Characteristics and Controlling Factors of the Drought Runoff Coefficient

Increasing water demand due to population growth, economic development, and changes in rainfall patterns due to climate change are likely to alter the duration and magnitude of droughts. Understanding the relationship between low-flow conditions and controlling factors relative to the magnitude of a drought is important for establishing sustainable water resource management based on changes in future drought risk. This study demonstrates the relationship between low-flow and controlling factors under different severities of drought. I calculated the drought runoff coefficient for six types of occurrence probability, using past observation data of annual total discharge and precipitation in the Japanese archipelago, where multiple climate zones exist. Furthermore, I investigated the pattern of change in the drought runoff coefficient in accordance with the probability of occurrence of drought, and relationships among the coefficient and geological, land use, and topographical factors. The drought runoff coefficient for multiple drought magnitudes exhibited three behaviors, corresponding to the pattern of precipitation. Results from a generalized linear model (GLM) revealed that the controlling factors differed depending on the magnitude of the drought. During high-frequency droughts, the drought runoff coefficient was influenced by geological and vegetation factors, whereas land use and topographical factors influenced the drought runoff coefficient during low-frequency droughts. These differences were caused by differences in runoff, which dominated stream discharge, depending on the magnitude of the drought. Therefore, for effective water resource management, estimation of the volume of drought runoff needs to consider the pattern of precipitation, geology, land use, and topography.


Introduction
The causes of droughts and adaptations to natural disasters have been studied from the perspectives of hydrology, environmental science, geology, meteorology, and agronomy [1]. The causes of droughts have been investigated in various regions by focusing on rainfall patterns [2][3][4], temperature [5,6], wind [7], and humidity [8]. In addition to the impacts of natural factors, intensification of drought is expected to occur because of growing water demand associated with population growth, economic development [9][10][11], and changes in the hydrological cycle associated with anthropogenic impacts, such as land-use-change [12][13][14].
Droughts are generally categorized into four types [15]. First, drought resulting from a lack of precipitation is defined as a meteorological drought [1,16]. Second, a shortage of surface or subsurface water in relation to water utilization, as determined by established water resource management, is defined as hydrological drought [17,18]. Stream water discharge is often used as an indicator hydrological droughts and is used in management and analyses of such droughts [19]. Third, agricultural drought indicates declining soil moisture, regardless of surface water resources, causing crop failure [20,21]. Finally, socioeconomic drought occurs in cases of defectiveness and incompatibility of the water resource system in relation to water demand [22,23].
Prolonged droughts cause severe socio-economic losses [24,25]. Economic loss arising from droughts has been estimated at USD 6-8 billion per year in the United States [26,27], with the EU suffering loss of 100 billion over the past 30 years [28]. The human damage caused by drought is even more serious. Droughts in Ethiopia/Sudan (1984) and the Sahel region (1974) killed 450,000 and 325,000 people, respectively [29].
Changes in the hydrological cycle resulting from climate change are expected to increase extreme drought events [1]. Unlike flood disasters, the influence of climate change on drought remains poorly understood. However, predictions of an intensification of drought due to climate change and population growth in central Africa [25] and increasing drought duration and severity in the interior southwest of the United States [30] have been reported. Furthermore, forecasts of drought using soil moisture as an indicator have indicated increasingly frequent drought events in Europe, regardless of the emission scenario applied [31].
Stream-flow discharge is an important indicator of hydrological drought because in many regions, water resources are obtained from surface water. Previous studies of stream discharge have focused on water resources, ecosystems, river channel formation, and flood management. In particular, the effects of alterations to flow regime on ecosystems have been studied [32][33][34], and the natural flow regime has been elucidated [35][36][37][38]. Research on the factors that influence flow discharge has focused on rainfall amount or pattern [39,40], land use [41,42], and watershed geology [43]. For research on flow regimes, the factors influencing low flows that are strongly related to drought have been investigated by focusing on watershed area, watershed elevation, ratio of urban area or forest cover, and geology [44][45][46][47][48]. However, these studies mainly focused on mountainous watersheds or a single factor. In addition, the low flows prevalent in these studies were not evaluated probabilistically. Therefore, the relationship between the frequency of low flow and its controlling factors remains unknown.
Increasing water demand, due to population growth and economic development and/or changes in rainfall patterns due to climate change, alters the duration and magnitude of droughts. To establish sustainable water resource management based on changes in future drought risk, it is important to understand the relationship between low flow and its controlling factors, in relation to the magnitude of drought. Consequently, I formulated the hypothesis that the factors controlling low surface flow vary according to the severity of the drought. This study is a first attempt at revealing this relationship. The surface water volume of each drought-occurrence probability was calculated based on long-term observational data. The relationships among the drought water volume of each occurrence probability and the controlling factors were analyzed. Multiple controlling factors related to geology, land use, and topography were introduced. Since my results identified the controlling factor of drought for each occurrence probability, they may contribute to the development of effective water resource management strategies through prediction of drought water volumes or the impact of climate change on surface water runoff.

