Evaluating the impact of climatic change on hydrologic variables is highly important for sustainability of water resources. Precipitation and temperature are the two basic parameters which need to be included in climate change impact studies. Thirty years (1985–2015) climatic data of Astore, a sub-catchment of the Upper Indus River Basin (UIRB), were analyzed for predicting the temperature and precipitation under different climate change scenarios. The station data were compared with the results of two global climate models (GCMs) each with two emission scenarios, including Representative Concentration Pathway (RCP) 2.6 and 8.5. The Mann–Kendall test and Sen's slope were applied to explore various properties of precipitation and temperature data series for a trend analysis. The commonalities and dissimilarities between the results of various GCMs and the trend of the station data were investigated using the functional data analysis. Two cross distances were estimated on the basis of Euclidean distances between the predicted time series; subsequently, the differences in their first derivatives were used to evaluate their mutual dissimilarities. The long-term predictions by GCMs show a decreasing trend in precipitation and a slight increase in temperature in some seasons. The result of GCMs under both the emission scenarios showed almost the same pattern of changes in the two hydrologic variables throughout the century with their values reporting slightly higher for the RCP8.5 scenario as compared to those for RCP2.6. Validation of the GCM results using GCM-CSIRO-Mk3.6 revealed an overall agreement between the different models. The dissimilarity analysis manifested the difference between the results of temperature predicted by various GCMs.

For sustainable water resources management, considering the impacts of climate and environmental changes on various hydrologic quantities has become extremely important. In this regard, the investigations should initiate with the analysis of future patterns of rainfall, temperature, and other hydrologic parameters which can significantly impact the streamflow (Daneshvar et al. 2019; Elgaali & Tarawneh 2019). However, simulating the future precipitation and temperature under the changing climatic conditions is a tedious job because of the complex nature of global climate models (GCMs) (Adefisan 2018; Alotaibi et al. 2018; Giorgi et al. 2019; Schädler et al. 2019). Several past publications have highlighted the complications in investigating the climate change impacts on various hydrologic parameters (Hassan & Ghumman 2015; Alotaibi et al. 2018; Tarawneh & Chowdhury 2018; Emami & Koch 2019; Näschen et al. 2019; Zaz et al. 2019). Likewise, the trends analysis of the meteorological variables has also be carried out (Dogar & Sato 2018). The impacts of climatic change depend on the geographical location of the region being investigated. In a case study conducted at meteorological stations near the US borders, long-term precipitation and temperature trend analysis showed fewer significant trends (Chattopadhyay & Edwards 2016). While the studies on the Greater Himalaya showed a warming trend (Chand et al. 2019; Dahal et al. 2019; Zaz et al. 2019), the trends of precipitation and temperature in the Upper Indus River Basin (UIRB) have also been analyzed in the past (Rauf et al. 2016a, 2016b; Garee et al. 2017; Arfan et al. 2019; Bilal et al. 2019; Dimri et al. 2019); however, all these studies demanded further research in this field of specialization.

GCMs are used widely for investigating the impact of global climate changes (Dogar et al. 2017). These are factually the mathematical representations of interactions between the atmosphere, oceans, and continents in various dimensions. GCMs are usually based on the future emission scenarios developed by the Intergovernmental Panel on Climate Change (IPCC) to forecast the future climate patterns (IPCC 2013; IPCC 2014; Alotaibi et al. 2018). Although GCMs can perform highly complex analysis for various physical processes related to the climatic systems (IPCC 2001; Krysanova et al. 2017), predicting the impact of climate change on hydrological parameters using GCMs is a daunting task. In addition, as the GCMs forecast in a broader dimension, the results of GCMs need to be downscaled for a specific basin which requires additional efforts.

Another important aspect of using the GCMs is the selection of greenhouse gas (GHG) emission scenarios. An emission scenario actually envisages a future world based on the outcomes of processes governed by socio-economic development, technological advances, and demography (IPCC 2001; IPCC 2013; IPCC 2014; Ritchie & Dowlatabadi 2018). The emission scenarios were developed by the IPCC on the basis of the increasing intensity of carbon and sulfur emissions (IPCC 2001; IPCC 2013; IPCC 2014; Ritchie & Dowlatabadi 2018). Various uncertainties were observed in climate simulations which should always be addressed while analyzing sustainable water resources, including imperfect boundary conditions, parameterizations of small-scale processes, and simplifying the structure of the models (Asadieh & Krakauer 2015; Hosseinzadehtalaei et al. 2017; Vetter et al. 2017; Beigi et al. 2019; Holtanová et al. 2019; Zhuan et al. 2019). The findings provide a rationale, based on more reliable projections, for effective decision-making regarding climate change control measures.

