The Relationship between Precipitation and Elevation of the Watershed in the Khirthar National Range

Precipitation plays a pivotal role in the evolution of the ecosystems. Many watersheds in Pakistan and particularly in parts of Sindh are ungagged, which urge to estimate the precipitation and other parameters using feasible models for effective planning and management of water resources. Regression analysis is usually employed to understand the hydro-climatic relationships of a watershed. The present study is aimed to investigate the relationship between precipitation and elevation through developing linear regression models for various levels of precipitation data and map their spatial variability in the KNR (Khirthar National Range), Sindh, Pakistan. The precipitation data of 7 meteorological stations covering the study area were used with DEM (Digital Elevation Model) data of 90 m resolution for altitudinal trend analysis. The results of the linear regression model showed a close relationship between the precipitation of various time-scales and elevation, i.e. coefficient of determination R 2 values ranging within 0.8206-0.9604. The correlation was significant at P<0.05 for mean annual, mean monthly, and mean seasonal (Rabi) precipitation. The spatial variation in precipitation was between 127.78-697.98 mm at annual and from 10.84-58.09 mm at mean monthly level. The lapse rate of increase in precipitation with elevation was 27.03 mm per 100 m for annual and 2.24 mm per 100 m for monthly level. At seasonal level, precipitation varied from 24.17-137.87 mm during Rabi (winter) and between 105.78-525.36 mm during Kharif (summer) season. Similarly, the monsoon precipitation (July-September) ranged between 92.24-359.93 mm in the study area. The higher precipitation estimated over elevated areas of the region at seasonal and annual levels needs to be harvested through adopting adequate water management techniques for improving agriculture productivity in the downstream areas.


INTRODUCTION
A ssessing and forecasting spatial variation and the potential of precipitation play a major role in planning and management of water resources to provide for the diversity of activities of human beings, socio-economic, hydrology, and ecology [1][2][3]. Many studies have investigated the relationship among spatial-temporal distribution of precipitation versus elevation features [4][5][6][7][8][9][10] geographical location [7][8]
Bassist and Bell [4] revealed through their research that the applied techniques have enhanced the relationship of altitude, worked on the variables, which belong to the spatial distribution of yearly and mean precipitation.
Konrad [6] concluded that elevation was associated strongly with concerning light-shower precipitation patterns; however, the closeness to water bodies was linked to the heavy precipitation patterns. Hayward Clarke [5] estimated the relationship between precipitation, elevation, and sea distance by interpreting many regression models. They did investigations on the relationship between monthly precipitation versus elevation using the regression model and found strong relation for rain gauging stations as compared to coastal gauging stations.
Katsoulis et. al. [12] discovered spatial-temporal variations of rainfall in Greece, describing the change between the wetter western (windward) and the drier eastern Greece (leeward), although there was minimal quantity of rainfall over the Greek Islands. Pedgley [13] reported that rainfall in the mid-latitudes is associated closely with the flat topography near to the rain-gauge. Chaun and Lockwood [14] selected an average elevation for the rain gauge within an 8 km radius of the gauging station and revealed strong relation within elevation and precipitation. Hill et. al. [15] preferred normal altitudes in a 4 km 2 grid during the observation of radar and orographic experiment. Konrad [6] used the average altitude within a 10x10 km 2 grid; he revealed a strong relationship of altitude and event basis precipitation. Johansson and Chen [16] re-managed the sample and used altitude from a 50 km² area into a strip of a 4 km² of the resolution, the results showed influences of wind on the distribution of rainfall slightly, overall found good the relationship of altitude and precipitation in the study area. Gouvas et. al. [17] explored the variable of neighboring elevation of gauging stations and found better results, during enhancement of precipitation in hilly areas compared to elevation of the gauging station itself. Alijani [10] estimated an average elevation for a 2½ km 2 radius of study area around the precipitation gauging position, which revealed the suitable relationship of altitude within the spatial distribution of precipitation in the mountainous range of study area.
Recently, Subyani [2] proposed that the use of a "Z" variable with elevation in the range of 2 ½ km 2 enhanced the forecasting results by interpolation techniques. A linear regression model gradually shows the differences between independent and dependent variables, which can be used for the estimation of spatial data [18][19]. The study regarding the relationship between precipitation and altitude is extremely important to comprehend hydroclimatology in watershed mountainous areas for better water resources management. Regression investigation concerns the study of association amongst quantitative variables with the object of classifying, assessing, and validating the relationships, a technique known as a linear regression model would be the best option. Accordingly, the goal of the current research is to discover and comprehend the relationship between elevation and precipitation at annual, seasonal (winter, summer, and monsoon) monthly time-scales. The study is focused on to analyze relationship between precipitation and elevation; develop linear regression equation, and to map spatial extent of precipitation concerning altitude through geo-statistical modeling approaches for the KNR, Sindh province.

