Discussion of “Development of Soil Moisture Drought Index to Characterize Droughts” by Mohammad M. Sohrabi, Jae H. Ryu, John Abatzoglou, and John Tracy

Abstract

In the discussed paper, Sohrabi et al. presented a new drought index, termed soil moisture drought index (SODI), which is based on the difference between water supply and water demand [in other words, the moisture departure from the field capacity (FC) of soil] at a given site. The moisture departure [Eq. (1) in the discussed paper] used in SODI is the improved form of the moisture departure in Plamer Drought Severity Index (PDSI) [Eq. (17) in the discussed paper]. In the following, some cases presented in the discussed paper about SODI’s moisture departure are discussed: 1. There are some ambiguities in methodology of SODI’s moisture departure. Although the SODI is a two-layer soil-water balance model, the discussed paper has not clearly explained the relations of soil-water components between the first and second soil layers. Are these relations considered just like the Palmer approach when calculating the soil-water components of the moisture departure? 2. According to Eq. (1) of the discussed paper, when Pi > ðPEi þ SMDi−1Þ, the equation can simply be rewritten as Di 1⁄4 ROi þ ROi−1 ð1Þ where ROi (surface runoff in the current month) = Pi − ðPEi þ SMDi−1Þ; Pi = total precipitation; PEi = potential evapotranspiration; SMDi−1 = soil moisture deficiency; Di = moisture departure; and i = month number in the calendar year. All variables are expressed in terms of millimeters. Under this condition, the term Li (moisture loss from soil column in Eq. (1) of the discussed paper) is zero. Therefore, for the some successive high-precipitation months, the moisture departure may be calculated only based on sum of the surface runoffs in the current and previous months. There are two issues with Eq. (1) of this discussion paper: (1) the surface runoff in the previous month (ROi−1) is considered as important as the surface runoff in the current month (ROi), and (2) there is no upper limit for surface runoff and it is assumed that any value of surface runoff can be retained in soil column. The latter is unlike the PDSI, where the potential surface runoff is assumed to be the available water balance (AWC). The state where Pi < ðPEi þ SMDi−1Þ can be envisaged and anticipated to occur in a dry month, but the surface runoff in the previous month (ROi−1) is high enough to compensate the moisture deficiency in the current month. Such a state may be occurred due to the two previously mentioned issues. 3. In addition to the surface runoff, the soil moisture deficiency in the previous month (SMDi−1) is accounted for calculating the moisture departure in the current month. While the maximum value of SMDi−1 is considered AWC, there is no maximum value for ROi−1 in SODI’s moisture departure equation. This lead to the moisture departure series be strongly skewed, which in turn needs to be normalized by a proper transformation method such as that used in the discussed paper (i.e., Box-Cox transformation method). Box-Cox transformation should be used with caution in some cases because the transformed data may not be satisfactory even when the best value of transformation parameter had been chosen. There are some alternatives for BoxCox transformation such as Manly (1976) and Yeo and Johnson (2000), which can be used where the Box-Cox method is unable to satisfactorily convert nonnormal data to normal ones. The Manly transformation function is of the form