River discharge is a very reliable and integrated observation of the continental water cycle which is always used as a validation variable . Over the headwater catchments, there are 13 hydrological gauges recorded in the Hydrological Yearbooks of China issued by the Ministry of Water Resources, though only six gauges are selected with consideration of their locations and data completeness. Two gauges (1, 2) are in the upper Yarkand River, two (3, 4) are in the upper Hotan River, and two (5, 6) are in the upper Aksu River, while no gauge is found on the Kaxgar River. For the gauges in headwater catchments, the discharge is considered free of human intervention, i.e., irrigation or reservoir regulation, so to a large extent they represent the natural environment . This facilitates model validation. Moreover, on the mainstream of Tarim, one gauge (7, Alar) was selected at the junction of three upstream rivers (Fig. ). Different from the headwater gauges, the river discharge at Alar has been significantly altered by human consumption after flowing through the irrigation area . Hence, the observations are no longer natural values but can be used to quantify the influence resulting from human activities.

Near-surface atmospheric conditions are crucial to hydrological responses . However, both the model simulation and gridded forcing generated from observations are proven to have large uncertainties where observations are sparse and heterogeneity is strong , i.e., in the arid and mountainous area, so that, in practice, several forcing datasets are always used in parallel to generate an ensemble of climate conditions which hopefully tracks the uncertainties . Alternatively, when possible, regional datasets which contain more information than global datasets are used to move the forcing closer to true values . In this study, several sets of estimated forcing inputs based on WATCH (Water and Global Change; ; ) are developed and then used to drive the land surface model (Fig. ). The best simulations among them will be used to analyze the accompanying bias with its driving forcing.

A pair of reference forcing datasets are WFD (WATCH Forcing Data, 1958–2001; ) and WFDEI (WATCH Forcing Data methodology applied to ERA-Interim data, 1979–2012; ). They use the same methodologies but have slight differences in the basic data, processing and formatting . In brief, WFDEI is an evolution of WFD where the underlying re-analysis is now ERA-Interim but using the same bias correction methodology. This product has been proven to be superior to WFD. CRU (Climate Research Unit) monthly total precipitation observations were used to bias-correct the precipitation in WFD and WFDEI datasets. However, the WFD uses a previous version CRU TS 2.10 before the CRU TS 3.1 used in WFDEI was released . The two CRU datasets differ in the time period (CRU TS 2.10: 1901–2002; CRU TS 3.1: 1979–2009; ), in the stations used and in the methods employed; see for details. Hence, there are still some differences between the two which could further affect the hydrological responses. The two datasets are named WFD-CRU and WFDEI-CRU for later description, and the time step for all the forcing variables is 3 h.

The CRU datasets were constructed by monthly observations at meteorological stations across the world's continents. The observations were then interpolated to 0.5∘ longitude–latitude grid cells. Though the CRU compares favorably to some other gridded datasets, it has significant deviations over regions and time periods with sparser observational data . Moreover, because only the monthly total precipitation was used to correct WFDEI and WFD, it cannot improve the temporal variabilities at smaller time steps (i.e., daily or sub-daily). However, the precipitation variations in a short period would result in different hydrological responses even in the condition of the total monthly amount remaining the same .

Hence, in addition, the WFDEI-CRU dataset was further corrected by the gridded daily precipitation data from the China Meteorological Administration (named CMA). The CMA precipitation product compiles 2416 national meteorological monitoring stations over China, using the climatological optimal interpolation method to generate the gridded 0.5∘ precipitation field from 1951 to 2016 (). PRISM (Parameter-elevation Regression on Independent Sloped Methods; ) was used to lessen the orographic effects . The density of meteorological stations used in the CMA is much higher than that used for CRU. For instance, there are only six gauges over the Tarim Basin in the CRU database, while 39 gauges are recorded in the CMA system so that it can to a certain degree improve the data applicability where precipitation is spatially inhomogeneous compared to CRU datasets. Given that the CMA data provide the daily information, it also improves the temporal variations of precipitation rather than using the total monthly value in CRU datasets. The corrected atmospheric input dataset is hereafter referred to as WFDEI-CMA.