Location of the Study Area
In this study, 44 watersheds across the Japanese archipelago, where discharge observations have been conducted over 30 years, were used. Only stations where the impact of flow regime regulation is small due to a dam were used in this study. Thus, observation stations whose watershed included a sub-catchment in which a dam is located were excluded if the sub-catchment exceeded 10% of the total area of the watershed. (Figure 1). Information about the sub-catchment areas of dams was obtained from the Japan Dam Foundation [49]. Watershed areas ranged from 47 to 8208 km 2 .

Calculation of the Hydrological Data
The runoff coefficient (calculated by dividing the depth of runoff by the amount of rainfall) has a clear relationship with controlling factors, including topography, land use, and geology [50,51]. Therefore, various analyses were conducted in this study, using the runoff coefficient during drought conditions.

Calculation of the Hydrological Data
The runoff coefficient (calculated by dividing the depth of runoff by the amount of rainfall) has a clear relationship with controlling factors, including topography, land use, and geology [50,51]. Therefore, various analyses were conducted in this study, using the runoff coefficient during drought conditions.
Although various time-scale indices have been used in the assessment of drought, propagation of a precipitation anomaly to streamflow was explained at the annual timescale [52,53], and annual discharge was frequently used as an evaluation indicator of drought [54][55][56][57]. Therefore, I used annual total discharge as an indicator to calculate the drought runoff coefficient. To investigate the relationship between the various frequencies of droughts (from low to high) and the controlling factors, the drought runoff coefficients for six different probability years of occurrence (1/2, 1/10, 1/30, 1/50, 1/100, and 1/400) were calculated. Further, I defined the runoff coefficient for six different probability of years of occurrence as the drought runoff coefficient.
The drought runoff coefficient of each occurrence probability for the 44 watersheds was calculated using the following equation: where Qn is the estimated total discharge of each occurrence probability, Pn is the estimated precipitation amount of each occurrence probability, n = 2, 10, 30, 50, 100, and 400; and A is the watershed area. The annual total discharge of each watershed was obtained from the Water Information System (http://www1.river.go.jp/ access on 10 April 2019).). Annual precipitation data were obtained from the database of the Japan Meteorological Agency (http://www.jma.go.jp/jma/index.html access on 10 April 2019). Data from observation stations with an observation period exceeding 30 years were used based on the research results, which indicates that the stability of reproduction statistics increases if the samples exceed approximately 30 [58]. A sample of the average depth of rainfall over the watershed area was calculated using a Voronoi diagram to objectively consider the effect of area on the amount of rainfall at the watersheds.  Although various time-scale indices have been used in the assessment of drought, propagation of a precipitation anomaly to streamflow was explained at the annual timescale [52,53], and annual discharge was frequently used as an evaluation indicator of drought [54][55][56][57]. Therefore, I used annual total discharge as an indicator to calculate the drought runoff coefficient. To investigate the relationship between the various frequencies of droughts (from low to high) and the controlling factors, the drought runoff coefficients for six different probability years of occurrence (1/2, 1/10, 1/30, 1/50, 1/100, and 1/400) were calculated. Further, I defined the runoff coefficient for six different probability of years of occurrence as the drought runoff coefficient.
