Roles of hillslope and channel on spatial distribution of peak lag times during heavy storms at 4.5km2 mountain watershed

Abstract:

1 INTRODUCTION

Understanding flood flows and mechanisms are essential for the prediction and prevention of water and sediment related disasters in mountain watershed. Detailed observations at hillslope scale have revealed age, source and flowpath of water at each studied hillslope, while some studies have suggested that each hillslopes are unique, in other words, response to rainfall even varies among adjacent hillslopes within a same watershed. However, as we have seen that detailed observation of hillslope flow process require considerable labor, it is not realistic to measure many hillslopes to capture spatial variation of hillslope response at given watershed.

While flows and tracer concentrations of streams are relatively easy to measure, thus, they have been measured at multiple locations within watershed. Stream flows and tracer concentrations integrate hydrological information of drainage watershed, thus they should be generally influenced by hillslope and channel processes at steeply incised mountain watershed. Therefore, if we could successfully eliminate the influence of channel processes, we could gain knowledge on spatial variability of hydrological responses of hillslopes. During storms, relative contribution of hillslope and channel to watershed hydrographs may change; however we have very limited information during high flow because there are very few studies conducted during high flow.

Previous studies on hillslope hydrology during storms have demonstrated that;

(1) Most of rainfall infiltrated into soil and temporally develop perched water table above bedrock and/or layers with low infiltration capacity.

(2) When some condition is achieved during large storm, for instance when perched water table is extended to upper hillslope, lateral subsurface flow increase suddenly.

(3) During condition (2), changes in water storage in hillslope become small and shape of hyetograph and hydrograph become similar, that is, response time between rainfall input to discharge output become shorter.

Previous studies conducted at individual hillslopes have demonstrated (2) and (3) but there are only few studies conducted to capture spatial variation of (2) and (3) on watershed scale and further demonstrated spatial variation of hillslope processes on the stormflow of watershed. Thus, focusing on timing of flood peak arrival, we will test following hypothesis, assuming that condition described as (2) and (3) are fundamental to all hillslopes within watershed,

a) When wet, hillslope response time between rainfall input to discharge output become short and variation in hillslope response become small, thus, spatial variation in peak lag time is almost explained by channel process.

b) Spatial pattern of hydrological response of hillslopes to storms may change depending on storm size and pattern.

2 METHODS

2.1 Study site

Studied channel was located at the Aono Research Forest of the Arboricultural Research Institute of Tokyo University Forest, in Japan (Figure 1, 34°41'N 138°58'E). Average annual precipitation is 2,148 mm, and temperature is 15.3 oC. We have two rainy season, June to July and September to October and between those rainy season, we have relatively dry mid-summer and winter. Watershed is underlined by Tertiary sedimentary rock and covered with forest. Channels are incised thus watershed are dominantly composed of hillslope and channel and very small riparian area existed. Morphology of the channel is classified as step-pool and cascade according to Montgomery and Buffington (1997).

2.2 Water level measurements

We installed water level recorders at total of 16 locations within watershed (Figure1). At first in 2009, we used capacitive water level logger (Trutrack WT-HR Water Height Data Logger and Odyssey Capacitance Water Level Logger). Those have to be installed with pipes standing in the channel and unfortunately we have lost 7 out of 13 water level loggers during flood in 17 Jan 2009. Thus, in 2012 and 2013, we used pressure type water level loggers (HOBO U20 Water Level Data Logger) that can be installed submerged in water, assuming they have less risk of damage and/or lost during large flood. We recorded water level with 1 minute interval for all the location except for location A and C in 2009 and 2012 and location B for all three years (Table 1). Rainfall was measured with tipping bucket rain gauge at 6 minutes interval (Figure1). We defined peak arrival time as the differences in recorded time between maximum precipitation and maximum water level. For each storm, we collected peak arrival time for each measurement location.

Table 1 Characteristics of measured location, measurement interval and period of each studied location

Location ID	Catchment Area (km2)	Stream order	Bed slope	Measurement interval (min.)	period of measurements
A	0.02	1	0.26	5 (1 in 2013)	2009, 2012, 2013
B	0.06	1	0.21	5	2009, 2012, 2013
C	0.09	2	0.11	5 (1 in 2013)	2009, 2012, 2013
D	0.14	1	0.04	1	2009, 2012, 2013
E	0.26	2	0.03	1	2009, 2012, 2013
F	0.44	3	0.08	1	2009, 2012, 2013
G	0.53	3	0.07	1	2009, 2012, 2013
H	0.55	3	0.20	1	2012, 2013
I	0.90	3	0.08	1	2012, 2013
J	1.11	4	0.02	1	2009, 2012, 2013
K	1.19	3	0.04	1	2009, 2012, 2013
L	1.27	3	0.05	1	2009, 2012, 2013
M	1.35	4	0.03	1	2009, 2012, 2013
N	2.55	4	0.03	1	2012, 2013
O	2.68	4	0.05	1	2009, 2012, 2013
P	4.54	4	0.04	1	2009, 2012, 2013