As mentioned in Sect. 2, glacier melt is a vital water input to the Tarim. However, glacier runoff measurement is so difficult for such large regions that model-based estimates of the glacier melt are necessary. In general, a glacier module is not coupled in LSMs . Hence, rather than building a separate glacier module, we use an independent daily glacier melt dataset obtained from the glacier model called HYOGA2 (meaning glacier in Japanese), which has been proven reliable over the globe . HYOGA2 is a temperature-index-based model utilizing an extensive global-scale glacier inventory and has several improvements compared to its first version (HYOGA) in model parameter simulation as well as the temporal extent. More details can be found in the original papers . The glacier melt is added to the rainfall series of WFDEI-CMA as an additional water flux to the system. The melt water hence participates instantaneously in the water cycle without delays such as stores in ice, glacier pack or groundwater recharge beneath the ice being considered. This method was chosen for its simplicity and the lack of knowledge on the details at the transition between the glacier and the soil. Daily values are uniformly distributed over the eight time steps per day of WFDEI. By adding the glacier melt, the fourth new forcing dataset is generated as WFDEI-CCG.

On top of precipitation, evapotranspiration and potential evapotranspiration are two important fluxes, and their errors are key to the water cycle modeling. In ORCHIDEE, the evapotranspiration is calculated with energy balance and resistance concepts. The potential evapotranspiration is defined as “the amount of evapotranspiration that would occur if enough water was available at the surface”, as explained in . The PET is computed as the sum of the potential soil evaporation and the potential transpiration from vegetation. For soil evaporation, the diffusive equations are taken with the ratio of the humidity gradient, the aerodynamic resistance and the air density. The virtual surface temperature is used instead of the actual one to compute the saturate humidity, while the virtual surface temperature is calculated through an unstressed surface energy balance. The method has been proven superior to other diffusive methods in the reference paper . The potential transpiration is driven by the potential evaporation between the evaporating surface and the overlying air but is limited by vegetation resistances. The maximal water loss under stress-free conditions is the potential transpiration . The actual evapotranspiration is a function of the potential evaporation but is modeled by a series of resistances (canopy and aerodynamics) of the surface layer. The details of the methods in simulating PET and ET can be found in , and .

There is on key improvement which has been implemented in the current version of ORCHIDEE, that is, the snow and soil freezing scheme. Snow and soil freezing are two crucial water processes in cold regions; snow covers nearly half of land area , and the frozen soils occupy 55 % to 60 % of the land surface of the Northern Hemisphere in winter . Snow plays an important role in both the energy and water flux as the snow cover is first an insulation which prevents the heat loss from the soil. It also increases the thermal inertia of the surface by adding a new phase change and acts as a moisture reservoir which stores winter precipitation that is released in spring or early summer. In the old ORCHIDEE version, a constant density and very simple heat capacity are applied for the snow. The snowmelt directly feeds the runoff without refreezing, and the snow layer is mixed with the first soil layer so that they are equal in temperature. While in the new snow scheme, the snow layer is defined and separated from the soil layers. The snowpack is represented in three layers which adequately resolve the snow thermal gradients between the top and base of the snow cover. The energy balance and the temperature of the snow body become more realistic. Refreezing of the snowmelt is allowed, which makes the energy changes more reliable. The snow properties are more detailed than before, i.e., the density, albedo and roughness. All the improvements have been validated over France and northern Eurasia and already implemented in the current ORCHIDEE .

