Abstract
Although there is a general consensus that spatial heterogeneity is ubiquitous in hydrological responses, it is common practice to assume a constant specific discharge among nearby catchments. This study addressed the contradiction in a ~18,000-km2 loess area of the Chinese Loess Plateau using 11-year streamflow records at 16 streamflow gauging stations. The studied watersheds were intensively cultivated during the observational period but human regulation such as dams, irrigation, and diversions, was scarce. Results show that the high spatial variability observed at the intra-annual scale was smoothed out such that the specific discharges of total streamflow, baseflow, and surface flow at multi-annual scales were fairly uniform among the studied watersheds. As a result, a direct scale extrapolation was applicable across four orders of magnitude in drainage area sizes (from 0.107 to 3,893 km2); meanwhile, a constant would suffice for spatial predictions of the mean annual specific discharge with a moderate predictive error of ~13%, showing that a larger catchment is hydrologically the sum of its smaller catchments in the homogenous loess landscape.
Résumé
Bien qu’il y ait un consensus général sur le fait que l’hétérogénéité spatiale est omniprésente dans les réponses hydrologiques, il est courant de supposer que le débit spécifique est constant entre des bassins versants proches. Cette étude s’est penchée sur cette contradiction dans une zone de lœss d’environ 18,000 km2 du plateau de lœss chinois en utilisant des enregistrements de débit sur 11 ans dans 16 stations de mesure du débit. Les bassins versants étudiés ont été intensivement cultivés pendant la période d’observation, mais la régulation humaine, telle que les barrages, l’irrigation et les dérivations, était rare. Les résultats montrent que la forte variabilité spatiale observée à l’échelle intra-annuelle a été lissée de telle sorte que les débits spécifiques du débit total, du débit de base et du débit de surface à l’échelle pluriannuelle étaient assez uniformes dans les bassins versants étudiés. Par conséquent, une extrapolation directe à l’échelle était applicable sur quatre ordres de grandeur de la taille des aires de drainage (de 0.107 à 3,893 km2)s; d’un autre côté, une constante suffirait pour les prédictions spatiales du débit spécifique annuel moyen avec une erreur de prédiction modérée de ~13%, montrant qu’un grand bassin versant est hydrologiquement la somme de ses petits bassins versants dans le paysage homogène de lœss.
Resumen
Aunque existe un consenso generalizado en que la heterogeneidad espacial es una característica generalizada en las respuestas hidrológicas, es una práctica común asumir una descarga específica constante entre cuencas cercanas. Este estudio aborda esta contradicción en una zona de loess de unos 18,000 km2 de la Chinese Loess Plateau utilizando registros de caudales de 11 años en 16 estaciones de aforo de caudales. Las cuencas estudiadas estaban intensamente cultivadas durante el periodo de observación, pero la intervención humana, como presas, riegos y desvíos, era escasa. Los resultados muestran que la alta variabilidad espacial observada a escala intra-anual se suavizó de tal manera que las descargas específicas del caudal total, el caudal base y el caudal superficial a escala multi-anual fueron bastante uniformes entre las cuencas estudiadas. Como resultado, una extrapolación directa de la escala fue aplicable a través de cuatro órdenes de magnitud en los tamaños de las áreas de drenaje (de 0.107 a 3893 km2); mientras tanto, una constante sería suficiente para las predicciones espaciales de la descarga específica media anual con un error predictivo moderado de ~13%, mostrando que una cuenca más grande es hidrológicamente la suma de sus cuencas más pequeñas en el paisaje homogéneo de loess.
