stage [5].

Although sorghum is tolerant of some waterlogging, it suffers damage under prolonged wetting of soil under very high rainfall [6]. Researchers from Australia, Germany, and the US have quantified the overall of extremes climate effects like drought, heat wave problems and precipitation on the crop yield variability of different staple crops around the world [7]. The year-to-year overall changes in the climatic factor in the growing season of maize, rice, sorghum, and wheat accounted the fluctuations of 20% to 49% of total yields [8]. Climatic extremes like hot and cold climates, drought, and heavy rainfall accounted for 18% to 43% of inter-annual variations in different crops yields [9]. Therefore, it is important to understand the consequences of climate extremes on crop yields to secure our food supply. A large body of literature already exists for drought. However, studies on the consequences of extremely high precipitation on crop yield are sparse, especially for grain sorghum. Therefore, an attempt is made in this study to analyze the consequences of high precipitation on rainfed grain sorghum yields.

Extreme precipitation events are producing more and more rain, and are now becoming one of the most common events since the beginning of the 1950s in many regions of the world, including the US. Scientists expect heavy rainfall as a consequence of a warming planet [10,11]. Warmer air mass can hold more water vapor content than cold air mass. For each degree of warming in the earth, the air mass capacity for holding water vapor goes up by about 7%. An atmosphere with more moist air can produce more heavy and continuous rainfall events, which is what has been observed all over the world since the 1950s [10,11].

An increase in continuous heavy rainfall events may not always show the increases in total rainfall over a season or year. Some studies show a small decrease in rainfall and show an increase of dry periods, which offsets rainfall increases falling during heavy events. The most immediate effect of heavy rainfall is the flooding. There are several recent examples of heavy rainfall events. In August 2017, Hurricane Harvey produced 1220 mm (48 inches) of heavy rainfall on Houston, Texas from a single event and was the biggest threat from tropical cyclones. In July 2016, more than 150 mm (6 inches) of heavy rainfall occurred in less than two hours in Ellicott City, Maryland, the estimated cost of the damage is more than \$22 million dollars. In summary, we incur a huge economic loss because of heavy precipitation events, including some losses coming from a reduction in crop yields.

Precipitation is generally useful in recharging the soil profile, which is very important for crop growth. The precipitation efficiency in recharging the soil profile depends on intensity and rate at which precipitation occurs. Precipitation that falls on the soil at rates greater than 127 cm/h (0.5 inches an hour) are less efficient compared to lighter rain, because the water that runs off from the surface carries the fertile soil to the streams, lakes, and rivers which decreases future yields. The timing of rainfall while crops are growing is critical. During germination and stand establishment, either heavy rainfall or little rainfall can substantially affect the yield.

In general, the more precipitation during the crop growing season, the better the crop growth. However, too much precipitation will damage the crop by saturating the soil profile and removing air, which is also important for healthy plant growth. The majority of the previous studies relating extreme climate events and food production are focused on increasing temperatures and drought. The consequences of high precipitation on probable reduction in crop yields are often ignored. There is a big knowledge gap of understanding the consequences of extremely high precipitation on the yield of food crops and relating it to subsequent consequences in food production scenarios at different spatial scales. Addressing the knowledge gap and exploring the less-studied relationship between excess precipitation and rainfed food crop yields are the novelties of this study. Detailed analysis of the above-mentioned relationship using a combination of established mathematical principles and graphical tools are some of the unique aspects of this study. The results from our study and other similar studies have applications in crop insurance, parameterization of computer models (estimating crop yield reductions based on aeration stress), policy level decisions on rainfed crop selection, yield forecasting, estimating food production, and water footprint analysis.

The specific objectives of the study are to: (1) Identify historic extreme high precipitation events during the crop growth of rainfed sorghum in Texas, (2) Extract continuous serially complete crop yield information for rainfed sorghum by county, (3) Collect continuous records of daily average precipitation corresponding to the sorghum crop yield data, (4) Estimate the growing season total precipitation and 4-day maximum precipitation using the precipitation data, and (5) Relate items 3 and 4 above using visual patterns and statistical principles to quantify the consequences of high precipitation on crop yields.