Soil freezing impedes water infiltration and drainage, thus leading to changes in hydrological responses . At small scales, the soil freezing alters the soil structure and therefore its water capacity, which has a consequence on the water flux between soil and atmosphere, as well as the water availability for plants . On the other hand, the frozen soil changes the latent heat exchange, which delays the soil temperature signal . Soil thermal characteristics are also improved due to the different thermal properties of ice and water. In the old soil thermal equations, thermal advection and phase change of the water are not considered when resolving the latent heat exchanges . The mechanical effects of soil freezing are therefore ignored. In the new soil freezing scheme, the apparent soil heat capacity can be increased by considering the ice content of the soil layer during a freezing-temperature window between 0 and -2 ∘C. A temperature correction is applied if any soil layer is entirely frozen or thawed. Moreover, the soil heat conductivity is changeable according to the ice content in the soil, which affects the thermal propagation in the vertical soil column. Finally, the hydraulic conductivity is reduced as a function of the ice content. Liquid water is not allowed to cross the frozen soil layers. Thus infiltration and drainage are forced to stop. Full descriptions of the new freezing soil equations and the parameterizations setting can be found in .

Irrigation is included in the current version of ORCHIDEE. The irrigation requirement is estimated as the deficit of the available water of the corresponding grid to the potential evapotranspiration. The irrigation extracts water from the local grid first and then its neighboring grids if necessary . This solution is acceptable for most of the humid regions at a 0.5∘ resolution since the rivers are very likely within 100 km. However, for dry regions, the Tarim for example, the irrigation area is concentrated, with controlled irrigation infrastructures. The nearby rivers are far from the irrigation area, and the irrigated water is not taken directly from the rivers but transported from upstream by channels. Due to the shortcoming of the scheme and the lack of knowledge on the local irrigation, we turned off the irrigation in ORCHIDEE. In the Tarim Basin, the irrigation accounts for more than 95 % of the consumed water , so that the difference between the simulated discharge and observations can be attributed to neglecting irrigation in the model.

In conclusion, as shown in Fig. , four different forcing inputs are prepared to drive the ORCHIDEE simulations, two basic forcing datasets (WFD-CRU and WFDEI-CRU), one after correction by CMA (WFDEI-CMA) and then one after adding glacier melt (WFDEI-CCG). Among them, the input water amounts are different, while WFDEI-CMA and WFDEI-CCG have the same other forcing variables as WFDEI-CRU. Additionally, the experiment with the newly developed snow and soil freezing scheme is named WFDEI-CCG-SF based on the forcing dataset WFDEI-CCG. Because the WFD covers the overlapping period 1901–2002, the WFDEI covers the period 1979–2014, CMA covers years 1951–2016 and the glacier melt dataset covers 1958–2001, all the simulations and analysis in this paper are over the overlap period 1979–2001. The monthly discharge measurements for those chosen hydrological gauges over 1979–2001 are then compiled. Spatial resolution for all the forcing inputs remains 0.5∘ (about 50 km at the Equator), and the time step is 3 h.

The Tarim Basin is one of the areas where significant deviations exist among different modeled precipitation estimates and observation-derived datasets because of the sparse observations and orographic effects . Meanwhile, the precipitation bias might not be well addressed in the CMA system because the number of meteorological gauges is still too limited in the Tarim region to build a reliable interpolation climate field . Although have tried to use other gauges outside China, the density of the gauge distribution is extremely low around the boundaries of the Tarim Basin where most of the precipitation is generated. Furthermore, due to the orographic effects, the precipitation over the mountainous area is larger and with more significant heterogeneity than that in the plains , while the center of the precipitation events is hard to observe for the nearby gauges. has pointed out that the orography could cause 41.6 % underestimation of the precipitation over the northwestern North American mountainous ranges, and the deviations are larger at higher altitude.

The differences between WFDEI-CRU and WFDEI-CMA are not only in the total amount of precipitation but also in the proportion of rainfall and snowfall (Table ). Compared to the rainfall, the snowfall is more difficult to observe and affected by a large uncertainty; hence in the CMA dataset, only the rainfall was recorded and then used to scale the CRU dataset but keeping the relative proportion of liquid and solid precipitation provided by WFDEI-CRU. The energy needs for phrases change are considerably different for the liquid from the solid water. suggested snow will lead to more runoff than rain in similar conditions based on the observations over the US and China. The impact of the precipitation type on the evapotranspiration rate is affected by many factors and hard to measure.