摘要
一般认为流域水文过程普遍存在高度的空间异质性, 然而, 水文研究中通常也假定临近的流域具有相似的径流模数。很少有研究对这一矛盾给予关注, 本文以中国黄土高原典型黄土流域对该问题进行了研究。研究区面积为18,000 km2, 所采用数据包括16个水文站点11年的流量观测记录。研究时段内研究区人类耕作活动强烈, 但对水资源的人为调控(如水坝、灌溉、引水)较少。数据分析表明, 尽管在年内尺度, 径流模数的空间变异较高, 但随时间尺度变大, 径流模数的空间变异逐渐变小。在多年时间尺度上, 总径流模数、基流模数、地表径流模数在不同流域间变异较小, 表现出较好的空间均质性。这使得可直接采用尺度外推的方式来预报径流, 尺度外推适用的流域面积范围跨越四个数量级(从0.107 到 3,893 km2)。验证结果表明, 采用一个常量进行研究区多年平均产流的空间预报时, 预报的中值误差仅为~13%。这表明, 由于黄土区景观特性的空间均质性, 黄土区大流域从产流上可视为小流域之和。
Resumo
Embora haja um consenso geral de que a heterogeneidade espacial é onipresente nas respostas hidrológicas, é prática comum presumir uma descarga específica constante entre bacias hidrográficas próximas. Este estudo abordou a contradição em uma área de loess de ~18,000 km2 do Platalto Chinês de Loess usando registros de vazão de 11 anos em 16 estações de medição de vazão. As bacias hidrográficas estudadas foram cultivadas intensivamente durante o período de observação, mas a regulação humana, como represas, irrigação e desvios, era escassa. Os resultados mostram que a alta variabilidade espacial observada na escala intra-anual foi suavizada de modo que as descargas específicas do fluxo total, fluxo de base e fluxo superficial em escalas plurianuais foram bastante uniformes entre as bacias hidrográficas estudadas. Como resultado, uma extrapolação em escala direta foi aplicável em quatro ordens de magnitude em tamanhos de área de drenagem (de 0.107 a 3,893 km2); entretanto, uma constante seria suficiente para previsões espaciais da vazão específica anual média com um erro preditivo moderado de ~13%, mostrando que uma bacia hidrográfica maior é hidrologicamente a soma de suas bacias menores na paisagem homogênea de loess.
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Introduction
As fundamental features of hydrologic systems, spatial variability and the related drivers have been important topics in the hydrology community (Seyfried and Wilcox 1995; Karlsen et al. 2016). Knowledge of the spatial variability in the specific discharge of water (streamflow per unit area) can not only improve hydrological modeling and extrapolation of the models, but it can also add to understanding of the landscape structure and catchment functioning (McDonnell and Woods 2004; Buttle and Eimers 2009). Moreover, the variability is relevant to both ecological and biogeochemical processes (Teutschbein et al. 2015)—for example, chemical outputs from a landscape are closely related to the spatial patterns of specific discharge (Temnerud et al. 2007; Basu et al. 2010; Marinos et al. 2020). Hence, studies on the spatial patterns of specific discharge have influence across disciplines (Temnerud et al. 2007; Lyon et al. 2012; Teutschbein et al. 2015).
As is commonly perceived, spatial heterogeneity characterizes hydrological processes at all scales (McDonnell et al. 2007). High spatial variability occurs even within catchments covering a few hectares (Yair and Raz-Yassif 2004). There are numerous catchment characteristics that have the potential to influence the discharge variability, of which land cover or vegetation, soils, and topography seem to be most frequently mentioned (Seyfried and Wilcox 1995; Tetzlaff et al. 2007; Didszun and Uhlenbrook 2008; Lyon et al. 2012; Teutschbein et al. 2015). Oudin et al. (2010) even found that the catchments that are similar in physical characteristics are not necessarily similar in hydrologic behavior. Karlsen et al. (2016) and Lyon et al. (2012) showed that in a boreal landscape in northern Sweden, although the catchments were neighboring and apparently similar in topography, climate, and land cover, adopting a uniform specific discharge was troublesome and would confound the interpretations of hydrological and biogeochemical processes. Furthermore, Teutschbein et al. (2015) demonstrated that these similar boreal catchments would show different hydrological responses to the same projected signal of climate change. Hydrological processes are not only spatially heterogeneous but are also scale dependent (Cammeraat 2002). A number of studies have shown that specific discharge decreases with increasing catchment size (Cerdan et al. 2004; Yair and Raz-Yassif 2004; Kirkby et al. 2005; Lesschen et al. 2009; Cantón et al. 2011). The pervasive heterogeneity in combination with the scale effect has considerably hampered the predictive capability of hydrological models and their extrapolation (Seyfried and Wilcox 1995; Sivapalan 2003; McDonnell et al. 2007; Didszun and Uhlenbrook 2008).
