A high-resolution global runoff estimate based on GIS and an empirical runoff coef ﬁ cient

This paper reviews 110 years of global runoff estimation. By employing the method of ordinary least square regression on a sample region ’ s runoff coef ﬁ cient, an empirical formula of a runoff coef ﬁ cient is calculated for China. Based on this empirical formula applied with a high-resolution grid of precipitation, runoff is calculated resulting in an equally high-resolution map of global runoff using a geographic information system (GIS). The main results are (1) the global total runoff volume is 47,884 km 3 , (2) the average runoff depth is 359 mm, (3) the interior drainage region ’ s runoff volume is 1,663 km 3 , and (4) the average runoff depth is 58.4 mm. The results are compared with the results of the existing literature on global runoff. This study emphasizes the importance of runoff and groundwater recharge in arid and semi-arid regions where the estimation value of runoff depth is signi ﬁ cantly increased.


LITERATURE REVIEWS
The estimation of global water resources has a long history of more than 110 years. According to Lvovitch (), Penck first proposed the water balance formula: P ¼ R þ E (Precipitation ¼ Runoff þ Evaporation) in 1896. Geints modified the formula in 1903 as P ¼ S þ U þ E (Precipitation ¼ Surface runoff þ Groundwater þ Evaporation) and deemed that groundwater should be an integral part of the runoff calculation. Brikner estimated in 1905 that the global total runoff volume was 25,000 km 3 . Wust's estimation in 1920 was 37,100 km 3 . Nace's 1968 estimation was 42,600 km 3 , while Zubenok's 1970 estimation was 46,337 km 3 . Korzoun et al. () calculated that the global total runoff volume was approximately 48,000 km 3 , of which 1,000 km 3 was runoff from interior drainage basins; the world's total runoff was 45,560 km 3 if Antarctica is excluded. Grabs et al. () calculated that the global runoff was 42,709 km 3 , which is less than Korzoun's estimation, but his estimation for Africa's runoff was 8,585 km 3 , which is the maximum value for Africa presently. The latest estimations for global runoff are found in the 2014 GRDC's Report 44 (Wilkinson et al. ), which estimates that global runoff into the ocean (excluding runoff in Antarctica and in the interior drainage basins) is 41,867 km 3 ; and FAO's Aquastat database in 2016 lists that the world's interior renewable water resources (excluding Antarctica) are 42,811 km 3 , including surface runoff and groundwater which is not repeatedly accounted for in surface runoff (Table 1).
According to the statistics of 15 global runoff volumes for oceans and 17 global runoff volumes for continents in GRDC's Report 44, the maximum volume is 46,931 km 3 , and the minimum volume is 29,485 km 3 , with the average of 40,342 km 3 by the ocean and 40,258 km 3 by continent. This paper collected 44 sets of global runoff data with an average value of 39,365 km 3 and a median value of 39,381 km 3 . The modal's interval is 38,829-43,438 km 3 , which utilizes 50% of the total number of frequencies. The minimum value is 25,000 km 3 , and the maximum value is 52,657 km 3 .
The Global Runoff Data Centre (GRDC) is located at Koblenz, Germany. It hosts the global runoff database, a collection of river runoff data from 9,200 hydrological stations in 160 countries, which provides reliable raw data for contemporary studies about global runoff. However, due to the lack of runoff data for interior drainage basins where runoff is mainly seasonal and underground, runoff volume is possibly underestimated by GRDC's annual report and FAO's Aquastat database. On the other hand, the interior drainage runoff is ignored by defining runoff as strictly runoff flowing into oceans, which does not include runoff flowing into inland lakes or playas. The runoff consumed by human use or evaporation from river surfaces and washlands before passing through a gauge station is also ignored.
Theoretically, by taking a large river basin as a research unit, it is easy to ignore the evaporation and utilization of runoff at an intermediate point in the basin, but also the higher the spatial resolution the higher the runoff volume calculated. The phenomena are more significant in regions with strong evaporation or high-water consumption by human activities. Therefore, obtaining a high-resolution global runoff field will increase the precision and accuracy of runoff measurements, leading to a more correct calculation of the runoff within small watersheds and within interior drainage basins, thus resulting in a greater overall runoff volume. The spatial resolutions of studies thus far are generally low due to researchers using large basins as research units for global runoff estimation. For instance, the University of New Hampshire (UNH) generated a global runoff field with a resolution of 0.5 longitude and latitude by using the GRDC data 2000 (Fekete et al. a), but because of the coarser resolution, it is not         Step 1: Regress the empirical formula in the sample area.
According to the formula: Wros ¼ f(SLs, Ps, PETs) and AIs ¼ Ps/PETs: Because Wros ¼ Rs=Ps: So that the empirical formula can be expressed as follows: where Wros is the sample area's runoff coefficient, SLs is the sample area's ground slope, Ps is the sample area's precipitation depth, PETs is the sample area's potential evapotranspiration, AIs is the sample area's aridity index, and Rs is the sample area's runoff depth.
Step 2: To calculate the global runoff coefficient.
Based on the empirical formula of the sample region, the global runoff coefficient is calculated.
Step 3: To calculate the global runoff depth.
To calculate the global runoff depth based on global runoff coefficient and global precipitation depth, according to the formula: Wro ¼ R=P: Rearranging terms where Wro is the global runoff coefficient, R is the global runoff depth, and P is the global precipitation depth. Steps to calculate the global runoff coefficient and runoff volume are as follows: Step 1, use a global geographic projection, using the Resample command in the Grid module, to transform the grid data of global precipitation, AI and slope into 0.1667 ground resolution.
Step 2, using the Combine command in the Grid module at geographical projection, to combine three sets of grid data, the global precipitation depth, the global ground slope, and the global aridity index, into one set.
Step 3, in the combined grid data America's runoff coefficient is also the highest, which is up to 0.5074, followed by Asia, North America, and Europe, which is close to or higher than the global average, Africa's runoff coefficient is the lowest, which is only 0.3449 (Table 6).
According to the grid data by Worldclim, global precipitation depth ranged between 0 and 11,120 mm. The low-    () and Shiklomanov (). In all of the 24 sets of data,    Those groundwaters are not included in the runoff accounting of the Yellow River. In addition, water evaporation on the lakes, wetlands, and river channel along the river, urban landscape water use, ecological water consumption, industrial and mining water consumption, residential water consumption creates the huge net dissipation of water. If this water consumption is not gauged, then it is normally not accounted for in the runoff of the Yellow River ( Figure 7).