HYOGA2 is a state-of-the-art global glacier model but has not been calibrated over the Tarim Basin. The general bias for global estimation is around -5.0 % compared to the available global glacier mass balance measurements . The estimated annual glacier melt amount is 81.0×108 m3 yr-1 for the whole Tarim Basin (Table ), significantly lower than previous estimations (: 133.4×108 m3 yr-1; : 144.16×108 m3 yr-1). On the one hand, the difference in the forcing which drives the glacier melting model is probably one of the causes of the deviation. On the other hand, all the glacier melt is evenly distributed in a whole grid. It leads to a higher infiltration ratio and thus feeds more evaporation . This also artificially forces part of the glacier melt to flow out of the grid not belonging to the right basin. However, it is unable to eliminate this problem with the current gridded concepts. Finer spatial resolution in glacier dataset and model simulation is needed to lessen the impacts of discretization.

As described in Sect. 3.2.1, the PET estimation is independent of underlying conditions (e.g., topography, vegetation) because enough water is provided. It is therefore determined only by forcing conditions, especially the humidity gradient and aerodynamic conditions (e.g., radiation flux, wind). Temperature also plays a role in its estimation. Thus, the bias in PET is mainly propagated from various forcing variables.

Overestimation (underestimation) of the actual ET will also result in the discharge underestimation (overestimation). Many processes can cause ET errors either by the biases in PET or the stress functions which limit the potential evaporation. The vegetation fraction, vegetation type, surface slope and soil properties are all the uncertain sources affecting the final ET estimation.

With the main biases listed as above, we consider bias in any processes that changes P or PET as bias from forcing and bias in any processes that directly changes ET as bias caused by model structure. Although the shifts in forcing variables will change the ET estimation – for example, the P restricts the available water for ET – this shift still belongs to the forcing category since the relation is indirect. The biases which directly affect ET include biases in infiltration, soil water movement, snow processes, vegetation representation and many other model processes. And all these are considered as biases caused by model structures.

We specify P as the sum of all the water inputs into the system, which include the atmospheric water flux (in its liquid and solid phases) and glacier melt. The precipitation for the three headwater catchments and the upper Tarim is listed in Table  for each simulation. The interannual variations and the intra-annual cycle of total precipitation over upper Tarim Basin are plotted for different forcing in Fig. .

The annual cycle of the two basic forcing datasets WFD-CRU and WFDEI-CRU are similar, while the precipitation in WFDEI-CRU is slightly larger in monthly values (Fig. a, red and blue lines). The deviation is the result of their expanding differences after 1990 (Fig. b). The precipitation difference is mainly due to the fact that two different versions of CRU (CRU TS 2.10 and CRU TS 3.1) are used for precipitation correction in WFD and WFDEI see Sect. 3.1.2 or. The precipitation difference between the two CRU datasets is relatively small, while the CMA dataset increases the precipitation to a large extent, by 37.3 %, compared to CRU for the upper Tarim Basin (Table ). The changes mostly occur during summer when the peak of CMA precipitation is more than twice as large as precipitation in CRU. The shape of the annual cycle changes greatly as the timing of the peak is shifted from April to July. However, the precipitation amount in winter (DJF) decreases in CMA, to which the decrease in snowfall is the major contributor. The changes in rainfall and snowfall are similar in all three headwater catchments (Table ) and the upper Tarim Basin.

Adding the glacier melt leads to negligible changes during winter and spring but large increases in the total water inputs in summer (JJA) when the temperature is higher. The estimated glacier melt is 9.1 %, 25.8 % and 6.1 % to the total water inputs for the upper Yarkand River, upper Hotan River and upper Aksu River. It significantly increases after 1990 (Fig. ; the trend is +3.8×108 m3 yr2, p=0.024), being consistent with its ratio to the total water input (r=0.918, p<0.001). The trend is mainly caused by climate warming as the glacier melt is highly correlated with the summer temperature (r=0.852, p<0.001). The increasing trend has also been documented in glacier runoff observations .