Despite the consensus of seemingly ubiquitous spatial heterogeneity, it is often assumed that there is a constant specific discharge among nearby catchments, although it has rarely been verified (Lyon et al. 2012). The so-called drainage area ratio method, which directly scales discharge to the catchment area, has been commonly applied to estimate discharge for ungauged catchments (Archfield and Vogel 2010). The rationale behind the method is that the nearby catchments would have similar hydrological behaviors, as climatic and catchment conditions typically vary gradually over space and remain roughly constant among catchments in a particular region. Indeed, many studies have demonstrated spatial proximity to be a valuable indicator of hydrologic similarity (Merz and Blöschl 2004; Carey et al. 2010; Sawicz et al. 2011).
The assumption of constant specific discharge is somewhat consistent with the widely noticed concept of the representative elementary area (REA). The REA concept argues that the spatial variability in hydrology attenuates with increasing drainage area as large basins tend to average the local patterns of runoff generation and water flux (Wood et al. 1988, 1995). Stimulated by the REA concept, many studies during the past two decades have examined the spatial pattern of specific discharge. The studies reported a similar specific discharge among catchments greater than a critical drainage area, which was site-specific and generally ranged between 0.1 and 20 km2 (Woods et al. 1995; Shaman et al. 2004; Temnerud et al. 2007; Didszun and Uhlenbrook 2008; Asano and Uchida 2010; Lyon et al. 2012).
The apparent contradiction regarding the spatial pattern of specific discharge, as previously mentioned, needs to be adequately addressed in various physiographic regions. Three noticeable shortcomings occur in the related literature as follows: firstly, as noted by Karlsen et al. (2016), most studies have been based on short-period observations, for example, synoptic snapshot surveys during a few days (Woods et al. 1995; Temnerud et al. 2007; Asano and Uchida 2010; Lyon et al. 2012). The observed variations are thus likely to be transient and be smoothed out over a longer time scale. Using 5 years of streamflow observations from 14 partly nested catchments, Karlsen et al. (2016) found that although the short-term variability in specific discharge between catchments can be large, it alternated such that the long-term variability remained stable and small. Secondly, previous work has been primarily concerned with small to mesoscale catchments (<300 km2), although there have been repeated calls for examining large-scale discharge variability (Woods et al. 1995; Asano and Uchida 2010). To date, limited information is available regarding the large-scale discharge variability. Thirdly, baseflow and surface flow, two dominant components of streamflow, do not have identical environmental relevance. Surface flow is important with respect to soil erosion and flood risk, while baseflow is crucial for riparian ecosystems and human water consumption. Hence, watershed managers require information on both the total streamflow and its components; however, most studies (e.g. Lyon et al. 2012; Karlsen et al. 2016) focus only on total streamflow (particularly low-flow discharge), lacking an integrated analysis of spatial patterns of the total streamflow as well as its components.
One limitation in examining large-scale discharge variability has been a lack of hydrological data intensively collected at a series of drainage-basin scales. A second limitation has been that human regulation mechanisms such as dams, irrigation, and diversions, frequently distort catchment hydrologic behavior. The present study examined the spatial pattern of specific discharge over a ~18,000-km2 loess area on the Chinese Loess Plateau by comparing 11 years of streamflow data collected from 16 streamflow gauging stations during the period 1959–1969 (Fig. 1), during which human regulation had limited influence on the river systems.