The drought runoff coefficient of each occurrence probability for the 44 watersheds was calculated using the following equation: where Qn is the estimated total discharge of each occurrence probability, Pn is the estimated precipitation amount of each occurrence probability, n = 2, 10, 30, 50, 100, and 400; and A is the watershed area. The annual total discharge of each watershed was obtained from the Water Information System (http://www1.river.go.jp/ access on 10 April 2019). Annual precipitation data were obtained from the database of the Japan Meteorological Agency (http://www.jma.go.jp/jma/index.html access on 10 April 2019). Data from observation stations with an observation period exceeding 30 years were used based on the research results, which indicates that the stability of reproduction statistics increases if the samples exceed approximately 30 [58]. A sample of the average depth of rainfall over the watershed area was calculated using a Voronoi diagram to objectively consider the effect of area on the amount of rainfall at the watersheds. A sample of annual total discharge and the average depth of rainfall over the watershed of each observation point were calculated to estimate the total discharge and annual precipitation for occurrence probabilities of 2, 10, 30, 50, 100, and 400 years. The hydrological statistics utility (ver. 1.5.) was used for the statistical analysis. I calculated the estimated design magnitude using 13 probability distributions, including the exponential distribution (EXP), Gumbel distribution (Gumbel), exponential-type distribution of maximum (SqrtEt), generalized extreme value distribution (Gev), log-Pearson type III distribution (real coordinate space) (LP3Rs), log-Pearson type III distribution (log coordinate space) (LogP3), Iwai method (Iwai), Ishihara Takase method (IshiTaka), the logarithmic normal distribution with three parameters (quantile method) (LN3Q), the logarithmic normal distribution with three parameters (Slade II) (LN3PM), the logarithmic normal distribution with two parameters (Slade I, L-moments method) (LN2LM), the logarithmic normal distribution with two parameters (Slade I, moments method) (LN2PM), and the logarithmic normal distribution with four parameters (Slade IV, moments method) (LN4PM) [59][60][61][62][63][64][65][66][67][68]. Among the 13 probability distributions, the estimated design magnitude was selected based on the standard least-squares criteria [69].
Numerous definitions of hydrological droughts have been proposed [15,70]. In this study, with reference to Whipple [71] and Changnon [72], low flow discharge was defined as being less than the average annual total discharge, and drought was defined as being less than 75% of the average annual total discharge. Furthermore, a discharge of 50%-75% of the average annual total discharge was defined as high-frequency drought, and a discharge of less than 50% was defined as low-frequency drought.

Collecting Data for Controlling Factors
Twelve indicators were assessed and classified into three categories (geological, landuse, and topographic factors) as controlling factors of the drought runoff coefficient.
As a geological factor, I focused on surface geology. Surface geology was classified into four groups (volcanic rock, plutonic rock, metamorphic rock, and sedimentary rock), based on geological creation processes, using a subsurface geological map at a scale of 1:200,000 (http://nrb-www.mlit.go.jp/kokjo/inspect/landclassification/download/ access on 12 April 2019). The ratio of each surface geology was calculated using a geographic information system (GIS). In addition, metamorphic rock was excluded from the analysis because the composition ratio was less than 5% for all target watersheds.
Land-use data were obtained from the National Survey on the Natural Environment, conducted by the Japan Ministry of Environment (http://www.vegetation.biodic.go.jp/ legend.html access on 12 April 2019). Five classes of land use were recognized in this study (coniferous forest, broadleaf forest, mixed coniferous-broadleaf forest, cropland, and urban areas), and each class was considered to have different effects on runoff. The proportion of land use for each of the 44 watersheds was calculated using GIS.
I calculated the inverse of the channel slope and topographical gradient, form ratio, and roundness, as topographic factors. Channel slope was defined as the difference in elevation between the observation station and headwater divided by the length of the stream channel. Topographic gradient was obtained by averaging the slope angles calculated using the average maximum method in the watershed [73]. The form ratio was calculated by dividing the watershed area by the square of the length of the stream channel [74]. The form ratio approaches 1.0 if the shape of the basin is almost square or circular. Roundness was calculated by dividing the circumference of the watershed area by the watershed boundary length [75]. Topography data were obtained from the Global 3D Map Service (ALOS World 3D-30 m).

