Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.

Abstract:Rapidly depleting unconfined aquifers are the primary source of water for irrigation on the North China Plain. Yet, despite its critical importance, groundwater recharge to the Plain remains an enigma. We introduce a one-dimensional soil-water-balance model to estimate precipitation-and irrigation-generated areal recharge from commonly available crop and soil characteristics and climate data. To limit input data needs and to simplify calculations, the model assumes that water flows vertically downward under a unit gradient; infiltration and evapotranspiration are separate, sequential processes; evapotranspiration is allocated to evaporation and transpiration as a function of leaf-area index and is limited by soil-moisture content; and evaporation and transpiration are distributed through the soil profile as exponential functions of soil and root depth, respectively. For calibration, model-calculated water contents of 11 soildepth intervals from 0 to 200 cm were compared with measured water contents of loam soil at four sites in Luancheng County, Hebei Province, over 3 years (1998)(1999)(2000)(2001). Each 50-m 2 site was identically cropped with winter wheat and summer maize, but received a different irrigation treatment. Average root mean-squared error between measured and model-calculated water content of the top 180 cm was 4Ð2 cm, or 9Ð3% of average total water content. In addition, model-calculated evapotranspiration compared well with that measured by a large-scale lysimeter. To test the model, 12 additional sites were simulated successfully. Model results demonstrate that drainage from the soil profile is not a constant fraction of precipitation and irrigation inputs, but rather the fraction increases as the inputs increase. Because this drainage recharges the underlying aquifer, improving irrigation efficiency by reducing seepage will not reverse water-table declines.

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Abstract:Because the traditional Soil Conservation Service curve-number (SCS-CN) approach continues to be used ubiquitously in water quality models, new application methods are needed that are consistent with variable source area (VSA) hydrological processes in the landscape. We developed and tested a distributed approach for applying the traditional SCS-CN equation to watersheds where VSA hydrology is a dominant process. Predicting the location of source areas is important for watershed planning because restricting potentially polluting activities from runoff source areas is fundamental to controlling non-point-source pollution. The method presented here used the traditional SCS-CN approach to predict runoff volume and spatial extent of saturated areas and a topographic index, like that used in TOPMODEL, to distribute runoff source areas through watersheds. The resulting distributed CN-VSA method was applied to two subwatersheds of the Delaware basin in the Catskill Mountains region of New York State and one watershed in south-eastern Australia to produce runoff-probability maps. Observed saturated area locations in the watersheds agreed with the distributed CN-VSA method. Results showed good agreement with those obtained from the previously validated soil moisture routing (SMR) model. When compared with the traditional SCS-CN method, the distributed CN-VSA method predicted a similar total volume of runoff, but vastly different locations of runoff generation. Thus, the distributed CN-VSA approach provides a physically based method that is simple enough to be incorporated into water quality models, and other tools that currently use the traditional SCS-CN method, while still adhering to the principles of VSA hydrology.

[1] Effective control of nonpoint source contaminants in runoff from urbanized watersheds requires knowledge about the locations of runoff source areas under a variety of conditions. Physical monitoring of spatially variant processes, such as runoff production form variable source areas, is time-consuming and expensive. Thus modeling the processes may provide a valuable cost-effective alternative. In this paper we adapt and validate a variable source model for an urban watershed to predict areas of the landscape prone to elevated soil moisture levels and saturation excess runoff. We modified the soil moisture distribution and routing (SMDR) model to simulate hydrologic processes in an urban upstate New York watershed by considering the impact of impervious surfaces, hydraulic control structures (detention basins), and land use on the water balance. In our model, infiltration excess runoff from impervious surfaces infiltrates in the surrounding soils. Simulated and observed streamflow agreed well, and more importantly, the distribution of soil moisture levels and overland flow throughout the watershed were well predicted. Removing urban features from the model resulted in substantially lower peak stormflows than observed, and the base and interflows increased accordingly. Both modeled and measured distributed results indicated that the more urbanized areas of the study site had both higher soil moistures and runoff losses due to shallower soils, greater upslope contributing areas, and a larger area of impervious surfaces generating runoff. The model results helped identify processes that describe how urbanization impacts integrated and distributed hydrology, which provides useful information for targeted water quality management.