Zheng (2017, 2018) demonstrated the spatial uniformity both in specific sediment yield and suspended sediment concentration of surface flow over the loess areas in the Wuding river basin of Loess Plateau (Fig. 1), respectively. The present study further hypothesizes a spatially uniform specific discharge. To test this hypothesis, the present study aims to: (1) quantify the spatial variability of the specific discharges of total streamflow, surface flow, and baseflow at multiple time scales; (2) assess the trend of the spatial variability with time scales and determine the time scale at which spatially uniform discharge emerges; and (3) show the relevance of the spatial pattern of discharge with respect to the hydrological prediction.
Materials and methods
Study area and data
The Loess Plateau lies in the central Yellow River basin. Two neighboring rivers on the Loess Plateau, the Wuding and the Qingjian (Fig. 1), were selected as the study area. The Qingjian River drains an area of 4,086 km2 and is fully covered by loess, while the Wuding River drains an area of 30,261 km2 with a loess area of 13,800 km2; other parts of the basin are desert. This study is interested in the loess areas of the two rivers, which combined cover an area of ~18,000 km2.
The loess mantle in the study area averages >100 m in thickness, representing a typical landscape of the Loess Plateau. Loess is dominated by the silt fraction (0.005–0.05 mm). As an eolian deposit, it is loosely compacted and highly susceptible to detachment by flows. Soil loss can be up to 20,000–30,000 t km−2 year−1, causing the loess areas to be severely dissected and the topography to show considerable relief. The climate is semiarid and temperate. Mean annual precipitation is approximately 450–500 mm, with ~70% occurring as short-duration, high-intensity storms. Infiltration-excess overland flow dominates the runoff generation, but groundwater flow contributes much to the river streamflow. Baseflow separation by Dai (1996) showed that the baseflow component accounted for 56.1% of the total streamflow.
The analysis in this study was limited to the period 1959–1969. During this period, most of the area was intensively cultivated (Jing et al. 1997), except those areas that were too steep. For instance, the cultivated lands accounted for 65% of the whole drainage area of the Chabagou Creek (No. 9 in Fig. 1), while the percentage of land steeper than 20° was as high as 68%. Soil conservation practices, including terracing, revegetation, and check dam (i.e. sediment trapping dams) construction, were not extensively implemented until 1970. Such practices probably have altered the catchment hydrological response since 1970; thus, this study did not consider the post-1970 period.
Unless stated otherwise, all data used were produced by the Yellow River Water Conservancy Commission (YRWCC), the official agency in China conducting hydrological surveys in the Yellow River basin. The key data are the daily streamflow records of the 16 streamflow stations. For the two gauged headwater basins (Nos. 1 and 3), water discharges were obtained using Parshall flumes. For other gauged stations, water stages were first observed at a staff gauge and then converted to water discharges using stage-discharge curves. The curves were calibrated regularly using water discharge values measured by means of current meters or floats. The daily mean flow discharges were calculated using the arithmetical mean of the instantaneous water stages if the water stages did not change much (<0.1 m) over a day. Otherwise, the daily mean flow discharges were calculated as the time-weighted mean discharges. Please see Li et al. (2005) for details of hydrometric measurements and data processing.
Spatial variability depends on given time scales. To calculate the inter-site discharge variability at various time scales, the daily records were aggregated over time scales from a 10-day to a multiyear period. At the annual time scale, the aggregated data include specific discharges of total streamflow (ha, mm), surface flow (haSF, mm), and baseflow (haBF, mm) of a single year (see section ‘Baseflow separation’ for procedures on baseflow separation). h, hBF, and hSF (mm year–1) are the arithmetical means of ha, haSF, and haBF throughout the observational period, respectively.