The runoff volume in interior drainage basins
This study calculated the detailed runoff pattern of the interior drainage basins. The runoff data of the interior drainage basins by continents and 31 sub-regions are calculated ( Figure 8). The global interior drainage region's total area is 28.47 million km 2 , Asia and Africa's interior drainage basins are the largest, which are 11.69 and 9.68 million km 2 , respectively. These are followed by Oceania and Europe, whose interior drainage basins are 3.56 and 1.99 million km 2 , respectively. North America and South America's interior drainage basins are the minimum, which is only    high runoff mountains and its runoff depth is 24 mm, which is higher than the above four desert areas' runoff depth (Table 10).

Comparison of runoff volume in Africa's interior drainage basins
According to this study's calculation, the area of the interior drainage basins of Africa is 9.6797 million km 2 , the annual    The case analysis of the typical interior drainage basins shows that the runoff depth field calculated by the empirical formula is in accordance with the actual runoff distribution.
Due to the spatial resolution is this study > Korzuon 1977 > UNH 2000, and the estimated runoff value is also this study > Korzuon 1977 > UNH 2000, the theoretical hypothesis is confirmed for the interior drainage basins sub-region; the higher the spatial resolution, the larger the calculated runoff values.

CONCLUSION
The main conclusions of this study are as follows: (1) The spatial resolution of this study is 0.1667 , which is three times the resolution of most studies that have computed a runoff calculation. As a result of this higher spatial resolution, the runoff volume from our study is higher than the runoff volume reported in the majority of prior studies.
Therefore, the theoretical hypothesis that a higher spatial resolution of a runoff field can lead to a higher runoff volume estimation is confirmed.
(2) The difference between the runoff estimation of this study and the actual measured runoff should be the regional water consumption by evaporation from natural water surfaces and wetlands, the net water consumption by agricultural irrigation, and the net dissipation of water resources from urban and industrial land use in the watershed.
(3) The current literature's underestimation of water resources is mainly due to the exclusion of evaporation from water bodies and wetlands, plus the net dissipation of artificial water usage in watersheds, and from ignoring the runoff in interior watersheds.
Some issues need to be further addressed to improve the accuracy of runoff distribution simulation. For instance, data error transmission between different climate data sources in regional runoff calculations is one issue, while geographical location accuracy in complex terrain regions is a second issue, both of which are critical for accurate runoff model calculations. Other issues include the quality of original precipitation, runoff, and PET data which can affect the