Various techniques have been developed to investigate the uncertainties, commonalities, and dissimilarities in predicted results from various models. Holtanová et al. (2019) used the functional data analysis (FDA) for distinguishing the time series data related to climatology. Burdejová and Härdle (2019) suggested a dynamic functional factor for the FDA of climatologic data, including precipitation and temperature. Zambom et al. (2019) applied the FDA to study the yeast gene and fat spectrum in Canada. Sottile & Adelfio (2019) used the FDA for investigating various socio-environmental factors, such as lung function response, behaviors of earthquakes, and environmental pollution. Further details of the FDA can be seen from Rice & Shang (2017), Shang (2017) and Chamroukhi & Nguyen (2019). It is noticed that the application of the FDA for the time series of precipitation and temperature is relatively rare and needs further investigations.

This research aims to answer the research question that what are the commonalities and dissimilarities in the observed data time series and the results of various GCMs. The specific objectives are to (i) perform the trend analysis of temperature and precipitation for a catchment of the UIRB using Sen's slope and the Mann–Kendall test, (ii) forecast temperature and rainfall for the time span from 2015 to 2100 by GCMs under the two extreme emission scenarios RCP2.6 and RCP8.5, and (iii) investigate the commonalities and dissimilarities between the results of various GCMs using the FDA. To achieve these objectives, a step-by-step framework is developed and implemented on a case of the Indus River Basin in Pakistan.

A step-wise methodology used in this research is presented in Figure 1. A variety of methods regarding the data analysis have been applied. Firstly, the Mann–Kendall and Sen's slope tests are used to find the magnitude of the trends. Secondly, two GCMs, each with two emission scenarios, are used to predict the climate change impacts on temperature and precipitation. Finally, the FDA is exercised to quantify the dissimilarities between the data time series of precipitation and temperature generated by various models.

Figure 1

Methodology framework.

Figure 1

Methodology framework.

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Study area and data collection

The Indus River Basin emerges from the north-western borders of Pakistan, and its east extends up to the Punjab Province. In the south direction, it extends to the boundary of the Sindh Province. The Indus River Basin is spread over an area of 970,000 km2 and is one of the world's largest basin. This study area is located in the part of the UIRB above the Tarbela Reservoir with 175,000 km2 of area (Rauf & Ghumman 2018). UIRB lies in the Himalayas, Karakoram, and Hindukush and also known as the home to three mightiest mountain ranges in the world. These mountains meet each other at 40 km from the city of Gilgit.

Precipitation and glacier melt over these mountains are the sources of flows in the River Indus and its branches. Major tributaries of UIRB are Astore, Drosh, Gupiz, Gilgit, and Skardu rivers; out of these, the Astore basin having the drainage area of about 3,995 km2 has been studied in the present research. The groundwater resources of Lower Indus Plains up to the Arabian Sea directly rely on the River Indus system. Excluding the Polar regions, UIRB glaciers are the largest glaciers in the world.

Since 1958, the Pakistan Water and Power Development Authority (WAPDA) has taken various steps for the study of the Upper Indus Basin Cryosphere. The department has also established hydro-meteorological networks in the 1960s for its monitoring through its Surface Water Hydrology Project (see Figure 2(a)).

Figure 2

Study area: (a) climatic and river gauging stations in the Upper Indus Basin and (b) recorded data collected from WAPDA and PMD for precipitation and temperature.

Figure 2

Study area: (a) climatic and river gauging stations in the Upper Indus Basin and (b) recorded data collected from WAPDA and PMD for precipitation and temperature.

Close modal

For the present research, the mean monthly and annual records of temperatures and precipitation, for the period 1985–2015, were collected from the Pakistan Meteorological Department (PMD) and WAPDA, Peshawar. Both the data sets are presented in Figure 2(b). The data sets represent the average areal values for the basin. The climate in the UIRB is not affected in the same manner as that of the Himalaya region, because the precipitation of spring and winter depends on the climate of the West. Although the unexpected monsoon results in occasional rains, the monsoons are not the only source of precipitation in the UIRB during summer (Bilal et al. 2019; Dimri et al. 2019). It is evident from the alteration in vegetation and the change in the closure period of the Karakorum Highway that the winter precipitation has been decreased in the UIRB over the last 30–40 years (Bilal et al. 2019; Dimri et al. 2019).

Climatic change modeling

As described in the Introduction, two main aspects, including downscaling and emission scenarios, should be carefully evaluated for climatic change modeling. There is a long history of the development of emission scenarios and downscaling of GCM results. The details of various emission scenarios may be seen from the IPCC-Assessment Report 5 (AR5) and the following references (Ritchie & Dowlatabadi 2018; Wang et al. 2019). Six emission scenarios were approved by the IPCC in the early 1990s, called IPCC Scenarios 92 (IS92). The recent research developments, changes in the driving forces for emission scenarios, and the advancements in modeling techniques needed an upgradation of the emission scenarios and the downscaling methods. Consequently, an advanced (so-called) set of four emission scenarios was developed by the IPCC. These scenarios are well documented in the Special Report on Emissions Scenarios (SRES) and in several published papers (IPCC 2001; IPCC 2013; IPCC 2014).