The inter-site discharge variability was quantified using spatial coefficients of variation (CV), i.e. the ratio of the standard deviation to the mean: \( \mathrm{CV}=\sqrt{\sum \limits_i{\left({x}_i-\overline{x}\right)}^2/\left(n-1\right)}/\overline{x} \), where x represents specific discharge of the ith station aggregated over a time scale, and n is the number of the examined stations. As shown in Table 1 and Fig. 1, a number of gauged catchments are nested within larger ones. The nested runoff data cannot be considered to be independent and so introduce bias into calculating CV, but the bias should not be significant as the portion of the nested catchment area was not large (<50%) in almost all cases.
The 16 streamflow stations had observational periods ranging from 7 to 11 years with a mean of 10 years. The upstream areas of the stations varied between 0.1 and 3,893 km2 (Table 1). According to the drainage area size, the upstream areas were divided into two groups: watershed and subwatershed. The subwatersheds are headwater basins of the first-order channels (Strahler order) typically draining an area less than 1 km2. They are ephemeral with no baseflow discharge, while the watersheds are perennial or intermittent. Two subwatersheds under examination (Nos. 1 and 3) therefore had an h much lower than that of the watershed group (Table 1); thus, they were excluded from the calculation of CV unless surface flow was being addressed.
To analyze the spatial pattern of climatic conditions, rainfall data were collected at 15 sites (Fig. 1). At least eight annual precipitation records, which were aggregated from the daily records, were available at each site during the period 1959–1970. In addition, pan evaporation measurements were obtained at six sites (Fig. 1). There were 6–8 annual records at the sites during the 1960–1967 period. Pan evaporation can be considered an indicator of potential evaporation, which integrates the effects of many climatic factors other than rainfall, including temperature, wind speed, solar radiation, sunshine duration, and vapor pressure. The evaporation measurements were made through a combined use of pans of 80 cm (April to October) and 20 cm (the remaining months) in diameter.
Baseflow separation
Baseflow separation was conducted by means of the widely used Lyne and Hollick filter method (Nathan and McMahon 1990). To determine the associated parameters, the method was compared with Zheng’s method (2015), which yielded comparable and probably more accurate results than the Lyne and Hollick filter method in the central Yellow River basin (Zheng 2015). Zheng’s method estimates baseflow through the regression equation: SSYa = cha + b, where SSYa represents area-specific sediment yield for a single year (t km−2), and c and b are the regression coefficients. Zheng et al. (2015) argued that the intercept term of this linear equation, i.e. –b/c, effectively representing the nonerosive-flow component of streamflow, can be used an estimation of hBF. By comparing the two methods, the filter parameter a was set at 0.925 and only one forward filter was passed over the daily streamflow hydrograph. Such settings yielded an hBF more comparable to that of Zheng’s method (2015), with discrepancies ranging between 0.46 and 22.3% with a mean of 10.7%, than that of other settings (Fig. 2).
Results
For the purpose of examining the intersite variability at various time scales, the spatial CV of the specific discharge of the streamflow stations was calculated at a series of aggregated time from the daily to the whole observational period. According to a 49-year rainfall record of the study area (1956–2004), the year 1964 had the greatest annual precipitation (590 mm), while 1965 had the least (150 mm). Thus, the 1960s period represented much of the hydrologic spectrum of this landscape.
Figure 3 clearly demonstrates that the spatial CV was more temporally variable at the intra-year scale, as opposed to the inter-year scales, as evidenced by the wider interval between the 25th and 75th percentiles. This observation suggests that a short-term observation (<1 year) may hardly capture the long-term pattern of a hydrological system. Figure 4 further demonstrates that the spatial CV was more temporally erratic during a low-flow or dry period than a high-flow or wet period.