Statistical Analyses
To investigate the characteristics of the drought runoff coefficient and its relationship with the controlling factors, an analysis using nonmetric multidimensional scaling (NMDS) [76] was conducted. NMDS refers to a family of related ordination techniques, all of which use rank order information in a (dis) similarity matrix [77][78][79]. Similarity in the drought runoff coefficient between watersheds was calculated using the Bray-Curtis similarity [80]. From the permutation test (n = 999), controlling factors closely related to the classification of the drought runoff coefficient (p < 0.01) were presented as vectors.
Of the indicators used as controlling factors, topographical gradient was excluded from the analysis because of the strong positive correlation (r > 0.07) between it and cropland. In addition, to investigate the difference in controlling factors among groups classified by similarity of the drought runoff coefficient, the controlling factors of each group were analyzed using one-way analysis of variance and the Kruskal-Wallis test. Further, Tukey's honestly significant difference (Tukey's HSD) and the Steel-Dwass test were conducted to reveal differences between groups if a significant difference was confirmed among groups. A generalized linear model (GLM) was subsequently developed to formulate a predictive model for the drought runoff coefficient for each occurrence probability. Ten controlling factors were used as explanatory variables, similar to the NMDS. The GLM is an extinction model of a linear model that allows the incorporation of non-normal distributions of the response variables and linear transformations of the dependent variables [81]. I compared the obtained Akaike information criteria (AIC) [82] for each model using the stepwise selection method [83]. Finally, the lowest AIC model was adopted as the best model for each species. GLM was conducted using MASS (version 7.3-50).
The average runoff coefficient was largest in group A and smallest in group C in all occurrence probabilities. In addition, the difference in the drought runoff coefficient between occurrence probabilities was smaller in Group A than in the other groups, exhibiting a slight difference between the occurrence probabilities of 2 and 400 years. However, in Group C, the drought runoff coefficient tended to decrease with increasing occurrence probability. In Group B, the change in drought runoff coefficient with occurrence probability indicated an intermediate behavior between Groups A and C. Although the drought runoff coefficient decreased to an occurrence probability of 30 years, it had an almost constant value at occurrence probabilities exceeding 30 years (Figure 3). A significant difference between groups A and C was confirmed in all occurrence probabilities (p < 0.01). In addition, a significant difference between groups A and B was confirmed in the occurrence probabilities of 10, 30, 50, 100, and 400 years (p < 0.01). Figure 4 presents a boxplot of the controlling factors for each group. The geological factors VR and SR yielded similar results. The highest values for both indicators were observed in group A, followed by those in groups C and B. One-way analysis of variance indicated a significant difference among the three groups (p < 0.01). Tukey's HSD test revealed a significant difference between Group B and the other two groups (p < 0.01) for both factors. However, the PR exhibited the opposite trend. The average value for PR was highest in group B (41%), followed by those in groups C (7.2%) and A (2.7%). The Kruskal-Wallis test revealed significant differences among the groups (p < 0.01). In addition, the Steel-Dwass test revealed that the PR of group B was significantly higher than that of groups A (p < 0.01) and C (p < 0.01).   Figure 4 presents a boxplot of the controlling factors for each group. The geological factors VR and SR yielded similar results. The highest values for both indicators were observed in group A, followed by those in groups C and B. One-way analysis of variance indicated a significant difference among the three groups (p < 0.01). Tukey's HSD test revealed a significant difference between Group B and the other two groups (p < 0.01) for both factors. However, the PR exhibited the opposite trend. The average value for PR was highest in group B (41%), followed by those in groups C (7.2%) and A (2.7%). The Kruskal-Wallis test revealed significant differences among the groups (p < 0.01). In addition, the Steel-Dwass test revealed that the PR of group B was significantly higher than that of groups A (p < 0.01) and C (p < 0.01).