The new developments were approved on the basis of socioeconomic storylines. With the passage of time, a further new set of emission scenarios was published on the basis of the radiative forcing phenomenon. These scenarios were named as representative concentration pathways (RCPs). These RCPs include RCP2.6 representing a very low level of radiative forcing, RCP4.5 based on the medium level of stabilization, RCP6.0 representing also the medium level of stabilization, and RCP8.5 meant for a situation of very high emission. The in-depth survey of available literature and comparing the predictions by the application of different scenarios indicate that the SRES A1FI is similar to RCP8.5, the predictions under SRES A2 lie in between the predictions under RCP8.5 and RCP6.0. The scenario SRES A1B simulates the changes in climatic parameters nearly the same as predictions of RCP6.0. The emission scenario SRES B1 produces results similar to the results of RCP4.5.

In this paper, the forecasts of temperature and rainfall for the time span from 2015 to 2100 were made by two GCMs based on emission scenarios, including RCP2.6 and RCP8.5.

Rainfall and temperature trend analysis

Mann–Kendall test

The Mann–Kendall Statistic S is given as (Mann 1945; Kendall 1975)
formula
(1)
where xi represents the time series; i is the rank of time series from 1, 2, … … …, n − 1, and xj is the data points ranked from j = i + 1, i+ 2, … … …., n. Each of the data points xi is taken as a reference point which is compared to the rest of the data points xj so that
formula
(2)
The variance is given as
formula
(3)
where ti is the number of ties up to sample i. The test statistics Zc is computed as follows:
formula
(4)
Zc here follows a standard normal distribution. A positive value of Z shows an increasing and a negative value of Z shows a decreasing trend. A positive or negative monotonic trend is tested using a critical value or significance level α. If the value of Zc obtained is larger than Zα/2, it shows that the trend is significant. This trend is compared in terms of Z-statistics for the 5% significance level (i.e. the result is 99.5% free from any error). The value of Z-statistics comes out to be ±1.96. If the value of Z-statistics is above or below ±1.96 it implies a positive or negative trend, respectively. The value of Z-statistics in the range of ±1.96 represents no trend.

Sen's slope estimator test

Sen's estimator is used to estimate the magnitude of the trend (Sen 1968). The slope (SSi) of all data pairs is then determined using the following equation:
formula
(5)
where xj and xk are taken as data values at time j and k (j>k) equally. The median of these n values of SSi is represented as a Sen's estimator (SEi) of the slope, given as follows:
formula
(6)

Sen's estimator is computed as SEmed = SS(n+1)/2 if the value of n is determined to be odd. It is taken as SEmed = [SSn/2+ SS(n+2)/2]/2 if n is determined to be even. Finally, SEmed is determined by a two-sided test at a confidence interval of 100 (1 − α)% and then a real slope can be determined by Sen's slope test. Increasing or an upward trend is shown by the positive value of SEi and a downward or decreasing trend in the time series is obtained by a negative value of SEi.

The limitations of using Sen's slope estimator test should also be kept in mind. This method does not perform well for extreme events. Furthermore, the removal of serial dependence is one of the main hurdles in applying this method. This test strongly depends on the assumptions like serial relationship and non-normality of data. The application of Sen's slope estimator to detect trends can affect significantly the results if the data are not processed properly to fulfill the assumptions of the test (Ali & Abubaker 2019; Rathnayake 2019; Totaro et al. 2019).

GCM modeling

In this study, results of two GCMs, i.e. BCC-CSM1-1 and GFDL-CM3, each with RCP2.6 scenarios, have been applied to study changes in precipitation and temperature over the Astore basin. BCC-CSM1-1 is developed by the Beijing Climate Center (BCC), China Meteorological Administration, China, and GFDL-CM3 is developed by the NOAA Geophysical Fluid Dynamics Laboratory (NOAA GFDL) (Griffies et al. 2011). The BCC-CSM has been used effectively in climate impact studies, and the model limitations are also evaluated over some regions of Southeast Asia (Gong et al. 2017, 2018). According to Ahmed et al. (2019), the performance of BCC-CSM1-1 is plausible for simulating precipitation in Pakistan. They have ranked the performance of 20 GCMs on the basis of seven different indices for simulating the precipitation of Pakistan using base period data of 1961–2005. They have concluded that the performance of 20 GCMs is nearly similar to one another for a given season. Rehman et al. (2018) have also reported that the BCC-CSM model results for precipitation and temperature are acceptable. Many other publications have used successfully the results of BCC-CSM1-1 and GFDL-CM3 for precipitation and temperature (Motiee et al. 2019; Singh et al. 2019; Wei et al. 2019; Xin et al. 2019; Yu et al. 2019). On the basis of this literature, the BCC-CSM1-1 and GFDL-CM3 were selected for the present paper.