Study Area
The study area KNR lies between longitudes 67.028- Hamal Lake in district Qambar Shahdad Kot, Manchar Lake in district Jamshoro, Pakistan, which is one of the largest lakes in the Asia and Keenjhar Lake situated in district Thatta. Torrential floods feed that through a several spates.
The community living in the area earns its livelihood from rain-fed agriculture employing spate irrigation techniques.
Physiographically the area consists of numerous watersheds that are further divided into several sub-basins and streams.

Climate in Khirthar National Range
The concerning source of water resources in the area is rainfall; which has an average annual downpour from 135-

Data Collection
The

The Relationship between Precipitation and Elevation of the Watershed in the Khirthar National Range
The seasonal data were categorized into two seasons, winter (Rabi cropping season from October-March) and summer (Kharif cropping season from April-September).
The authors calculated the mean annual, mean monthly,

Linear Regression Model
The statistical relationship between gauges lying within the study area and outside was calculated by using a linear regression equation [22][23]. LRM (Linear Regression Model) is a relatively simple and straight forward method for determination of precipitation variations concerning elevation. As the relationship between variables (elevation and precipitation) is different at each site [18], thus, the technique was used to develop an individual equation for each scenario (winter, summer, annual, mean monthly and monsoon). The raster calculator was used through map algebra by using spatial analyst tool and was used to generate a raster map of the precipitation distribution for each scenario. The resultant precipitation trends were interpreted with elevation retrieved from SRTM, DEM, similar to a study conducted in southern Nevada, the USA on establishing individual rainfall relationships with altitude for the area with insufficient gauging stations [24].
The coefficient of determination (R 2 ) showed the relationship between both variables. It is a quantity of how suitably the regression line signifies the data. If the regression line passes preciely through every point on the scatter plot, it would be able to explain all of the variations. If it is suitable, it provides the proportion of the variance of a "dependent variable" and "independent variable" respectively [25]. Consequently, precipitation at variable levels versus altitude was predicted by developing individual equations for each scenario [22]. This allows us to estimate how confidently one can be in developing a forecast from a convinced model/graph [25]. The developed elevation map was made using the SRTM, DEM 90m spatial resolution [21] in the ArcMap ver.10.30.1 version (Fig. 1). Subsequently, a linear regression equation between precipitation and DEM was developed for each feature, which was used for spatial precipitation mapping using the raster calculator function of ArcMap software. Output results showed spatial variation of precipitation in the context of elevation in the study area. Similarly, linear regression models and raster maps were developed for each time-scales of precipitation.

RESULTS
The results of the linear regression model showed a close relationship between the precipitation at various levels and the elevation of the study area as indicative from the coefficient of determination R 2 values range of 0.8206-0.9604 Figs. 3(a-c) and Table 1). The correlation was significant at P<0.05 for mean annual, mean monthly, and mean seasonal (Rabi) precipitation. The spatial distribution of various levels of precipitation in the study area is shown in Fig. 4(a-c). At the annual level, precipitation indicated variation 127.78 mm in the low lands to 697.98 mm at higher altitudes in the west and northwest of study area.
Similarly, precipitation exhibited an increase from 10.84-58.09 mm towards the west and northwest of the study area at the mean monthly level shown in Fig. 4(a). The lapse rate of increase in precipitation with elevation was  Fig. 3

(b) and
Monsoon Precipitation Fig. 3(c), due to good correlations the Zhob gauging stations were excluded for both trends.