Characteristics of Controlling Factors in Each Group
MCBF was the only land-use factor confirmed in watersheds belonging to Group A. The average value for UA was highest in group B (12%), followed by groups C (6.4%) and A (2.9%). The Kruskal-Wallis test revealed significant differences among groups (p < 0.01). In addition, the Steel-Dwass test revealed that the UA of group A was significantly lower than that of groups B (p < 0.01) and C (p < 0.05).
By contrast, one-way analysis of variance and the Kruskal-Wallis test indicated no significant difference for land-use factors BF, CF, and CL, and all topographical factors.

Difference in Drought Runoff Coefficient between Areas
Observation stations located on the Japanese archipelago were classified into three groups, A, B, and C, on the basis of their drought runoff coefficient. Furthermore, as a result of this classification, geographically close rivers tend to be classified into similar MCBF was the only land-use factor confirmed in watersheds belonging to Group A. The average value for UA was highest in group B (12%), followed by groups C (6.4%) and A (2.9%). The Kruskal-Wallis test revealed significant differences among groups (p < 0.01). In addition, the Steel-Dwass test revealed that the UA of group A was significantly lower than that of groups B (p < 0.01) and C (p < 0.05).
By contrast, one-way analysis of variance and the Kruskal-Wallis test indicated no significant difference for land-use factors BF, CF, and CL, and all topographical factors.

Difference in Drought Runoff Coefficient between Areas
Observation stations located on the Japanese archipelago were classified into three groups, A, B, and C, on the basis of their drought runoff coefficient. Furthermore, as a result of this classification, geographically close rivers tend to be classified into similar groups. The tendency of geographically adjacent rivers to show similar hydrological characteristics has been confirmed in previous studies [84]. Sawicz et al. [85] explained that this tendency was caused by climatic and landscape characteristics changing slowly in space. The drought runoff coefficient of Group A exhibited high values, regardless of changes in occurrence probability. However, the drought runoff coefficient of Group C decreased with increasing occurrence probability. Catchment classification using runoff characteristics is important from the standpoint of prediction in ungauged basins or the creation of a common language [86]. Carely et al. [87] analyzed the runoff coefficient of rivers in Sweden, Scotland, Canada, and the United States, and divided rivers into two groups (catchments that rapidly generate precipitation runoff and catchments that more readily store water and exhibit a more delayed release). In addition, Laaha and Blosch [48] demonstrated that seasonality of rainfall was the optimal parameter for the classification of watersheds using low-flow data. The change in the drought runoff coefficient with increasing probability of occurrence for Group B exhibited a trend intermediate between Groups A and C. In this study, I used the drought runoff coefficient as the indicator, which was calculated by dividing total river runoff by total rainfall in each area. The drought runoff coefficient was calculated annually and therefore, the difference in the trend of the drought runoff coefficient of occurrence probability among groups was thought to be partly caused by the seasonality of rainfall across different time-scales. However, it is clear that watershed factors exerted a strong influence on the drought runoff coefficient because the characteristics of the watershed indicator differed for each classification, based on the NMDS results. The stable and high drought runoff coefficient of Group A, which was composed of watersheds in regions experiencing heavy snow, can be attributed to its specific pattern of precipitation, compared to those of other areas. This is also due to low evapotranspiration in high-latitude areas [88,89]. Takahashi et al. [90] investigated the drought water volume of this water source area and concluded that the large drought water volume of north Japan results from the stable water supply induced by spring snowmelt, and associated runoff and intermittent rainfall in fall. This water supply contributes to the maintenance of groundwater during the drought season. In addition, the drought risk of the area influenced by spring snowmelt runoff will increase owing to the decreasing depth of precipitation in winter and spring as a result of climate change. This confirms the importance of snowmelt runoff in water resource recharge [91].
A trend of decreasing drought runoff coefficient with increasing occurrence probability was found in Group C, which is composed of watersheds within the southwest Japanese archipelago. In these watersheds, the depth of precipitation largely depends on the intense rainfall of a typhoon or rainy season [92]. Therefore, the low supply of water into the ground during drought results in a low drought runoff coefficient when the probability of occurrence is high. In addition to the influence of the pattern of precipitation, the geology of the watersheds belonging to Group C also influenced the low drought runoff coefficient. Group C was composed of watersheds with a high proportion of sedimentary rock (Figure 4). Furthermore, the geological age of the sedimentary rock of these watersheds (the Mesozoic and Paleozoic ages) is older than that in other areas [93]. The low drought runoff coefficient was thought to be caused by the high degree of agglomeration of the rock, which is a result of the high geological age influencing the deep percolation of precipitation. Group A is also an area with a large proportion of sedimentary rock, but it is thought that the difference in geological age and the influence of rainfall patterns was dominant, resulting in a difference in the rate of drought outflow from Group C.