RCP stands for Representative Concentration Pathways. The extended RCP2.6 pathway assumes sustained net negative anthropogenic GHG emissions after the year 2070 (Collins et al. 2013). ‘Negative emissions’ means that in total, humans absorb more GHGs from the atmosphere than they release. In the extended RCP2.6 pathway, atmospheric CO2 concentrations reach around 360 ppmv (in parts-per-million-by-volume) by 2300. While in the extended RCP8.5 pathway, CO2 concentrations reach around 2000 ppmv in 2250 which is nearly seven times the pre-industrial level (Collins et al. 2013). For the extended RCP2.6 scenario, global warming of 0.0–1.2 °C is projected for the late-23rd century (2281–2300 average), relative to 1986–2005 (Collins et al. 2013). For the extended RCP8.5, global warming of 3.0–12.6 °C is projected over the same time period (Collins et al. 2013).

Model performance evaluation

There are several indices for the performance evaluation of GCMs based on the comparison of predicted and measured data. It is worth noting that the gridded data of GCMs and the station recorded data differ very much in their approach. The area under study (Astore) is a sub-catchment of the UIRB. The gridded data of GCMs were further downscaled so that to obtain the grid locations (under study) very close to the location of meteorological gauging station installed by the WAPDA, Peshawar. Some researchers linearly interpolate further the results of GCMs to bring the predicted values to the locations close to their observation stations (Rehman et al. 2018). Fortunately, the grid location of GCM after downscaling in this study was very close to the measuring station. The climate station data were collected from a station installed at 35.330N to 74.900E (with an elevation of 2,394 m.a.s.l), and the GCM simulated the data very close to these coordinates.

The performance of GCMs was evaluated on the basis of comparison between the observed and the predicted data. Nevertheless, the comparison of GCM results with the recorded station data (the stationary climatic conditions with no emission scenario) always helps to comprehend the expected future changes and the performance of GCM results. It is important to note that around 30 years (1985–2015) of recorded data, i.e. the era of the industrial revolution, may implicitly capture the impacts of climatic change. Thus, it would be highly useful for decision-makers to see the results of GCMs in comparison to the base period data under the prevailing past conditions. A similar approach has been adopted in the past studies (Alotaibi et al. 2018; Ahmed et al. 2019).

The parameters adopted in this study to measure the performance of the models are given in the following (Rauf et al. 2016a, 2016b). The Nash–Sutcliffe model efficiency (NSE) is given as follows:
formula
(7)
where y is the variable representing precipitation or temperature, o represents the observed value, p denotes the predicted value, and n is the total number of data points in the time series. According to Rauf & Ghumman (2018), the values of NSE from 0.75 to 1 can be considered as ‘very good’, 0.65 to 0.75 as ‘good’, and 0.5 to 0.65 as ‘satisfactory’, and the values between 0.4 and 0.5 can be considered the ‘acceptable’ performance of the model. The second parameter, the mean bias error (MBE), was estimated using the following equation:
formula
(8)

The positive values of MBE represent overestimated, whereas its negative values are for underestimated predictions (Rauf & Ghumman 2018).

Functional data analysis

The dissimilarities between various precipitation and temperature data time series recorded or predicted by various GCMs have been analyzed for different time spans (1985–2014, 2015–2035, 2046–2075, and 2076–2100). The predicted data series was converted to a functional form by xi(t) and its first derivative xi’(t) in the form (Holtanová et al. 2019):
formula
(9)
formula
(10)
where the Bj(t) are polynomials of a certain order (order four in the present analysis) with some (20 in this case) equally spaced knots and cij were taken as some real coefficients in Bj(t).
For the conversion of simulation to the functional form, the XLSTAT 2019 was used with an FDA-package. The cross-distance separation between two-time series was estimated to show the magnitude of dissimilarities (comparatively the higher the cross distance, the higher the dissimilarities between the two-time series). For two-time series f1 and f2, the cross-distance between the two is a nonnegative number d0 (Euclidean-Distance), as given below:
formula
(11)
where t1 is the starting time of series f and tk is the end of time span for which analysis is required. Similarly, d1-distance between the first derivatives of the series (curves) f1 and f2 is given as follows:
formula
(12)

The distances d1 are usually not influenced by the bias, whereas the common bias of predicted time series by the model is considered to have impacts on the similarity assessed by distances d0. Comparatively, smaller values of distances d1 between two predicted series show a similar shape of the temporal changes in the series.

The following eight comparisons have been made using the FDA.