As shown in Fig. 3, the intersite variability in specific discharge decreased with longer time scales. For total streamflow and baseflow, the median spatial CV was 37.6 and 33.4% respectively at the daily time scale and became progressively smaller when moving to the 10-day (33.9 and 29.7%), monthly (27.7 and 25.8%), seasonal (19.7 and 19.4%), and yearly (19.5 and 15.8%) scales. Surface flows showed higher spatial variability at all of the time scales; the median spatial CV was as high as 132% at the daily scale but gradually decreased to 28.4% at the annual time scale.
At the multi-year time scales, the median spatial CV continued to decrease (Fig. 3). Over the whole observational period, h, hBF, and hSF were fairly constant with a spatial CV as small as 11.3, 10.6, and 16.5% (Fig. 5), which implies that h, hBF, and hSF deviated from their spatial averages by no more than 21, 22, and 32%, respectively, at the 95% confidence level. Of particular interest is that the two subwatersheds had a lower h, but had a hSF closely comparable to their watershed counterparts (Fig. 5). As a result of the spatial constancy, the proportional function fitted the volumetric water discharge and the drainage basin area very well with an R2 near 1 (Fig. 6). The resultant proportionality coefficients imply the specific discharge averaged over the examined stations. A one-sample t-test demonstrated that h, hBF, and hSF showed no significant difference from the proportionality coefficients almost at all of the stations (p > 0.1; Table 2). Although it was not the case for hBF at some stations (Nos. 4, 6, 8, 10, and 13; p < 0.05), they deviated from the proportionality coefficient by less than 20%. Hence, it is reasonable to use the proportionality coefficient, a constant term, for the spatial prediction of h, hBF, and hSF. The Jackknife procedure, a method of leave-one-out cross-validation (Shao and Tu 1995), showed that the constant-term approach performed well with a moderate error (ME, %) of ~13% (see the first row in Table 3).
The spatial constancy approximately remained at a single-year time scale. As listed in Table 3, the spatial CVs of ha and haBF were on the order of 12–30%; accordingly, the constant-term approach, which derived the constant term by establishing the proportional discharge-drainage area relationship for the single years, remained applicable with an ME averaging 20.6 and 18.6%, respectively (Table 3). Although haSF had a greater spatial CV on the order of ~20–48%, the constant-term approach, producing an ME ranging between 17.5 and 48.4% with a mean of 27.7%, was acceptable in many cases (Table 3).
The spatial uniformity in specific discharge fosters the applicability of direct scale extrapolation from small to large watersheds. Watershed Nos. 12 and 52 have the largest drainage basin area. Figure 7 compares their streamflows with those of watershed No. 4 (the smallest watershed), No. 11 (having the smallest h), No. 8 (having the greatest h), and subwatershed No. 3. Despite up to three to four orders of magnitude difference in basin size, most of the data points are scattered around the 1:1 line, lending support to the direct scale extrapolation. It is particularly encouraging that the observed surface runoff of the subwatersheds (Fig. 7m,n) can be directly used to predict that of a large watershed. In Fig. 7, there were indeed several noticeable outliers. All of the outliers correspond to the observations in 1966 and within watershed No. 9. In 1966, several localized extreme rainfall events occurred on watershed No. 9 and are responsible for the outliers. The effect of the local extremes were smoothed out over longer time scales, thereby allowing direct-scale extrapolation at a multiyear time scale.
Discussion
This study observed decreasing specific-discharge spatial variability with longer time scales in the ~18,000-km2 study area. The standard sampling theory suggests that the variance of a sample mean decreases with sample size (Young and Young 2013). Hence, the observation should find wide applicability, as in the boreal Krycklan watershed in Sweden (Karlsen et al. 2016). The Krycklan watershed is 68 km2 in size. The striking difference in basin size between the Krycklan watershed and the present study area has profound effect on the hydrological regime. In the Krycklan watershed, the spatial variability of the weekly specific discharge rapidly decreases with increasing flow rate and eventually converges on the level of the annual scale (Karlsen et al. 2016). The decreasing trend with flow rate, however, is not pronounced in the present study area, as shown in Fig. 4. A storm with partial areal coverage would generally cause a low flow rate at the basin outlet as well as high inter-site discharge variability within the basin; in contrast, a storm with full areal coverage would lead to a high flow rate as well as low inter-site variability. The small size of the Krycklan watershed should allow it opportunities to be fully covered by a single rain cell, resulting in low inter-site discharge variance at high flow rates. On the Loess Plateau, a rainstorm typically covers an area smaller than tens of square kilometers (Zhang 1983), several orders of magnitude smaller than the study area in size. As a result, the specific discharge still shows considerable spatial variance at high flow rates, distinctively greater than that at the annual scale (Fig. 4).