Occurrence Probability of Drought and Controlling Factors
Hydrologic units reflect the characteristics of climate, geology, topography, and land use of watersheds [86,94]. Therefore, in this section, I describe the relationship between the watershed characteristics (geology, land use, and topography) and the drought runoff coefficient for each occurrence probability. The GLM investigated the relationships between the drought runoff coefficient and controlling factors, and demonstrated that geological factors and land-use factors (vegetation) influenced the drought runoff coefficient in highfrequency drought. In contrast, land-use factors and topographic factors were selected as influencing factors in low-frequency drought. Comparing the standard partial regression coefficient obtained from the GLM as a function of the occurrence probability, the value of MCBF of land-use factors was higher than that of geological factors in the high-frequency drought. In the drought with an occurrence probability of 30 years, the value of land-use factor exceeded that of the geological factor, and CF was selected as the most influential indicator. Furthermore, CS was selected as an important factor in low-frequency drought, in addition to CF. This is considered to be due to the fact that the runoff components that control flow discharge differ, depending on drought frequency. Geological factors and land-use factors were selected as the controlling factors in the total discharge of occurrence probability of 2 and 10 years. These factors are closely related to surface runoff or subsurface flow. In contrast, for the low-frequency drought, factors related to a longer time-scale hydrological cycle, such as ground-water level, were selected. Previous research investigating the relationship between flood discharge and controlling factors for multiple occurrence probabilities demonstrated that a coniferous forest increases discharge in lowfrequency floods, whereas topographical factors increase discharge in high-frequency floods [51]. In addition, the controlling factor for stream discharge changes from rainfall to geological factors with the threshold of ordinary water discharge [44]. From these results, it is clear that the controlling factors change according to the frequency of both flood and drought events.