  • C1: BCC-CSM1-1RCP2.6 and station data

  • C2: BCC-CSM1-1RCP8.5 and station data

  • C3: GFDL-CM3-RCP2.6 and station data

  • C4: GFDL-CM3-RCP8.5 and station data

  • C5: BCC-CSM1-1RCP2.6 and BCC-CSM1-1RCP8.5

  • C6: GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5

  • C7: BCC-CSM1-1RCP2.6 and GFDL-CM3-RCP2.6

  • C8: BCC-CSM1-1RCP8.5 and GFDL-CM3-RCP8.5

Rainfall and temperature trend analysis

The results given in Table 1 show few significantly increasing precipitation events in the months of February, March, June, and September for station data. The significant positive trends were found in temperature during spring, summer, and autumn seasons, while a decreasing trend in temperature was observed in the month of November by the analysis of the station data. It is evident from the results of Sen's slope estimator that there is a relation between the magnitude of Sen's slope and the Z-statistics values. The results of trend analysis under climate change conditions given in Table 2 show that the Z values are different for May, June, and November for BCC-CSM1-1-RCP2.6 and BCC-CSM1-1-RCP8.5. However, the trends in the precipitation under climate change scenarios remain the same as that of the station data.

Table 1

Mean monthly precipitation and temperature results for the trend analysis

Month/variableJanFebMarAprMayJunJulAugSepOctNovDec
Precipitation station data 0.463 0.745 −1.46 −1.14 −0.5 0.16 −0.54 −0.96 2.48* −1.29 0.11 −1 
SS 0.288 0.562 −1.12 −0.81 −.59 0.086 −0.2 −0.27 0.542 −0.34 −0.428 
Temperature station data 0.463 0.745 −1.46 −1.14 −0.5 0.16 −0.54 −0.96 2.48* −1.29 0.11 −1 
SS 0.288 0.562 −1.12 −0.81 −.59 0.086 −0.2 −0.27 0.542 −0.34 −0.428 
Month/variableJanFebMarAprMayJunJulAugSepOctNovDec
Precipitation station data 0.463 0.745 −1.46 −1.14 −0.5 0.16 −0.54 −0.96 2.48* −1.29 0.11 −1 
SS 0.288 0.562 −1.12 −0.81 −.59 0.086 −0.2 −0.27 0.542 −0.34 −0.428 
Temperature station data 0.463 0.745 −1.46 −1.14 −0.5 0.16 −0.54 −0.96 2.48* −1.29 0.11 −1 
SS 0.288 0.562 −1.12 −0.81 −.59 0.086 −0.2 −0.27 0.542 −0.34 −0.428 
Table 2

Mean monthly precipitation and temperature results for Z-statistics

Month/variableJanFebMarAprMayJunJulAugSepOctNovDec
Precipitation BCC-CSM1 − 1-RCP2.6 0.54 0.73 −1.62 −0.95 −0.12 1.53 0.23 −1.05 1.89 −1.45 1.87 −1.20 
Precipitation BCC-CSM1 − 1-RCP8.5 0.54 0.73 −1.62 −0.95 −0.12 1.53 0.23 −1.12 1.89 −1.66 0.66 −1.13 
Precipitation GFDL-CM3 − RCP2.6 0.54 0.73 −1.62 −0.87 −0.12 1.53 0.23 −1.12 1.89 −1.37 0.63 −1.16 
Precipitation GFDL-CM3-RCP8.5 0.54 0.73 −1.62 −0.87 −0.12 1.53 0.23 −1.12 1.89 −1.55 0.63 −1.09 
Temperature BCC-CSM1 − 1-RCP2.6 −1.52 −4.59* 1.34 1.98* −0.29 −1.38 −1.84 −2.43* −3.61* −2.1* −0.02 1.34 
Temperature BCC-CSM1 − 1-RCP8.5 0.20 −4.59 2.16* 1.98* −0.29 −1.38 −1.87 −2.43* −3.61* −2.1* 2.63* 2.91* 
Temperature GFDL-CM3-RCP8.5 0.05 −4.59* 1.63 2.23* 1.07 1.05 1.45 1.00 −1.39 −0.80 2.63* 2.91* 
Month/variableJanFebMarAprMayJunJulAugSepOctNovDec
Precipitation BCC-CSM1 − 1-RCP2.6 0.54 0.73 −1.62 −0.95 −0.12 1.53 0.23 −1.05 1.89 −1.45 1.87 −1.20 
Precipitation BCC-CSM1 − 1-RCP8.5 0.54 0.73 −1.62 −0.95 −0.12 1.53 0.23 −1.12 1.89 −1.66 0.66 −1.13 
Precipitation GFDL-CM3 − RCP2.6 0.54 0.73 −1.62 −0.87 −0.12 1.53 0.23 −1.12 1.89 −1.37 0.63 −1.16 
Precipitation GFDL-CM3-RCP8.5 0.54 0.73 −1.62 −0.87 −0.12 1.53 0.23 −1.12 1.89 −1.55 0.63 −1.09 
Temperature BCC-CSM1 − 1-RCP2.6 −1.52 −4.59* 1.34 1.98* −0.29 −1.38 −1.84 −2.43* −3.61* −2.1* −0.02 1.34 
Temperature BCC-CSM1 − 1-RCP8.5 0.20 −4.59 2.16* 1.98* −0.29 −1.38 −1.87 −2.43* −3.61* −2.1* 2.63* 2.91* 
Temperature GFDL-CM3-RCP8.5 0.05 −4.59* 1.63 2.23* 1.07 1.05 1.45 1.00 −1.39 −0.80 2.63* 2.91* 

