Stream discharge data are an important component in the assessment and management of ground water and surface water resources and can be applied across a broad range of scales, including engineering design, flood forecasting, reservoir operations, water supply, recreation, and environmental management. Growing populations and competing priorities for water are spurring the demand for more accurate, timely, and accessible water data. However, the field collection of data for modeling stream flow is time consuming and expensive. Time can be the most significant problem because five or more years worth of weather and stream data are commonly required to capture variation in seasonal trends and to produce accurate predictive and descriptive models using standard statistical methods (Cheng et al. 2002; Costa et al. 2000; Stiff 2000). As well, stream flow gauging station data are typically discontinuous as many stream gauging stations have not been maintained. If accurate models of stream discharge could be constructed from a temporally limited data set, such models would have considerable value.

To reduce the time and cost of collecting data, we propose the application of an advanced machine learning technique called inductive transfer to model stream discharge using artificial neural networks. Previously learned knowledge of related streams is used as a source of inductive bias in the development of a model for a new target stream.

This work should be distinguished from prior studies that employed neural networks to watershed management and focused on rainfall-runoff modeling (Bhattacharya and Solomatine 2003; Dawson and Wilby 2001; Dibike and Solomatine 2000; Jain and Chalisgaonkar 2000; Kompare et al. 1997), prediction of discharge (Muttiah et al. 1997), and modeling of chemical characteristics (Bastarache et al. 1997). These studies were done on large transboundary rivers such as the Brahmaputra (Sharma et al. 2005) and none employed inductive transfer from related streams. In this study we focus on 2nd to 4th order rivers, which are becoming an increasingly important surface water resource, and on the use of inductive transfer to supplement small sets of training data for these streams.

The streams investigated in this study are all located in Nova Scotia, Canada. The models make short-term predictions employing two consecutive days of weather data as input, with stream discharge predicted for the following day. This study is not a trivial undertaking, as the relationship between weather data and stream flow rate in Nova Scotia is complex (e.g., Stiff 2007).

The stream gauging station data used in this study were gathered from three, 2nd order to 4th order streams located in drainage basins in the Annapolis Valley in western Nova Scotia and in the Shubenacadie Valley in Central Nova Scotia (Fig. 1). The Annapolis Valley is about 100 km long and 10 to 15 km wide. The topography varies from the steep slopes and scarp of the North Mountain, to the low relief valley floor, to the slopes and the raised peneplain of the South Mountain (Neily et al. 2003; Hamblin 2004; Rivard et al. 2007; Trescott 1967, 1968).

The three gauging stations in the Annapolis Valley are located within 60 km of each other (see Fig. 1 and Table 1). They were chosen because robust and easily accessed data sets are available for all three sites and a weather station (Greenwood, Fig. 1) for which a high quality data set exists is located nearby. Two gauging station sites from which data were gathered for this study are located on the Annapolis River. One station is located near the town of Lawrencetown, Nova Scotia (Fig. 1). Henceforth this site will be referred to as the Annapolis River at Lawrencetown (ARL). The second gauging station site is also along the Annapolis River and is located near the town of Wilmot (Fig. 1) This site is referred to as the Annapolis River at Wilmot (ARW). The third gauging station site is located near the outlet of Sharpe Brook, a 2^nd order tributary of the Cornwallis River (Fig. 1). All three sites are located within the Annapolis Lowland physiographic region and Annapolis Valley climate region with headwaters in the Western Nova Scotia climate region. These climate zones are characterized by relatively low rainfall (800–1200 mm annually) and warmer temperatures than are typical of eastern Nova Scotia (Davis and Browne 1996).

Sharpe Brooke is a typical 2nd order valley side stream; it is ungraded along much of its length and has a fairly steep gradient averaging 27 m/km. The watershed for Sharpe Brook above the gauging station covers approximately 19 km². Sharpe Brook typifies streams in Nova Scotia for which discharge data may be available as these streams are typically used for irrigation or are part of a municipal water supply system. The Annapolis River above the ARW gauging station is a 3rd order, primarily valley bottom stream that is fed by streams very similar to Sharpe Brook. Most of the 190 km² watershed for this gauging station is located on the south side of the Annapolis Valley. The ARL gauging station is located about 17 km downstream of the ARW gauging station; the watershed for this site encompasses 780 km². The Annapolis River (and the Shubenacadie River, see below) is typical of the valley bottom streams in Atlantic Canada that are a significant component of the groundwater system and serve as sources of water for irrigation and power generation. These large rivers can also be prone to flooding and surface runoff contamination (Stiff 2007). Gauging stations are rare on these systems and data quality and quality are commonly poor, hence the need to explore methods of discharge modelling. The ARL is the target site for this study.

Weather data were gathered for the town of Greenwood on the floor of the Annapolis Valley from the National Climate Data and Information Archive (Fig. 1). The valley floor is primarily drained by the Annapolis River, which flows southwest to the Annapolis Basin, and the Cornwallis River, which flows northeast to the Minas Basin (Rivard et al. 2004, 2007). The population in the Annapolis Valley is rural, with towns and villages located primarily along the rivers. The most densely populated region in the Annapolis Valley is the Coldbrook-Wolfville Urban Corridor to the east of Greenwood which supports 40% of the population of Kings County (Fig. 1). Agriculture dominates the Annapolis Valley; in 1996 970 farms were recorded in Annapolis and Kings Counties with gross farm receipts totaling $152 M (Government of Nova Scotia 2002).