Geological Factors and the Drought Runoff Coefficient
Some studies have demonstrated that geology is one of the factors controlling the flow regime [95][96][97]. The reasons for differences in drought runoff or base flow as a function of geology are that (i) the retention capacity of groundwater differs based on geology; and (ii) the infiltration capacity of soils differs as a function of geology [98,99]. From the GLM, PR and SR (among the geological factors) were selected as controlling factors that decreased the drought runoff coefficient in high-frequency drought (Table 3). This is incompatible with the results of Mushiake et al. [44], who noted that granite (classified as a plutonic rock) is a factor in increasing drought discharge. This contrast in results was caused by the location of the study area and the observation period of the data. Mushiake et al. [44] used the average drought value based on a relatively short-term period. In steep mountain rivers with a small watershed area, rainfall rapidly flows out, and the ratio of surface and intermediate runoff to drought discharge is thought to be larger. In addition, the influence of local deep percolation in bedrock cracks appears to be highly significant in small watersheds. Therefore, a minimum basin area is necessary to evaluate the effect of geological factors on the drought runoff coefficient. In contrast, Yokoo and Oki [100] demonstrated that geological age exerts an influence on drought runoff. In particular, based on an investigation of watersheds with an area exceeding 100 km 2 , quaternary geology was found to be an increasing factor for drought runoff. Rocks of different geological ages differ in the degree of consolidation and result in a difference in the degree of deep percolation. Furthermore, as diagenesis progresses, water exchange between an aquifer and a river is less likely to occur. Therefore, geological age is an important factor for characterizing the drought runoff coefficient. Therefore, it is necessary to consider both geological type and geological age as indicators for predicting drought runoff. Table 3. Analysis of the relationship between drought runoff coefficient of each occurrence probability and controlling factors by GLM
In addition to plutonic rock, sedimentary rock was selected as a factor causing a decline of the drought runoff coefficient for occurrence probabilities of 2 and 10 years. The infiltration capacity of sedimentary rocks appears to change with the degree of agglomeration. However, flysch (classified as a sedimentary rock), is a factor for increasing drought or flood [101]. The GLM results support the finding that the low permeability of sedimentary rock is a controlling factor in high-frequency drought.
While much research has revealed the relationship between geology and drought discharge, some researchers have claimed a stronger influence of topography than that of surface geology on groundwater level [102]. To clarify the more precise influence of geology, it is important to analyze the relationship between drought and geology under the same conditions of watershed area, topography, land use, and drought magnitude. In addition, the degree of agglomeration of the rock is closely related to runoff phenomena, as discussed above. Further research is needed to quantify the relationship between drought runoff discharge and geology in various regions.

Land Use Factors and the Drought Runoff Coefficient
Changes in the number of available water resources due to an alteration in the rainfallrunoff relationship caused by vegetation changes have long been recognized [103]. In addition, runoff volume differs between coniferous and broadleaf forests, owing to the dissimilarities in evapotranspiration (ET) [104][105][106]. My research results also indicate the different functions of coniferous and broadleaf forests. Based on the GLM, the broadleaf forest was selected as an increasing factor for the drought runoff coefficient for highfrequency drought, whereas coniferous forest was a decreasing factor for low-frequency drought (Table 3). This is thought to be due to differences in ET. Previous research has indicated that the change in runoff volume is larger for a coniferous forest when a coniferous forest and a broadleaf forest are cleared [107]. Furthermore, the drought runoff volume increases because of the clearing of the coniferous forest [103,[108][109][110]. These results support the GLM results. Moreover, I presume that the reason for the coniferous forest decreasing the drought coefficient in low-frequency drought is as follows: Since ET and canopy interception occur constantly regardless of drought magnitude, the amount of precipitation available to generate surface runoff decreases as the depth of precipitation decreases, and the effects of coniferous forests become dominant. In contrast, ET and runoff volume are altered by the management status of the forest, the condition of the forest floor, and tree age [111][112][113]. This study examined the relationship between the runoff coefficient and vegetation type as land-use factors for relatively large watersheds. Therefore, the differences between broadleaf and coniferous forests have become clear. However, it should be noted that the runoff coefficient could change, even within the same forest type, if the targeted watershed is smaller.
Land use changes significantly alter the mechanism of runoff [114]. Among landuse changes, urbanization increases flood peak discharge [115] and decreases minimum flow [116]. The main cause of urbanization decreasing the minimum flow is a decrease in the infiltration area and a decline in the base flow due to the consolidation of pipe systems [117,118]. The GLM results indicate that urban areas are a decreasing factor for the drought runoff coefficient in low-frequency droughts. The composition of tree species in the forest is an important controlling factor for high-frequency drought because the source of surface water mainly depends on rainfall in the upstream area. Therefore, the impact of urbanization is assumed to be relatively low in high-frequency droughts. In contrast, surface water from the upstream area is decreased in low-frequency drought and therefore, the influence of urbanization, including the limitation of rainfall infiltration or supply of surface water from groundwater, is assumed to be dominant. In contrast to this study, Ralf and Bloschl [119] demonstrated that land use, soil type, and geology do not exert strong influences on the volume of runoff in the normal stage in 459 rivers in Austria. Based on the results of my analysis, the magnitude of the impact of land use on the runoff coefficient varied, depending on the scale of runoff.