Nearly similar trends in precipitation are found under GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 predictions. BCC-CSM1-1-RCP2.6 results show decreasing trends in temperature for some months and increasing trends in the months of February, August, September, and October. The results of the GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 differ from those of the BCC-CSM1-1-RCP2.6 and BCC-CSM1-1-RCP8.5 for the months of March, May, July, August, September, and October. These variations in the results clearly suggest to explore the dissimilarities in various GCMs. No relationship was found between the precipitation and temperature trends using the Mann–Kendall test because the changes in the phenomenon causing the precipitation are usually asymmetrical which make its occurrence highly uncertain. The trends of precipitation and temperature are shown in Figure 2(b). It can be seen in the plots that the precipitation has a small increasing trend until 1999 and then it started decreasing slowly. A similar trend can be seen for temperature variations.

FDA and GCM modeling

The performance indices (NSE and MBE) presented in Figure 3(a) show some uncertainties and dissimilarities in the results of various GCM models. The MBE is found to be in the range of −0.3 to −8.6 and NSE ranges from 0.62 to 0.81 in case of precipitation. For temperature, the MBE ranges between 3 and 6.5 and NSE between 0.62 and 0.73. As per these findings, the precipitation was underestimated, whereas the temperature was overestimated. There is a difference of up to 96% in the MBE for various GCMs. The time series data collected from the climate station differ with the data obtained from GCMs’ simulations. The primary reason for such difference is the inaccuracy in downscaling and the uncertainties of GCM results. As stated in the Model performance evaluation section, the data were measured from a meteorological gauging station installed at 35.33°N to 74.90°E and at an elevation of 2,394 m.a.s.l, while the GCM simulated the data close to these coordinates but not exactly at the same location. A further refinement in downscaling is required for better accuracy. These findings are in agreement with the past studies (Holtanová et al. 2019; Zhuan et al. 2019).

Figure 3

Comparison between different models: (a) error graph for results predicted by various GCMs for precipitation and temperature, (b) comparison of time series predicted by various GCMs for precipitation, and (c) comparison of time series predicted by various GCMs for precipitation temperature.

Figure 3

Comparison between different models: (a) error graph for results predicted by various GCMs for precipitation and temperature, (b) comparison of time series predicted by various GCMs for precipitation, and (c) comparison of time series predicted by various GCMs for precipitation temperature.

Close modal

The results of the two GCMs, i.e. BCC-CSM1-1 and GFDL-CM3 (each with RCP2.6 and RCP8.5 emission scenario) for the Astore sub-basin of UIB were further compared with another well-tested GCM-CSIRO-Mk3.6 (Rehman et al. 2018; Ahmed et al. 2019), to check their commonalities and dissimilarities. The comparison is presented in Figures 3(b) and 3(c) revealed that most of the time series lines lie nearly at 45° angle showing good performance of GCMs. Although a small deviation of data from 45° trend can be noted in the case of precipitation predicted from different GCMs, the models can be used confidently for further analysis.

The dissimilarities analyzed using the FDA, regarding temperature and precipitation simulated by various GCMs for a period from 1985 to 2015 (30 years), are described in this section. The graphs presented in Figures 4(a)–4(h) show that the station data slightly differ with the GCM results, particularly for the time series data of temperature. The GCMs and station precipitation data have similar decreasing trends from 1985 to 2015, while both have increasing trends in case of temperature during the said period. The lines of the two cross distances (d0 and d1) for temperature were found to be diverging from each other with respect to time. It indicates that some dissimilarities do exist among the two-time series data for temperature. Conversely, the values of the cross distances (d0 and d1) determined with the help of the FDA (Table 3 and Figures 4(a)–4(h)) show that the predicted precipitation by the two models is similar under both the climatic scenarios.