2.3 Topographic analysis

A 5-m digital elevation model (DEM) was used to compute topographic characteristics. Stream networks were determined using a channel-threshold area method. Using previous analyses of the area-slope relationship (e.g. Montgomery, 2001) we found that this relationship showed breaks at 0.02 km. We conducted a field survey to confirm the results of the area-slope relationship analysis. We measured the drainage areas of 7 stream initiation points and they ranged widely from 0.002 to 0.086 km². Thus, the channel-threshold area was set at 0.02 km². For location A with smallest area of 0.02km², we surveyed actual stream initiation points and defined channel initiation point with drainage area of 1656 m².

Each pixel was linked to the stream pixel to which it drained by assuming that the flow path followed the surface topography. Here, we used a single-direction flow algorithm to determine flow path. Based on these flow paths, we computed topographic indices for each pixel for upstream areas of each measured location. These indices are the hillslope length, which represented the distance from each hillslope pixel to the channel, the elevation of each hillslope pixel above channel, the mean hillslope gradient along each flow path to its entrance into the channel computed by dividing the elevation above a channel by the distance from a stream for each flow line. Likewise, we also calculated the total flowpath length, that are sum of hillslope and channel flowpath representing the distance from each pixel to each measurement location, the total elevation of each pixel above each measurement location. Then we calculated channel length, channel elevation, subtracting hillslope length and elevation from total length and elevation of each pixel, respectively. Mean channel gradient was computed as dividing channel elevation with channel length of each pixel. We also calculated the ratio of hillslope length and hillslope gradient and channel length to root of channel gradient. We also computed the upslope accumulated area for each location. Stream orders of measured locations were determined based on Strahler (1952). Above topographic analysis was done using free open source software SAGA. For the comparison of each location, we use median values of topographic index for the analysis since these distributions are typically skewed. To compare which topographic indices are more variable among locations, we calculated coefficient of variation of each topographic indices among median values of each location.

3. RESULTS

3.1 Observed rainfall events

We captured small to large storm events during observation (Table2). Maximum1-hour rainfall of observed event ranged from 9 to 90 mm and total rainfall ranged from 38 to 198 mm. Observed events shows variable wet to dry antecedent conditions as indicated with API₁₀of 0 to 67 mm and return period of 0.0 to 8 years. As is often the case, there was no same size rainfall falling on the similar antecedent condition during observed period.

Table 2 Characteristics of observed rainfall event. Rainfall events are ordered from large to small maximum 1-hour rainfall

Storm NO.	Date rainfall started	Maximum 1-hr rainfall (mm)	Total rainfall(mm)	API10	Return period (year)
1	Jul-09	90	198	2	8.0
2	Oct-12	45	133	0	0.8
3	Oct-12	39	69	10	0.2
4	Jul-13	39	54	2	0.1
5	Jul-13	36	102	9	0.3
6	Jun-09	33	94	50	0.7
7	Jun-12	32	127	23	0.4
8	Jun-09	31	63	43	0.1
9	Jun-12	25	44	56	0.0
10	Jun-12	24	42	8	0.0
11	May-13	23	149	2	2.0
12	Sep-12	21	81	39	0.1
13	Sep-12	20	41	0	0.3
14	Aug-13	20	64	10	0.1
15	Oct-09	18	118	36	0.3
16	Aug-09	12	38	1	0.0
17	Oct-13	12	111	10	0.7
18	Jun-13	11	114	67	0.3
19	Aug-12	11	44	13	0.0
20	Jun-09	9	40	2	0.0

3.2 Variation in peak arrival time

Changes in water levels were different depending on storms as we observed different patterns of rainfall event (Table 2). In addition, each location shows different pattern of water level changes for the same rainfall event within 4.5 km²watershed. For instance, storm NO.2 (Oct. 2012) shows distinct sharp peak responded to high intensity rainfall (maximum 1-hr rainfall of 45 mm). For this event, peak arrived earliest at the location B and latest at the location L and differences in peak arrival time between these two locations was 28 min. While some other event with characteristics of prolonged peaks shows more than 2 hours differences in peak arrival times. For instance during storm NO.9 (Jun. 2012), peak arrived earliest at location H and latest at location L and the differences were 289 minutes. During this storm, at locations such as E and L, first peak directly corresponding to peak rainfall was small and the delayed peak, probably indicating deeper groundwater discharge, was higher than the first peak. In this case, differences in 'peak arrival time' in our definition, shows large variation within watershed. Although correlations were not significant, the standard deviation of peak arrival times among locations for each storm tended to be smaller for the storms with larger 1-hr maximum rainfall, indicating variations in peak arrival time tended to be smaller for more intense rainfall.