The Annapolis Valley is underlain mainly by Triassic sandstone and conglomerate and is flanked to the south by meta-morphosed Paleozoic and granitic rocks of South Mountain and to the north by the Jurassic basalt highland of North Mountain (Rivard et al. 2007). Wisconsinan glaciation initiated at approximately 75 ka in Nova Scotia, and the Annapolis Valley was ice free by about 12 ka (Stea et al. 1992). In southwestern Nova Scotia, four regional ice flow stages have been recognized during this time (Stea 1987). The resulting surficial geology is complex. Till, glaciofluvial, and fluvial deposits underlie most of the study area. Till is the most common glacial deposit throughout the Annapolis Valley, mantling much of the study area, and varies in thickness from 1 m to possibly more than 20 m (Rivard et al. 2007; Trescott 1968). It rarely overlies a significant thickness of stratified drift, and may occur with inclusions of stratified drift. Till may also underlie bedded silt and clay estuarine deposits.

Local climatic conditions in the study area are heavily influenced by the topography of the Annapolis Valley. For instance, the North Mountain and South Mountain uplands effectively funnel westerly winds through the Annapolis Valley, yet also serve as buffers to provide some protection from weather systems travelling over the Bay of Fundy and the Atlantic Ocean (Neily et al. 2003; Rivard et al. 2007). No part of the study area is more than 60 km from a large body of water (Atlantic Ocean or Bay of Fundy), which can lead to significant variation in both temperature and precipitation. The valley floor is partially protected from direct coastal influences from the Bay of Fundy by North Mountain. As a result, some of the highest summer temperatures in Nova Scotia have been recorded in the Annapolis Valley, particularly in the eastern part. Winter temperatures normally average about -4.5 °C. Total annual precipitation generally ranges between 1100 to 1300 mm in the Annapolis Valley (Neily et al. 2003; Rivard et al. 2007).

The fourth stream gauging station is on the Shubenacadie River, located in the central Nova Scotia Uplands about 100 km east of the Sharpe Brook site (Fig. 1). The Shubenacadie River is primarily a 3rd and 4th order, low relief, valley bottom drainage system similar to the Annapolis River, with a water-shed above the gauging station that encompasses 900 km². The Shubenacadie River site is located in the Eastern Nova Scotia climate region, a diverse geographic area with high average rainfall (1000–1400 mm annually) and generally cool temperatures (Davis and Browne 1996). As in the Annapolis Valley, the local bedrock and surficial geology is complex and the thickness of overburden is highly variable. Land use in the region is primarily agricultural. This site was chosen to determine how regional climatological differences might affect transfer of knowledge from models of streams located in different physiographic regions.

Prior to the 1960s little hydrologic information was available for the Annapolis Valley other than weather records (Trescott 1968). Since the 1960s more data have become available, including water quality data for the Annapolis and Cornwallis Rivers (Clean Annapolis River Project and Friends of the Cornwallis River Society, respectively), discontinuous mean daily discharge recorded at eleven gauge stations from 1915 to 2002 throughout the Annapolis Valley, and weather data published to the internet that had been recorded at seven climate stations throughout the province by Environment Canada. A number of hydrological studies have been conducted in the Annapolis Valley. Trescott (1968) investigated groundwater resources and hydrogeology of the Annapolis-Cornwallis Valley. Hennigar (1992) studied the hydrogeological and groundwater conditions in the Annapolis-Cornwallis Valley, and Myers (1997) looked at the fluvial dynamics and river restoration strategies in Mill Brook, a tributary of the Cornwallis River. Fenton (1998) studied surface water - ground water interaction and stream discharge in Elderkin Brook, a moderate gradient, 1st order tributary of the Cornwallis River. Levy (1998) investigated connectivity between input and stream discharge for Fishwick Brook, a 1^st order, low gradient tributary of the Cornwallis River. Cook (2000) studied fluvial dynamics and river restoration strategies in Elderkin Brook and the South Annapolis River, a moderate gradient tributary of the Annapolis River. Blackmore (2007) completed a ground-water vulnerability assessment for the Annapolis-Cornwallis Valley and associated watersheds as part of a Geological Survey of Canada-funded investigation of the hydrogeology of the Annapolis-Cornwallis Valley region (Rivard et al. 2007). The study by Rivard et al. (2007) and associated studies by Blackmore (2007), Trépanier (2008), and Gauthier (2008) represent a comprehensive evaluation of the groundwater resources in the Annapolis Valley and have contributed significantly to understanding groundwater system dynamics in valley-ridge settings.