Table 3

Cross distances (d0 and d1) determined with the help of the FDA

VariablesCross distanceScenarios
C1C2C3C4C5C6C7C8
Precipitation d0 64.94 66.69 63.49 63.19 28.11 27.12 47.95 48.74 
d1 1.46 1.56 1.09 1.21 0.59 0.54 1.02 1/04 
Temperature d0 56.84 54.23 60.39 58.12 18.32 17.44 22.83 23.32 
d1 1.83 1.85 1.72 1.78 0.39 0.36 0.68 0.69 
VariablesCross distanceScenarios
C1C2C3C4C5C6C7C8
Precipitation d0 64.94 66.69 63.49 63.19 28.11 27.12 47.95 48.74 
d1 1.46 1.56 1.09 1.21 0.59 0.54 1.02 1/04 
Temperature d0 56.84 54.23 60.39 58.12 18.32 17.44 22.83 23.32 
d1 1.83 1.85 1.72 1.78 0.39 0.36 0.68 0.69 
Figure 4

Results of the FDA showing the comparisons of results of (a) BCC-CSM-1-1-RCP2.6 and station data for precipitation, (b) BCC-CSM-1-1-RCP2.6 and station data for temperature, (c) BCC-CSM-1-1-RCP8.5 and station data for precipitation, (d) BCC-CSM-1-1-RCP8.5 and station data for temperature, (e) GFDL-CM3-RCP2.6 and station data for precipitation, (f) GFDL-CM3-RCP2.6 and station data for temperature, (g) GFDL-CM3-RCP8.5 and station data for precipitation, and (h) GFDL-CM3-RCP8.5 and station data for temperature.

Figure 4

Results of the FDA showing the comparisons of results of (a) BCC-CSM-1-1-RCP2.6 and station data for precipitation, (b) BCC-CSM-1-1-RCP2.6 and station data for temperature, (c) BCC-CSM-1-1-RCP8.5 and station data for precipitation, (d) BCC-CSM-1-1-RCP8.5 and station data for temperature, (e) GFDL-CM3-RCP2.6 and station data for precipitation, (f) GFDL-CM3-RCP2.6 and station data for temperature, (g) GFDL-CM3-RCP8.5 and station data for precipitation, and (h) GFDL-CM3-RCP8.5 and station data for temperature.

Close modal

The short-term predicted results from the two GCMs (i.e. BCC-CSM1-1 and GFDL-CM3) each with RCP 2.6 and RCP 8.5 scenario are also compared to check their commonalities and dissimilarities. The graphs presented in Figures 5(a)–5(h) show that the BCC-CSM1-1 vs GFDL-CM3 under the similar emission scenarios have similar patterns for both the precipitation and temperature time series. Also, the BCC-CSM1-1-RCP2.6 vs BCC-CSM1-1-RCP8.5 and GFDL-CM3-RCP2.6 vs GFDL-CM3-RCP8.5, i.e the same models under the two different emission scenarios, have showed identical patterns for precipitation as well as for temperature. The lines of cross distances (d0 and d1) in case of precipitation are not diverging significantly, but a slight diverging tendency exists in the case of temperature showing some minor differences in prediction from the two GCMs. It is worth noting that the identification of dissimilarities with the help of divergence of d0 and d1 lines only may help in noticing even small differences in the behavior of models, otherwise an overall pattern of the results does not show any dissimilarities. Such findings validate the importance of performing the FDA.

Figure 5

Results of the FDA for 1985–2015 period – Comparison between the results of (a) BCC-CSM-1-1-RCP2.6 and BCC-CSM-1-1-RCP8.5 for precipitation, (b) BCC-CSM-1-1-RCP2.6 and BCC-CSM-1-1-RCP8.5 for temperature, (c) GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 for precipitation, (d) GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 for temperature, (e) BCC-CSM-1-1-RCP2.6 and GFDL-CM3-RCP2.6 for precipitation, (f) BCC-CSM-1-1-RCP2.6 and GFDL-CM3-RCP2.6 for temperature (g) BCC-CSM-1-1-RCP8.5 and GFDL-CM3-RCP8.5 for precipitation, and (h) BCC-CSM-1-1-RCP8.5 and GFDL-CM3-RCP8.5 for temperature.

Figure 5

Results of the FDA for 1985–2015 period – Comparison between the results of (a) BCC-CSM-1-1-RCP2.6 and BCC-CSM-1-1-RCP8.5 for precipitation, (b) BCC-CSM-1-1-RCP2.6 and BCC-CSM-1-1-RCP8.5 for temperature, (c) GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 for precipitation, (d) GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 for temperature, (e) BCC-CSM-1-1-RCP2.6 and GFDL-CM3-RCP2.6 for precipitation, (f) BCC-CSM-1-1-RCP2.6 and GFDL-CM3-RCP2.6 for temperature (g) BCC-CSM-1-1-RCP8.5 and GFDL-CM3-RCP8.5 for precipitation, and (h) BCC-CSM-1-1-RCP8.5 and GFDL-CM3-RCP8.5 for temperature.