Topographic Factors and the Drought Runoff Coefficient
To determine the relationship among topographic factors and drought runoff, the influence of river length, watershed gradient, average watershed width, and altitude on base flow were examined [100,[120][121][122][123]. The GLM indicated that channel slope is an increasing factor for the drought runoff coefficient at occurrence probabilities of 10 years or more (Table 3). This result supports the research of Moliere et al. [120], who demonstrated that zero flow days increase in high-gradient rivers. However, topographic factors were not selected as controlling factors for the drought runoff coefficient at an occurrence probability of 2 years. Runoff discharge in high-frequency droughts is mainly governed by surface runoff. Therefore, the geological or land-use factors closely related to surface runoff were dominant, rather than topographical factors. However, the ratio of groundwater appeared to increase with increasing river discharge during low-frequency drought. Therefore, the topographic factor most closely related to groundwater was selected. Moreover, this study focused on observation stations in various basins, including both mountainous and alluvial areas. The interaction between groundwater and surface water is considered to be more active in alluvial channels; therefore, the drought runoff coefficient was higher in low-gradient watersheds.

Conclusions
This manuscript reports relationships among drought runoff and controlling factors (geological, land-use, and topographical factors) as a function of occurrence probability.
Classification results of the drought runoff coefficient across multiple drought magnitudes indicated three types of behavior for the drought runoff coefficient. The group with watersheds influenced by snowmelt runoff had a high drought runoff coefficient, regardless of drought magnitude. However, the drought runoff coefficient of the group influenced by rainfall intensity decreased with increasing drought magnitude. The drought runoff coefficient of the remaining group exhibited intermediate behavior between these two groups. In addition, this classification result indicated a significant relationship between the proportion of plutonic rock, sedimentary rock (geological factors), urban areas, and a mixed coniferous-broadleaved forest (land-use factors).
The GLM revealed that the controlling factors differed depending on the magnitude of drought. In high-frequency drought, the drought runoff coefficient was influenced by geological and vegetation factors, whereas land use and topographical factors influenced the drought runoff coefficient in low-frequency drought. These differences were caused by the differences in the runoff component, which dominated stream discharge in relation to drought magnitude.
This research clarified that a change in the drought runoff coefficient due to occurrence probability differs depending on the precipitation pattern or climatic zone, and the controlling factors of the drought runoff coefficient changed in accordance with the occurrence probability. Therefore, for effective water resource management, estimation of the drought runoff volume needs to consider precipitation pattern, geology, land use, and topography to correspond to the magnitude of the drought. Because the results clarify the controlling factors of drought runoff for each occurrence probability, this study contributes to effective water resource management by estimating the drought volume for climatic zones and by predicting changes in drought volume due to climate change. Further research is needed to investigate applicable climate zones and the influence of catchment scale on the relationship between drought and the controlling factors. Although not included in this study, dimensionless numbers describing the geomorphological characteristics of catchments, including stream order [124,125], bifurcation or ratio hillslope form [126], were revealed to explain the hydrogeomorphological characteristics of the catchment. Therefore, I can improve my model by using these factors.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Conflicts of Interest:
The author declares no conflict of interest.