Evaluating the bias in precipitation over meteorological rain gauges is not convincing as most gauges are located at lower altitude, which makes it difficult to capture regional patterns as intensive precipitation occurs over higher mountains. Instead, the discharge measurement can serve as a better reference since it integrates the net water flux over the entire basin. Therefore, driven by the forcing, ORCHIDEE was used to simulate the river discharge and for comparison to in situ observations (Fig. ). The corresponding assessment using criteria for the three headwater catchments are plotted in Fig. . For the three headwater catchments where most of the discharge of the Tarim Basin is generated, the discharge is significantly underestimated, with the underestimation ratio reaching 90 % (Figs. b, d, f, a) for CRU datasets. Discharge increases after the precipitation is corrected by the CMA dataset, with the absolute bias decreasing to around 80 %. Adding glacier melt also increases the discharge but by a relatively small amount. Changes in the model structure (new snow and soil freezing scheme) further decrease the bias, especially for the Aksu River. The final biases of the discharge for the three subbasins are -71.1 %, -47.8 % and -49.4 %. The gradual improvements and corresponding magnitude changes are visible in the annual discharge variability in Fig. b, d and f.

Besides the increase in the annual mean discharge, the amplitude of the interannual cycle of the discharge is also improved by the progressive changes. The estimated discharge peaks have been shifted from April in CRU simulations to the summer (July or August) by CMA correction and adding glaciers (Fig. a, c, e). Correspondingly, the correlation of the annual variability between the estimated and observed discharge has increased above 0.9 for all the three subbasins with the WFDEI-CCG forcing (Fig. b). However, contrary to the upper Yarkand River and the upper Hotan River, the introduction of the new snow and soil freezing scheme decreases the discharge correlation for the upper Aksu River from 0.91 to 0.42. An early discharge peak exists in May, while not enough runoff is generated in the summer period (Fig. e). Although the correlation decreases, it does not mean the model/simulation deteriorates because correlation only evaluates the similarity of temporal variation but ignores the fact that the discharge amount has been better estimated (Figs. e and a).

By extracting the observed discharge in the first and last 5 years from the whole period, we can notice there is an obvious shift of the discharge peak from August to July in the three headwater catchments (Fig. a, c, e). The regional precipitation changes largely cause the shift, but the increasing temperature also allows the snow/glacier to melt at a higher rate in the most recent period. Furthermore, increasing trends are detected after the 1990s (Fig. b, d, f), as the increasing trend is 1.43×108 m3 yr2 (or 0.77×108 m3 yr2, 1.78×108 m3 yr2) for the upper Yarkand (or Hotan, Aksu) River. The increasing trends are consistent with the glacier melt, glacier proportion in water input and summer temperature in the same period (Fig. ).

The trends in the estimated discharge are also calculated and compared with the observed trends, expressed as the ratio of the trend in estimation to that in observations (Fig. c). For CRU simulations, no increasing trend is detected since the ratio is less than 0. The CMA correction increases the ratio for all three subbasins to around 0.3, which means the precipitation accounts for only around 30 % of the discharge increase. Adding the glacier melt increases the ratio from 0.35 to 0.54 for the upper Hotan River and from 0.31 to 0.76 for the upper Aksu River; the improvement of the glacier melting is comparable to the CMA correction. However, no apparent changes are detected for the upper Yarkand River. By comparing the criteria between WFDEI-CMA and WFDEI-CCG, we find that, although adding the glacier melt does not change much the absolute amount of discharge or the correlation, the increased trend in discharge has been considerably improved. The increasing glacier melt is, therefore, one of the contributors to the discharge trend in the Tarim. The modification of the snow and soil freezing scheme increases the trend ratio in the upper Aksu River up to 0.72, while slightly decreasing it for the two other catchments.