FIG. 4(a). MEAN ANNUAL AND MEAN MONTHLY PRECIPITATION IN THE STUDY AREA
Variations of significant correlation were found between the lowest and higher elevations.

DISCUSSION
The empirical equation of the LRM showed a strong relationship between precipitation and elevation in the watershed of the KNR.
The correlation results between the two parameters indicated R 2 (coefficient of determination) value of 0.9604 for mean annual and 0.959 for monthly levels, 0.929 for winter (Rabi), 0.888 for summer (Kharif) and 0.8206 for precipitation of monsoon. The analysis is based on the time-series precipitation data of 7 meteorological stations (at variable elevations between 22-1405 m). The data of all 7 stations has been utilized for mean monthly, mean annual, Rabi trends. However, the data for 6 rain gauge stations have been used for monsoon and Kharif trend due to the good correlation of determination values received by excluding the gauging station of Zhob.

The Relationship between Precipitation and Elevation of the Watershed in the Khirthar National Range
hilly region, and tropical regions [26] and in the Cisangkuy Watershed Bandung regency of Indonesia [21].
The results determined by an LRM shown the precipitation trend which increase in the mountainous area compared to low lying areas in the watershed of KNR. These types of discoveries express the physical association between elevation and precipitation [27][28][29], that has been explored by various researchers, who are engaged in several regions of the world [2,4,[9][10][30][31]. The precipitation radar satellites make the researchers capable of concerning more research findings by adopting the new technology. Uneven variability in rainfall results in dangerous trends of floods and droughts, which damage the natural resources and the biodiversity [33].
During the last few decades, researchers observed that the variation trend of monsoon precipitation is a natural and shifting process globally, which will create pressure these susceptibilities challenges on food security [34].
The developed linear regression model obtained successful results as [35] optimized parameters by developing a linear model successfully to estimate the rainfall relationship in the eastern region of the Sierra Nevada Mountains. The study of the relationship between elevation and precipitation in the KNR authenticates the outcomes of results that were achieved as by [36]. He estimated the relationship between precipitation and elevation regressions to measure the monthly and annual precipitation over several regions of the United States and discovered strong relationships. Hanson et. al. [37] explained that the associations between rainfall and altitude for a hilly watershed in Idaho were highly influenced by weather. No doubt from the above reference, USA and Pakistan are situated in different regions, but the procedure of this study in the watershed of KNR, Sindh Province validates the results and shows a strong relationship between precipitation and elevation.

CONCLUSION
Regional climate trending is most important to exactly reproduce expected volume, intensity, and duration of precipitation events with spatial variation. Most of the hilly mountainous watershed areas of the country are ungauged and have no previous records whatsoever of precipitation runoff processes. As climate data is essential in numerous planning activities related to watershed management, but accurate data about the precipitation is rarely obtainable on micro to the macro level of watersheds.
To overcome these types of complications, it is possible to generate precipitation data using LRMs coupled with RS and GIS technique, to identify the trend and estimate relationships between precipitation and elevation. The results of the LRM showed a close relationship between the precipitation and elevation, as indicative from R 2 (coefficient of determination) values 0.86-0.96 for various precipitation levels. The correlation was significant at P<0.05 for mean annual, mean monthly, and mean seasonal (Rabi) precipitation. While the variation was found an increasing trend of precipitation from lowest to the highest elevation of watersheds in the KNR. The excessive runoff generated from increased precipitation at higher altitudes (e.g. during summer monsoon) should be conserved for sustaining agriculture and livelihood during water stressed/ drought conditions in the region.