The spatial uniformity in specific discharge disagrees with that of many studies (Yair and Raz-Yassif 2004; Lesschen et al. 2009; Cantón et al. 2011), which suggests a decreasing streamflow with increasing basin size. Although the spatial uniformity is broadly in line with the REA concept, it appears that there was little signal of higher spatial variability at smaller spatial scales (Fig. 5), which is typical of the REA model (Woods et al. 1995; Lyon et al. 2012). A possible explanation is that the REA in the study area is less than 0.1 km2 (the smallest drainage area size under examination). Such an REA is similar to that in the Fudoji catchment, Japan (Asano and Uchida 2010), but much smaller than those reported elsewhere (Woods et al. 1995; Shaman et al. 2004; Temnerud et al. 2007; Didszun and Uhlenbrook 2008; Lyon et al. 2012). Egusa et al. (2013) argued that a higher drainage density would lead to more confluences and thus a lower REA. The loess headwaters are notoriously dissected by permanent gullies. Rills and ephemeral gullies are also well developed (see photographs in Zheng et al. (2005, 2013, 2015a). The exceptionally high hydrological connectivity associated with rills and gullies must allow for rapid mixing of random inputs and in turn an exceptionally small REA.
The spatial uniformity in specific discharge should be closely related to the homogenous landscape conditions in the loess area such as soil, topography, land use, and vegetation, which typically acts as major controls on the spatial pattern of specific discharge. As wind-borne dust, loess does not change much in properties over space unless at a macro spatial scale. The loess area has a simple topography consisting of two landscape units, hillslope, and valley, with no lakes or wetlands, and few urban areas. The topography is uniformly very steep (average basin slope > 20°). Land use was uniformly dominated by arable and barren (mainly consisting of escarpments and creek channels) lands. Vegetation cover was sparse throughout and could hardly alter the spatial pattern of a hydrological quantity. In these respects, the loess landscape is indeed comparable to those in REA-type studies, which typically assumed or adopted an apparently homogenous catchment whether for field studies (Shaman et al. 2004; Asano and Uchida 2010; Egusa et al. 2013; Karlsen et al. 2016) or numerical simulations (Wood et al. 1988; Blöschl et al. 1995).
Climatic factors, in combination with landscape conditions, determine hydrological behaviors of a watershed. Spatial variabilities of two climatic factors, rainfall and potential evaporation, were examined. Although it is well known that rainfall on the Loess Plateau is highly localized as previously mentioned, the case is different at a longer time scale. The annual precipitation during the 1959–1970 period had a rather small spatial variability with a CV varying between 9.9 and 22.3% with a median of 15.2% among the 15 rainfall stations in Fig. 1. The mean annual precipitation was more uniform with a CV of 7.9%. Pan evaporation had similar variability over space. At the annual time scale, the CV among the six evaporation stations shown in Fig. 1 ranged from 8.7 to 19.5% with a median of 12.2%; the CV further decreased to 11% at a multi-annual time scale. The less spatial variability in rainfall and pan evaporation at the >1 year time scales should be closely related to the attenuating variability with longer time scales shown in Fig. 3.