In brief, the gradual refinement of the forcing datasets (from WFD-CRU to WFDEI-CRU to WFDEI-CMA to WFDEI-CCG) is effective for improving the model performance using different criteria (bias, correlation, proportion to the trend) to compare the observed discharge. The three criteria are independent as they stand for the averages, the variation and the trend, which can capture the various aspects of the model agreement to the observations. The responses are similar for different catchments, but at different magnitude at different stages. The correction of the CMA dataset is the most significant improvement to all the criteria. The role of glaciers melting is critical for the trend analysis. The modification in the snow and soil freezing scheme increases the total discharge amount but could lead to adverse responses in the correlation and trend simulation. However, the impact of the modification of the model structure is not larger than changes resulting from the forcing biases. From the previous analysis, we can conclude that the simulations of WFDEI-CCG and WFDEI-CCG-SF are comparable in the correlation and trend analysis, while WFDEI-CCG-SF is better regarding the water quantity. Therefore, the further study on the bias is all based on the WFDEI-CCG-SF simulation.

The ORCHIDEE-estimated evapotranspiration rate (ET / P) against the estimated aridity index (PET / P) over each subbasin in each year is scattered as red points in Fig. . Point A represents the Budyko relation between long-term average annual ET / P and the long-term average annual PET / P. According to the categories introduced by , all three catchments belong to semiarid climate zones by the definition of the annual average precipitation (Table ). Hence the aridity index is supposed to range from 2 to 5. Regarding the high elevation and cold temperature, the PET rate is likely to be smaller than the representative climate of this aridity index. Thus the aridity index for the three catchments is supposed to be lower than expected. It is realistic for the upper Hotan River and the upper Aksu River as their aridity is 3.63 and 1.73, respectively. While the aridity index for the upper Yarkand River is 5.02, which can be categorized as a semiarid or arid region, this is not very likely since the upper Yarkand River is providing water resources for the irrigated area over the lower Yarkand oases .

However, because there is still a bias in the ORCHIDEE discharge estimations with the observations, the current state A is not correct. Based on the assumptions introduced in Sect. 3.5, the three possible “corrected” states by shifting the P, PET and ET are shown in Fig.  for the three headwater catchments. Taking the upper Yarkand River as an example (Fig. a), if we consider only P to be biased (assumption 1), the P has to be shifted from 247.3 to 435.4 mm yr-1. PET remains the same, and the ET changes accordingly, but the relation between ET / P and PET / P still follows the Budyko curve. The state is shifted from point A to point B with the P change ratio as 76.1 %. Reversely, the possible bias of P is -43.2 % ((247.3–435.4)/435.4×100 %). Similarly, to change the PET in order to shift the state to correct (point C, assumption 2), the PET has to be shifted from 1240.4 to 225.0 mm yr-1. The possible bias in PET is 451.2 %. To change the ET in order to shift the state to correct (point D, assumption 3), the ET has to be shifted from 188.3 to 106.9 mm yr-1, and the possible bias in ET is 76.1 %. The route is the same for the other two catchments, and their results are listed in Table .

The previous analysis is based on the assumptions that the P and PET are independent and only a single variable is uncertain, which might be invalid in reality. However, the three assumptions provide the bias boundaries of each variable, and the final system reproducing observed RO is likely to be located within the shaded area shown in Fig. . Taking the Hotan River as an example, to meet the discharge observation, the final changes in P will be 0 %–26.6 %, the decrease in PET will be 0 %–46.7 % and the decrease in ET will range 0 %–16.1 %. While in turn, we also conclude that the P is underestimated by 0 %–21.0 %, the PET is overestimated by 87.5 % at most and the ET is overestimated by 19.1 % at most. If we know the bias for any single variable, the feasible ranges will be narrower than at present.

Although the Budyko approach provides us with possible ranges for the bias of each variable, it is still difficult to determine the bias source without proper bias measurements for each of the forcing variables. We alternatively compare the regional diagnostics with nearby regions or regions with similar climatic and regional characteristics which have qualified observations in an indirect way. In doing so, we can generally rank the occurrence possibility of an uncertain variable.