The objective of this research is to determine the value of inductive transfer as applied to the modeling of discharge. The target stream (ARL) is typical of larger, 4th order and higher valley bottom streams in Atlantic Canada for which accurate discharge models are required. Our hypothesis was that previously developed models for discharge of a distinct gauging site (ARW) or stream (Sharpe Brook) can be used as a source of inductive transfer for a distinct but spatially and geomorphologically related stream (ARL). We also tested whether an unrelated stream (Shubenacadie River) in a distinct physiographic region could be used as a source of inductive transfer. In all cases, our results indicated that fairly accurate models can be developed.

It is important to compare the consistent performance of the models developed under transfer to those without transfer. The performance of MTL models varies only slightly as the amount of training data changes, particularly when the source of transfer is the ARW (see Figure 5). Clearly this site is the best source of prior knowledge for developing models for the ARL. This result makes sense as the two locations are closest to each other and are on the same river system.

The models for the ARL developed using the Sharpe Brook and Shubenacadie River as sources of inductive transfer do not perform quite as well as models developed with transfer from the ARW (Fig. 5). Both Sharpe Brook and the Shubenacadie River are in different drainage basins than the ARL. Sharpe Brook is a significantly smaller stream than the ARL and the Shubenacadie River is the more distant stream. This result supports the theory that more related prior knowledge leads to more beneficial inductive transfer. Combining Sharpe Brook with the ARL as a source of transfer creates models that perform better than models with transfer from only Sharpe Brook, but worse than models with transfer from only the ARW.

Although the ARL model developed with 180 days of training data and transfer from ARW (Fig. 6) does statistically as well as the STL model developed with 5 years of training data (Fig. 4), the model with transfer tends to be more conservative in its predictions. The MTL transfer model does not predict the highest discharge value (March 1994) as accurately as the STL model based on five years of training data. Two reasons for this are (1) portions of the chosen test set are atypical as they contain some very high discharge values, and (2) the models used only two days of weather data as input. The peak discharge recorded in March, 1994 (276 m³/s) for the ARL is the highest value recorded for all streams in the study. By comparison, the highest value in the 180 day training set is 168 m³/s, while the highest value in all other training sets is 205 m³/s recorded in 1987 (Government of Canada 2005b). Because none of the models are trained with target outputs of this magnitude the models perform poorly on the 1994 portion of the test set. This explains why models developed from the 180 day training set tend to under-predict peak values as compared to models developed with 5 year training sets. If the performance of the best models are examined using only the 1995 portion of the test set, the MAE decreases from 12.6 m³/s to less than 10 m³/s. This occurs because the highest value recorded in 1995 was a more typical 154 m³/s.

The second reason why the models err on extreme discharge values is that only two days of weather data are used and knowledge of recent discharge levels is not provided. This can lead to under-prediction when the stream level is at bankfull stage or higher (typically in the spring and late fall) and over-prediction when the stream level is at or below baseflow stage (typically in the summer). An efficient method of adding more days of weather data and knowledge of recent stream discharge would increase the performance of the models.

Based on the above, one could argue that the models developed with inductive transfer do better at predicting when an extreme in stream discharge will occur than they do in predicting the magnitudes of those extremes. Despite doing well in the normal range, the graphs show that the MTL models under-predict a number of the peak discharge values. Nonetheless, the models provide a significant performance advantage over the less accurate alternatives; models developed without transfer using standard STL. Therefore, we propose that the MTL models provide a valuable starting point when little data are available. As time passes, new data collected for the primary stream can be combined with the existing data so as to continually develop more accurate models.

The results of the research supports the hypothesis that inductive transfer of previously learned knowledge can reduce the number of years of training examples required to construct accurate models of stream discharge. Inductive transfer via MTL and task rehearsal with as little as 180 days of training data for the primary task produces predictive models that are statistically equivalent to models developed from five years of training data and no transfer. The experiments also demonstrated that the more related prior models of stream discharge (the Annapolis River at Wilmot) generated the best models for the target task (discharge at the Annapolis River at Lawrencetown). We conclude that inductive transfer methods should be considered when modeling river discharge and that value exists in the systematic retention and reuse of models from any environmental problem domain.

Several interesting directions for future work have been identified. More accurate models could be developed by increasing the amount of weather data used as input beyond two days. Extending this window of weather data should increase the accuracy of the models. Keeping in mind that additional inputs increase the sample complexity and training times, we are currently investigating the use of recurrent neural networks that can maintain a sense of context while only requiring a single day’s weather as input (Mitchell 1997). A second approach to improving model performance is to use the known discharge of one stream as an input to the model for another stream. For example, the discharge of the ARW, which is constantly monitored, could be used as an input to a model for the ARL. This approach would allow all streams in a drainage basin to benefit from monitoring one stream.

We have also identified several questions regarding the limits of inductive transfer applied to stream discharge and more generally to environmental modeling. Can we use data from large streams that have been monitored for some time to better model smaller secondary streams for which we have little data? Our intention is to explore this in future work. Can prior knowledge of a model in one region, using weather data from that region, be used to transfer knowledge to a stream in a different region, using weather data from that second region? There is no reason why this cannot be the case. An issue related to both of these questions is determining a measure of relatedness between streams and their associated watersheds and climatic conditions to ensure the approach is beneficial to the development of accurate models.