Figure 6 strongly supports the frequently applied assumption of a uniform specific discharge among nearby catchments. The assumption held true at the >1-year time scale, and for a region where climate and catchment conditions remain similar. One cannot further extrapolate the spatial uniformity up to the mainstream of the Wuding River. This is because its upstream desert is different from the loess area in terms of catchment conditions. In addition, extrapolation to ephemeral streams should be treated with particular caution, as high flow transmission loss is typical of them and can result in a decreasing runoff along the flow path (Lane et al. 1997).
The spatial uniformity in surface flow is of great relevance to the spatial pattern of source erosion and basin sediment yield. Eroded sediment within a watershed is the product of surface flow discharge and its sediment concentration. Zheng et al. (2013) and Zheng (2018) have demonstrated the spatial uniformity in sediment concentration of surface flow from headwaters to variously sized watersheds on the loess area of the Wuding Basin. The spatial uniformity in surface flow and its sediment concentration affords a sound foundation for the spatial uniformity of source erosion and specific sediment yield in the loess area, as argued by Zheng (2017).
The similar baseflow over the variously sized watersheds (4–4000 km2) is in contrast to the common speculation that baseflow increases with basin size, but it is mostly consistent with observations of some mesoscale watersheds such as the Neversink River watershed in the Catskill Mountains of New York (176 km2; Shaman et al. 2004), the Krycklan watershed in Sweden (68 km2; Lyon et al. 2012), and the Ottervattsbacken watersheds in Sweden (78 km2; Temnerud et al. 2007), in which the baseflow stabilized at drainage areas larger than a critical value (4–21 km2). The similar baseflow implies that the groundwater contributions to streamflow are similarly apportioned over space. In the study area, the similarity should be closely related to the less inter-site variability in loess properties as rainfall recharges the groundwater primarily through cracks and fissures developed in the loess mantle (Xue 1995; Yan and Wang 1983). The similar baseflow among variously sized watersheds suggests that all groundwater recharge occurs in the first-order drainage basin (i.e. the headwater or subwatershed area), while all groundwater outflow is along the second-order channel with no additional outflow further downstream. In this sense, a large watershed is simply the sum of its constituent small watersheds.
Conclusions
This study examined the spatial patterns of specific discharges of total streamflow as well as its components of baseflow and surface flow over a ~18,000-km2 loess area in the central Yellow River basin. It was found that although the discharge variability over space was high at the intraannual scale, it attenuated with longer time scales. Over the whole observational period, the mean annual specific discharges could be reasonably assumed to be constant across four orders of magnitude in drainage area sizes (from 0.107 to 3,893 km2) for total streamflow, baseflow, and surface flow. The results suggest that the assumption of a uniform specific discharge between catchments is well applicable in the study area at an interannual time scale, whereas a short-term observation (<1 year) can hardly capture the full extent of the hydrological variability. The spatial uniformity in the hydrological response is related to the spatially uniform rainfall in combination with the homogenous landscape traits such as soil, topography, land use, and vegetation. Although the exportability of the findings to similar geomorphoclimatic contexts needs to be proved, the results of this study question the universal validity of a highly variable specific discharge over space. To better understand the nature of hydrological variability over space, it is highly desirable to explore it over various physiographic settings at a series of spatio-temporal scales.
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Acknowledgements
The authors acknowledge the data support from “National Geographic Resource Science SubCenter, National Earth System Science Data Center, National Science & Technology Infrastructure of China (http://gre.geodata.cn).
Funding
This work was supported by the Guangdong Basic and Applied Basic Research Foundation (2021A1515011552), the GDAS’ Project of Science and Technology Development (2019GDASYL-0103043) and National Natural Science Foundation of China (41671278).
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Zheng, M., Liang, C., Huang, B. et al. Spatially uniform specific discharge from headwater to river basins on the Chinese Loess Plateau. Hydrogeol J 29, 2429–2439 (2021). https://doi.org/10.1007/s10040-021-02392-2
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DOI: https://doi.org/10.1007/s10040-021-02392-2