Close modal

The long-term predictions from various GCMs are illustrated in Figures 6(a)–6(h). The lines of cross distances (d0 and d1) in both the cases of precipitation and temperature are found to be diverging which indicate that under the influence of global warming, different GCMs predict dissimilar trends for precipitation and temperature. These results are in agreement with the findings reported in previous studies (Krysanova et al. 2017; Tarawneh & Chowdhury 2018). Moreover, the trend lines depicting the long-term predictions in Figure 6 indicate that the precipitation has an overall decreasing trend, whereas the temperature will be slightly increased.

Figure 6

Results of the FDA for 2015–2100 period showing a comparison between the results of (a) BCC-CSM-1-1-RCP2.6 and BCC-CSM-1-1-RCP8.5 for precipitation, (b) BCC-CSM-1-1-RCP2.6 and BCC-CSM-1-1-RCP8.5 for temperature, (c) GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 for precipitation, (d) GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 for temperature, (e) BCC-CSM-1-1-RCP2.6 and GFDL-CM3-RCP2.6 for precipitation, (f) BCC-CSM-1-1-RCP2.6 and GFDL-CM3-RCP2.6 for temperature, (g) BCC-CSM-1-1-RCP8.5 and GFDL-CM3-RCP8.5 for precipitation, and (h) BCC-CSM-1-1-RCP8.5 and GFDL-CM3-RCP8.5 for temperature

Figure 6

Results of the FDA for 2015–2100 period showing a comparison between the results of (a) BCC-CSM-1-1-RCP2.6 and BCC-CSM-1-1-RCP8.5 for precipitation, (b) BCC-CSM-1-1-RCP2.6 and BCC-CSM-1-1-RCP8.5 for temperature, (c) GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 for precipitation, (d) GFDL-CM3-RCP2.6 and GFDL-CM3-RCP8.5 for temperature, (e) BCC-CSM-1-1-RCP2.6 and GFDL-CM3-RCP2.6 for precipitation, (f) BCC-CSM-1-1-RCP2.6 and GFDL-CM3-RCP2.6 for temperature, (g) BCC-CSM-1-1-RCP8.5 and GFDL-CM3-RCP8.5 for precipitation, and (h) BCC-CSM-1-1-RCP8.5 and GFDL-CM3-RCP8.5 for temperature

Close modal

Interested readers would like to study the spatial variations of precipitation and temperature for water resources development and management. Absence of such results may be considered as a limitation of the present study. The selected region is only a small part of the UIRB in Pakistan. The resolutions of various GCMs were not sufficient to illustrate the spatial variations; therefore, an average spatial precipitation and temperature is simulated for a small region like Astore. However, Rehman et al. (2018) reported negligible spatial variations in temperature and precipitation over the Northern Province of Pakistan. According to Khan & Koch (2018), there is an almost uniform spread of climatic changes in temperature and precipitation across the whole UIRB for nearly all the emission scenarios.

The trend analysis of precipitation and temperature time series was performed using Mann–Kandal and Sen's slope tests. The FDA was used for the quantification of dissimilarities between the results of precipitation and temperature predicted by various GCMs under different emission scenarios. The methods were applied to a sub-catchment of the well-known river basin UIRB in Pakistan. The idea of Euclidean Distances between the predicted time series and the differences in their first derivatives were introduced to estimate the cross distances between various simulated precipitation and temperature values.

The recorded data revealed a significant increase in precipitation during the months of February, March, June, and September. There are significant positive trends in temperature during spring, summer, and autumn seasons and a decreasing temperature in the months of September and November. For different emission scenarios simulated with the same GCM, 64% difference in Z values were obtained during the month of November. Also, the two different GCMs produced different values of Z for both the variables (precipitation and temperature) even under the same emission scenarios.

The analysis on the basis of errors in predicted and measured precipitation and temperature discovered a highly useful finding that the precipitation is underestimated, whereas the temperature is overestimated by GCMs. It is concluded that a difference of up to 96% in the MBE may occur in precipitation time series predicted by various GCMs.

For the short-term predictions of temperature and precipitation under climate change conditions, neither the conventional trend analysis nor the visual inspection of plots show the exact features of these data series predicted by various models. While diverging lines of cross distances (d0 and d1) especially in case of temperature show that the main structure of the results predicted by various GCMs is different. These findings endorse that only the identification of dissimilarities by the FDA helps in noticing the differences (even very small) in the behavior of models, otherwise the overall pattern of the results does not show any dissimilarities. In cases of long-term climate change predictions, various GCMs predicted different changes both in temperature and precipitation. However, it can be concluded that the overall pattern of changes in the precipitation and temperature is similar.

For future water resources planning and development, it is helpful to note that the long-term predictions of GCM have shown the overall decreasing tendency of precipitation in UIRB, whereas there is an increasing trend in temperature. The present research investigated precipitation and temperature under climatic changes. The major variable in water resources studies is the runoff from a catchment. So, it is recommended that the impact of climatic changes on stream flow of the Upper Indus River may be investigated using various GCMs and FDA in future.

Authors acknowledge all the agencies for data sharing.

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