3.3 Results of topographic analysis

Distribution of hillslope length does not change much with watershed scale. While distribution of channel length clearly increase with scale. Hillslope length of each cell in watershed ranged between 0 m to 421 m. Distribution of channel length ranged between 0 m to 2788 m and they were larger than hillslope length. As a consequence, distributions of total flowpath length were almost similar to channel length distributions for each location and ranged from 0 to 3016 m in studied watershed.

Channel length and gradient were much variable than hillslopes length and gradient. Coefficient of variation (CV) of hillslope length among measured locations was 0.20 and it was 1/3 of that of channel length of 0.62. Coefficient of variation of hillslope gradient was also about 17% of channel gradient. Further, CV of hillslope length/hillslope gradient was 0.24 and it was 1/3 of CV for channel length/channel gradient^0.5 of 0.74. These results suggested that spatial variation in channel length and gradient should have larger impacts on spatial variation in peak arrival time compared to hillslope length and gradient.

3.4 Relationship between topography and peak arrival time

Peak arrival time clearly increased with median channel length for storm No.2. While there were no significant relationships with median hillslope length. Although scatters, both channel and hillslope gradient decreased with increasing peak arrival time. Peak arrival time increased with length/gradient^0.5 of channel but there were no clear relationship with length/gradient of hillslope. Similar relationship between topographical indices and peak arrival time were observed for most of intensive storms we observed. Peak arrives earlier at the location where channel length shorter and channel gradient steeper except 3 storms (No.6, 11, 12) for storms with maximum 1-hr rainfall over 20 mm. For storms with maximum 1-hr rainfall less than 20 mm, only 1 (NO. 20) out of 5 storms showed clear relationship with channel length and gradient. While hillslope length and length/gradient seldom show significant correlations and hillslope gradient had significant correlation for only 3 out of 20 storms.

Storms 6 and 12, that did not show any correlation with channel length, were characterized with prolonged, delayed second peaks that were higher than first sharp peaks right after rainfall peaks at some locations, thus, in our definition of 'peak arrival time' could varies largely. Storm No.11 occurred on very dry condition (API10 2.4 mm) during growing season and this may be the reason that show no correlation; it should have taken some rainfall to wet hillslope and develop groundwater to feed fast lateral flow during this storm. In this case, in addition to channel process, other process, such as variation in hillslope response might have affected more strongly to the variation in peak arrival time.

4, DISCUSSION

4.1 During most of intense storms, spatial variation in peak lag time was explained by channel process.

Our results showed that variations in peak arrival times within 4.5 km2 studied catchment were mostly derived from differences in channel length and the gradient and the effect of differences in hillslope length and gradient were small. This results coincided with our hypothesis (a) when wet, hillslope response time between rainfall input to discharge output become short and variation in hillslope response become small, thus, spatial variation in peak lag time is almost explained by channel process.

4.2 Spatial variation in hydrological response of hillslope to watershed runoff was different depending on rainfall pattern.

Our results suggested that spatial pattern of hydrological response of hillslopes to storms may change depending on storms size and pattern. Among observed storms, 7 out of 20 storms did not show significant correlation with channel length and gradient, suggesting other than channel length and gradient dominantly affected peak arrival time for these storms. Those storms were characterized with maximum 1-hr rainfall less than 33 mm. Storm NO.6 and 12 falls on relatively wet antecedent condition and were characterized with delayed large second peaks for some observed locations, suggesting deep groundwater contribution dominated for these locations. Storm No.11 was characterized with dry antecedent condition during growing season. Storm NO.16 ~ 19 have relatively small rainfall intensity with 1-hr maximum rainfall less than 20 mm. These suggested that although conditions descried as (2) and (3) are fundamental to all hillslopes within watershed, response to rainfall varies depending on rainfall size and pattern. Our results indicated that during intense storm on wet catchment condition, condition (2) and (3) can be achieved.

5, CONCLUSION

Our results demonstrated that peak arrival time during intensive storms can be predicted from detailed topographic information. We also showed that those relationship changes with storm size and pattern. Peak lag time is especially related to channel length and channel gradient during large storms, while hillslope length and gradient have litter impact. Almost liner relationships between median channel length and peak arrival time during intense storms indicated that flow velocity during flood peak can be almost homogeneous, while we knew mountain channels show heterogeneous morphology, consisting of variable sized material and resulting in variable channel resistance. Compared with downstream alluvial channels, we have little information on hydraulic characteristics of mountain channels. Our study suggested the need to understand more about mountain channels for flood prediction.