This study was a statistical evaluation of the prevalence of infiltration excess runoff ͑i.e., Hortonian flow͒ for undeveloped areas within New York City ͑NYC͒ watersheds. Identifying the hydrological processes generating runoff is central to developing watershed management strategies for protecting water quality. Fifteen-minute rainfall data from East Sidney, N.Y. ͑1971-2002͒ were used as maximum observed intensities. Maximum exceedance analyses were performed on a monthly basis to investigate seasonal rainfall intensity trends. Hortonian flow was assumed to occur whenever the rainfall intensity exceeded the soil permeability. Soil permeabilities were obtained from the U.S. Natural Resource Conservation Service soil survey. Results show that Hortonian flow is unlikely to occur anywhere for events smaller than the 3-year 15-min event. Only for the summer months, May-August, is Hortonian flow expected for 15-min intensities of Ͻ10-year magnitude. However, the summer results are overpredicted by this analysis because these months typically have the driest soil conditions and thus the highest infiltration capacity. This analysis concludes that infiltration excess runoff is not a dominant runoff process in undeveloped portions of NYC watersheds.

Abstract. Reducing non-point source phosphorus (P) loss to drinking water reservoirs is a main concern for New York City watershed planners, and modeling of P transport can assist in the evaluation of agricultural effects on nutrient dynamics. A spatially distributed model of total dissolved phosphorus (TDP) loading was developed using raster maps covering a 164-ha dairy farm watershed. Transport of TDP was calculated separately for baseflow and for surface runoff from manure-covered and non-manure-covered areas. Soil test P, simulated rainfall application, and land use were used to predict concentrations of TDP in overland flow from non-manure covered areas. Concentrations in runoff for manure-covered areas were computed from predicted cumulative flow and elapsed time since manure application, using field-specific manure spreading data. Baseflow TDP was calibrated from observed concentrations using a temperaturedependent coefficient. An additional component estimated loading associated with manure deposition on impervious areas, such as barnyards and roadways. Daily baseflow and runoff volumes were predicted for each 10-m cell using the Soil Moisture Distribution and Routing Model (SMDR). For each cell, daily TDP loads were calculated as the product of predicted runoff and estimated TDP concentrations. Predicted loads agreed well with loads observed at the watershed outlet when hydrology was modeled accurately (R 2 79% winter, 87% summer). Lack of fit in early spring was attributed to difficulty in predicting snowmelt. Overall, runoff from non-manured areas appeared to be the dominant TDP loading source factor.

A curve number based model, Soil and Water Assessment Tool (SWAT), and a physically based model, Soil Moisture Distribution and Routing (SMDR), were applied in a headwater watershed in Pennsylvania to identify runoff generation areas, as runoff areas have been shown to be critical for phosphorus management. SWAT performed better than SMDR in simulating daily streamflows over the four‐year simulation period (Nash‐Sutcliffe coefficient: SWAT, 0.62; SMDR, 0.33). Both models varied streamflow simulations seasonally as precipitation and watershed conditions varied. However, levels of agreement between simulated and observed flows were not consistent over seasons. SMDR, a variable source area based model, needs further improvement in model formulations to simulate large peak flows as observed. SWAT simulations matched the majority of observed peak flow events. SMDR overpredicted annual flow volumes, while SWAT underpredicted the same. Neither model routes runoff over the landscape to water bodies, which is critical to surface transport of phosphorus. SMDR representation of the watershed as grids may allow targeted management of phosphorus sources. SWAT representation of fields as hydrologic response units (HRUs) does not allow such targeted management.