From multiple-model analysis based on CMIP5 general circulation models (GCMs), the estimated PET over the western boundary of the Tarim Basin is about the same as over the Tibetan Plateau . However, because of the unpredictable biases in GCMs, the absolute values are not highly reliable in their simulation. Nevertheless, the equivalent relation provides us with the ranges of PET over the Tarim headwater catchments by referring to the observations over the Tibetan Plateau, where the topography changes are relatively small and the observations are more abundant. According to , who used site observations from 101 stations over the Tibetan Plateau, the annual average PET over the plateau ranges from 580 to 720 mm yr-1. Hence the PET over the upper Yarkand River and the upper Hotan River is probably overestimated (1240.4 and 1153.7 mm yr-1). Therefore, only changes in P or ET are not satisfactory because the PET is unchanged. For the upper Yarkand River, the PET is not the only error source, because, to match the discharge deviation by only decreasing PET, the PET should be decreased to 225 mm yr-1, which exceeds the referenced PET range. Moreover, because Yarkand and Hotan are neighboring regions which have similar climates, the PET should be a similar amount in each (615.2 mm yr-1 if only PET is uncertain in the upper Hotan River, while 225 mm yr-1 in the Yarkand River). The estimated PET over the Aksu River is realistic since the PET is 631.8 mm yr-1 for the current scenario, but it would decrease to 174.1 mm yr-1 if only the PET changed, which is too low. Besides the absolute value of PET, the ratio PET / P also shifts when PET changes, which means the climatic types can be changed. Only decreasing the PET in the upper Yarkand and the upper Aksu River would cause significant decreases in the aridity index (from 5.02 to 0.91 for the upper Yarkand, from 1.73 to 0.48 for the upper Aksu River), which are not realistic for these regions.

ET computation is sensitive to the climatic conditions and the surface conditions; hence the absolute value of ET significantly varies in time and space, and its bias very difficult to quantify. The evapotranspiration ratio to precipitation (ET / P) is typical for specific climatic types or regions with similar land cover types . estimated the evapotranspiration ratio to precipitation using a remote-sensing approach over regions of Canada. They concluded that the ratio ET / P is 32 % for barren land and 18 % for snow/ice land. In general, most of the catchment area of the three headwater catchments consists of barren and snow/ice land. Because of its lower latitude, the ET ratio could be higher but still below the rate for cropland (67 %). Therefore, only changes in P are not very likely for Yarkand and Hotan (ET / P is 0.68 for Yarkand and 0.70 for Hotan after the correction). Higher P for the upper Aksu River is likely to maintain a realistic ET / P ratio.

The biases of the three variables (P, ET, PET) have relatively weak dependence because they are governed by different processes. P and PET are quite independent because they relate to different forcing variables. Although the ET amount is linked to two other variables, the ET bias is weakly dependent, and it also comes more from the surface conditions and model biases. The chances of biases arising from each variable are about the same in theory. However, based on the analysis of the model output and the assumed bias-corrected scenarios, there are some priorities for the bias sources over each subbasin. The possibility of biases and the supporting arguments are listed in Table  for each headwater catchment. For instance, for the upper Yarkand subbasin, an increase in P, especially the glacier melt, is necessary because of the lower glacier melt ratio compared to the Hotan basin (Sect. 5.1.2.3) and the small trend in model discharge compared to the discharge observation (Sect. 4.2). However, only increasing the precipitation is not sufficient because the current PET is very likely too high compared to the surrounding regions (PET = 1240.4 mm yr-1, while PET ranges 580–720 mm yr-1 over the Tibetan Plateau). Meanwhile, only decreasing the PET without changing other variables would cause a very low PET rate (225 mm yr-1) and low aridity index (PET/P= 0.91), which is not realistic for this region. Modification in ET is possible but not adequate due to the overestimated PET. Hence, this error analysis reveals that increasing precipitation over the upper Yarkand subbasin is quite necessary, the overestimation of PET is very likely and modification in ET estimation is possible but not fundamentally necessary. For the upper Hotan River, the most likely biases come from the overestimation of PET, while the two other variables are possible sources. An increase in precipitation and changes in temporal variability are necessary for the upper Aksu subbasin, but they are not the only causes, as either the PET or ET, or both, is overestimated.